ABSTRACT. by Brian L. Sands

Transcription

1 ABSTRACT CHARACTERISTICS AND DYNAMICS OF A PASSIVELY STABILIZED HIGH POWER AND NARROW-BANDWIDTH BROAD-AREA LASER COUPLED TO AN EXTERNAL VARIABLE LENGTH CAVITY by Brian L. Sands We have constructed an external cavity diode laser (ECDL) with an easily adjustable, variable cavity length in the Littman-Metcalf configuration to improve the poor beam quality of a 2 W Coherent Inc. broad-area laser (BAL) as well as study the effect of varying dispersive feedback. Our results at four different cavity lengths show that the individual modal linewidth varies with an L 1/2 cavity length dependence while the effective bandwidth of the ECDL was not altered. This suggests that BALs behave differently in external cavities. We describe the detailed characteristics of our ECDL and the passive stabilization techniques employed to keep the laser at a fixed wavelength for long periods, which is important for our intended application to spin-exchange optical pumping experiments using a Rb- 129 Xe mixture. We discuss other applications of this laser that include high-resolution spectroscopy and laser cooling, and provide a review of BAL coupling techniques.

2 Characteristics and dynamics of a passively stabilized high power and narrow-bandwidth broad-area laser coupled to an external variable length cavity A Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirements for the degree of Master of Science Department of Physics by Brian L. Sands Miami University Oxford, Ohio 2005 Advisor Reader Reader S. Burçin Bayram Douglas Marcum Samir Bali

3 Contents 1 Introduction Alternate external coupling techniques External cavity diode lasers Applications Essential Background Laser basics Semiconductor lasers Basic physics Properties of semiconductor lasers Index-guided lasers Gain-guided lasers Propagation of lasers External cavity diode lasers: theoretical background ECDL physics Contrasting Littrow and Littman-Metcalf designs Application to spin-exchange optical pumping of noble gases Basic physics The effect of the laser Experimental Design ECDL design The cavity Collimating optics Diffraction grating and feedback mirror Laser and drive electronics Alignment procedures Data analysis Results ECDL characteristics Thermal tunability Laser gain profile Spectral narrowing Fine tunability ECDL stability ECDL dynamics External elements Grating and feedback mirror Collimating lenses ii

4 4.2.4 The laser Laser position Laser current Variable cavity length Conclusions and Future Work 68 A ECDL Schematics 71 B Experiment Photos 75 C Detailed Alignment Procedure 81 C.1 Laser rough alignment C.2 Collimating optics rough alignment C.3 Collimating optics fine alignment C.4 External cavity optics alignment iii

5 List of Tables 4.1 Summary of results at various cavity lengths. An insufficient number of measurements were made of the mid-long cavity s effective bandwidth to give a good statistical average. 67 iv

6 List of Figures level diagram of a quantum system in a state of amplified stimulated emission. Here, a population inversion is achieved between levels 3 and 2. Solid lines indicate the most likely transition paths. The inset shows the phase relationship between photons emitted by the stimulated transition Behavior of the population difference between energy levels 3 and 2 (c.f. Fig. 2.1) as a function of pump rate under lasing conditions. Pump rate units are arbitrary Energy band diagrams of various types of semiconductor laser. For each type, the case for unbiased and forward biased is shown Schematic of a typical single-stripe GaAs double heterojunction laser Schematic of semiconductor laser astigmatism Illustration of basic diffraction. The dashed line indicates the grating normal Littrow geometry for determining the synchronous tuning condition Littman-Metcalf geometry for determining the synchronous tuning conditions Optical pumping scheme of alkali gases Spin-exchange and spin-relaxation cross-sections for various combinations of noble gas and alkali atoms [46]. Open symbols represent theoretical estimates, and closed symbols represent experimental values Theoretical and measured polarization of 129 Xe versus temperature for W of freerunning output from a commercial LDA (open circles) and a narrowed 1.4 W BAL (closed triangles) [47] Overview of our experimental setup Average voltage response from a piezoelectric wafer attached to the base of the cavity s feedback mirror mount. The figure shows the signal a) with and b) without the optical bench floating The Littman-Metcalf scissor mount a) without and b) with cavity optics. The location of the geometrical pivot is indicated in the figure Parameters used in deriving constraint equations for our external cavity mount Smoothness of actuator motion characteristic of Zaber T-LA class actuators. The data, taken from T-LA technical notes [85], was taken with a load of 5 N and 20 N on the leadscrew Typical reflectance curves for aluminum and gold in the visible and NIR Laser and TEC mount. The location of the BAL chip is shown ECDL drive electronics Temperature-voltage calibration for the feedback thermistor attached to the laser diode case Apparatus used to align the major cavity components to the pivot point Image of grating alignment Image of feedback mirror alignment Image of laser alignment v

7 4.1 Temperature tuning curve for a 2 W Coherent Inc. single-stripe BAL centered near 790 nm Low-resolution spectrum of the free-running BAL. The FWHM was 2.5 nm. The inset shows a portion of the free-running mode spectrum taken with the 1.26 m highresolution spectrometer. There is no relationship between the absolute intensities shown in each image Coarse tunable range of our ECDL with strong coupling Typical Fabry-Perot spectra of the 30.5 cm ECDL a) with the grating feedback unblocked and b) with the top half of the feedback blocked Fabry-Perot spectra of the ECDL arranged with a 23 cm cavity length showing evidence of a superposition of transverse modes with the BAL operating below threshold Fabry-Perot spectra of a short cavity ECDL taken with an FSR of 15 GHz. The average bandwidth is noted A composite of high-resolution snapshots of the ECDL after each mode hop. The variable nature was characteristic of our cavity Magnitude of mode hops in nm versus distance covered by actuator in mm Data from two separate runs showing the relationship between the magnitude of the mode hop (in nm) and the fine tunable range (in GHz). In the general case, the tunable range reaches a stable value after tuning across several hops Impulse from movable arm actuator. Left-right: Amplitude of impulse with varying distance from the actuator contact tab. The sensor was placed a) on the aluminum contact tab, b) on the copper arm opposite the contact tab (almost 3 ) and c) on the feedback mirror mount. The stepsize was constant at 1.0 mm. Top-bottom: Amplitude of impulse with varying actuator stepsize, measured on the actuator contact tab. From the top, a) a 1.0 mm, b) a 0.1 mm and c) a 1 µm stepsize Fabry-Perot spectra taken three hours apart to demonstrate the stability of the ECDL. Note the change in mode structure reflecting a change in the transverse profile Spectra of the ECDL taken three hours apart. The wavelengths were separated by the resolution limit of the spectrometer Spectra of ECDL taken over a 12-hour period with an output power near 1 W Characteristic spectra from ECDL a) before and b) after insertion of a Faraday isolator Fabry-Perot spectra characteristic of data taken with a) a 1 grating, and b) a 2 grating Variation in effective bandwidth as the feedback is directed to a) the top, b) middle, and c) the bottom of the BAL. The injection current was A ECDL spectra with the cylindrical lens a) tilted about its vertical axis and b) perpendicular to the incident beam Characteristic spectra for a) a non-ar coated laser and b) an AR coated laser both tuned to the center of their respective gain profiles ECDL spectral broadening with the injection current a) just above threshold at 0.50 A and b) at 1.15 A Slow-axis beam quality (black circles) and typical ECDL bandwidth versus injection current (red triangles). The bandwidth data was taken with the Fabry-Perot spectrometer at an FSR of 15 GHz. Outliers indicate transitions to higher order transverse structure, and tended to occur at lower currents Modal linewidth as a function of cavity length fit with an inverse square root power law Fabry-Perot data from the first run at a 23 cm cavity length Fabry-Perot data from the second run at a 23 cm cavity length vi

8 A.1 Overhead schematic of the scissor mount in the fully open position. The open region behind the scissor mount contains the translation stages for the laser and collimating optics. The actuator interfaces with the movable arm at a contact tab affixed to the two holes on the left side of the figure. The size of the actuator prevents the mount from achieving this configuration in the current implementation, but this is not important since there are currently no spectral features of interest beyond the Rb D1 band A.2 Overhead schematic of the scissor mount in the fully closed position. In the current implementation, this position is not attainable because a resistive spring is mounted between the movable arm and the fixed arm. For accessing the Rb D1 band this is not a problem. If the D2 band needs to be accessed, the hex screw holding the spring in place may be shaved down. If the K D1 band is needed, the spring will need to be repositioned A.3 Depiction of the scissor mount in its current rest configuration with the actuator mount shown. In operation, the rest angle is a little smaller than 67 because of a rubber boot placed on the tab to attenuate vibrational noise from the actuator. This sets the laser wavelength near 796 nm at rest, just red of the Rb D1 band B.1 An outside view of our ECDL. The surrounding box is not air tight, though this does not significantly affect the stability of the coupled laser. A detailed image of the mount itself is shown in Fig B.2 Image showing instrumentation for analyzing the performance of the ECDL. Shown are the scanning Fabry-Perot interferometer and fiber optic inputs for the nm resolution Coherent Inc. wavemeter and nm resolution Czerny-Turner spectrometer. We are currently applying the ECDL to high-resolution absorption spectroscopy of a Rb vapor to be used in a 129 Xe spin-exchange optical pumping experiment B m Czerny-Turner spectrometer used for monitoring the output of the ECDL. The optics in front of the entrance slit reduce and collimate the fiber optic output and allow for near instrumental resolution at the CCD B.4 Drive electronics for the BAL. The TEC and laser current drivers are separate, but are commonly powered and grounded. Great care was taken to isolate each component from the chassis ground to properly power the laser. Not shown is a regulated 5 V reference used by the current modulation circuitry B.5 Screen capture of the scissor mount control interface (SMCI) program developed in LabView to communicate with the actuator mounted on the movable arm of the ECDL mount. A more detailed overview of the program will be provided in an addendum to this thesis C.1 Diagrams of the BAL image with various horizontal axis tilts of the aspheric lens. The lens mount is shown for orientation C.2 Diagrams of the collimated BAL image at a distance of 3-4m from the output facet showing errors in either the vertical translation of the aspheric lens or the horizontal axis tilt. The orientation of the tilt is the same as in Fig. C C.3 Distortions caused by cylindrical lens tilt about the optical axis. The effect is more pronounced due to the asymmetry in the beam. The magnitude of the tilts are exaggerated C.4 Effect of vertical axis tilt of the cylindrical lens. Looking down the vertical axis of the cylindrical lens, the aberrations result from a) counterclockwise tilt and b) clockwise tilt. A collimated HeNe laser was used to acquire the images C.5 Effect of small horizontal laser displacements with respect to the optical axis of the aspheric lens. The magnitude of the displacements are exaggerated vii

9 To my parents for footing the bill and emotional support throughout college, and to myself, because no one was expecting that. viii

10 ACKNOWLEDGMENTS Several people helped this project come together in its final form. I would like to thank my advisor, Dr. S. Burçin Bayram, for interesting me in this project and for guiding me through it while giving me the freedom to shape the experiment as I wanted. I am also appreciative of Dr. Douglas Marcum s presence in our lab over the past year and thank Dr. Samir Bali for interesting and helpful discussions. Important contributions also came from Bobby Seymour, who helped me bring the laser to life, Lynn Johnson for helping us troubleshoot early electrical problems and helping us design electronics for our low-frequency NMR apparatus, Mark Fisher for technical support of all kinds, and Barry Landrum, who was essential in helping to fine tune the design of our ECDL and machining a cavity mount that has exceeded our expectations. Thanks also goes to our lab group, Seda Kin, Morgan Welsh and Jacob Hinkle who never hesitated to help, and to Ryan Coons and Matt LaRoche for their future contributions to the ECDL and related sputter deposition chamber. ix

11 Chapter 1 Introduction Since the first laser was constructed in the early 1960s [1], their use has pervaded nearly every aspect of modern life. The theory behind the stimulated emission that forms laser light was introduced years earlier by Albert Einstein who showed that it was equally likely for an incident photon of the right energy to stimulate either an absorption process (well known by then) or an emission process in a quantum system. If an excited energy level were somehow overpopulated so that electrons were more likely to be found there than in a lower level, a condition known as a population inversion, then stimulated emission would take over as the dominant process. The nature of the quantum system is irrelevant, as long as these conditions hold true. The easiest quantum system with which to develop the first lasers was an atomic/molecular system, in which electrons are pumped to a metastable state that has a lifetime much greater than other excited levels in the pumping scheme. Ruby lasers are an example of a three-level system, and helium-neon gas lasers are an example of a four-level system. Atomic and molecular systems are not the only quantum systems that can support lasers. In 1963, Zhores Alferov and Herbert Kroemer proposed a laser based on semiconductor heterostructures, using the bandgap between the valence and conduction bands as the quantum transition to set up the population inversion [2, 3]. Semiconductor lasers are among the most popular laser designs that exist today, and were utilized in this work. There have been many methods proposed for improving the spectral quality and tunability of semiconductor lasers over the years [4]. This work will demonstrate the use of a high power 1 broadarea semiconductor laser (BAL) coupled to an external cavity oscillator. Such external cavity diode lasers (ECDLs) are used to narrow the intrinsic spectral bandwidth of the semiconductor laser, as well as allow for wide spectral tuning without mode hopping. However, there are other methods that have been developed. Of those, we will focus for a bit on two of the more popular alternatives, master-slave injection locking and phase-conjugate feedback, before returning to the focus of this work. 1 In this work, high power will refer to output powers of at least several hundred mw. 1

12 1.1 Alternate external coupling techniques One of the challenges of producing a widely tunable and narrow-bandwidth (WTNB) 2 BAL with high output power is the complicated, multimode free-running spectrum (unaltered laser gain profile) that these lasers typically exhibit. Although it has been readily shown that the linewidth of low power single-mode oscillators decreases with increasing power [5 9], high power BALs are characterized by much larger bandwidths over low power diodes. By their design (c.f. 2.2), high power laser diodes typically do not operate in a single mode. The competition of multiple modes dramatically increases the bandwidth over low power, single-mode designs (typically of order GHz bandwidth) [10, 11]. The job of external coupling schemes then is to somehow isolate the laser to a single oscillating mode, so that the spectral quality of low power laser diodes can be recaptured. One method of doing this is master-slave injection locking [12, 13]. In this scheme, a low power master laser, which lases in a single transverse and longitudinal mode, is injected into the oscillating cavity of a high power slave laser. The slave laser is generally many times more powerful than the master laser, and as such lases in multiple longitudinal modes. If the longitudinal mode of the master laser is injected in phase with the slave laser, the entire cavity will lock to that single longitudinal mode regardless if that mode was originally lasing in the slave laser cavity. In this way, high coupling efficiencies can be achieved [14 17] and the high power of the slave laser can be realized with the tunability and spectral quality of the master laser. In order to successfully couple two lasers by direct injection, the two lasers must have similar coherence lengths and similar optical path lengths (i.e. be phase matched), matching polarization states, and be free from relative instabilities caused by thermal or mechanical variations and current source fluctuations [18, 19]. In most cases, the slave and master lasers are isolated systems insofar as they are not physically connected. Thus, the phase matching condition is often difficult to satisfy in this coupling scheme. The master laser must be injected at a small angle into the slave laser [14], and relative path length differences and environmental effects must be actively compensated to satisfy this condition over long periods [19]. The injection locking technique has been applied to large arrays of slave lasers mounted on a common chip to achieve very high output powers [14, 19, 20], and more recently has been directly applied to laser cooling of alkali gases [21, 22], where high powers allow for large trapping volumes. Another prominent method of frequency locking a diode laser is by using phase-conjugate feedback [23 26]. This process takes advantage of the nonlinear polarization of so called third-order media to eliminate the phase inversion of feedback reflected back into a diode laser. In this way, the process resembles master-slave injection locking. In these media, the polarizability of the molecules is nonlinearly dependent on the incident electromagnetic field. Thus, when a photon is scattered off of molecules in these media, high-order oscillation frequencies can be excited in the molecules, increasing the probability that frequencies of light other than those of the input beam are re-emitted. The nonlinear polarization of phase-conjugate media is represented by the third order term of a power series expansion of the material polarization, given by P (3) ( E 1, E 2, E 3 ) = 1 2 χ(3) E1 E2 E 3, (1.1) where χ (3) is a second rank electric susceptibility tensor [27]. Interactions of this type are known as four-wave mixing processes, as the three input waves of Eq. 1.1 are combined to give a fourth output wave. Solutions of Maxwell s nonlinear wave equations require that the phase propagation vectors obey the phase matching condition k 1 + k 2 k 3 k 4 = 0. Under this condition, the nonlinear 2 This term includes lasers characterized by a single-mode linewidth and those characterized by a multimode bandwidth. 2

13 interaction produces an output wave of frequency ω 4 = ω 1 + ω 2 ω 3. Yariv and Pepper showed that for counter-propagating pump fields (taken as E 1 and E 2 ), an input wave ( E 3 ) of arbitrary phase will generate a counter-propagating output field ( E 4 ) that is everywhere the complex conjugate of E 3 with frequency ω pump ω, where ω is the amount of frequency detuning from the pump field [23]. The phase-conjugate material acts to reflect the incident light without imparting a 180 phase shift. For sufficiently high feedback (defined in terms of the reflectivities of the diode laser facet and the phase-conjugate mirror (PCM), and set by the amount of input detuning from the pump frequency), there exists a single-frequency wave solution to the rate equations governing the semiconductor laser with feedback only for the case where the input laser is locked in frequency and phase to the pump [28]. For this reason, PCM oscillator designs where the pump and input lasers are from a common source absolutely satisfy the single-frequency locking condition. Tuning without mode hopping can be accomplished by placement of an intracavity grating without the alignment constraints of ECDLs. The physics of master-slave injection locking is similar, except in that case two lasers need to be independently controlled and the phase locking is not guaranteed. Several oscillator schemes have been designed on this principle of phase-conjugate feedback [29,30], and successful experimental designs have been tested using such PCMs as barium titanate [31 33], various atomic vapors [34 36], and even the semiconductor lasers themselves [37 39]. Because of the guarantee of phase locking using PCM feedback, this method has clear advantages over master-slave injection locking and even external cavity feedback. There are some notable disadvantages though. For one, the phase locking is rather strongly dependent on the response time of the PCM [40]. If the current or temperature control is sufficiently noisy and the PCM is slow to respond, mode hopping can occur that is difficult to actively compensate for. Also, stronger feedback is needed to sustain singlemode behavior using PCMs instead of conventional mirror feedback [41], although this is generally not a problem due to the high coupling efficiencies of PCMs. Because the response of PCMs is dependent on the mixing fields, fluctuations of these fields in the PCM can lead to instabilities as well. Long term single-mode operation therefore can be difficult [31], but not impossible [42] to achieve. 1.2 External cavity diode lasers Multiple designs have been put forth for ECDLs that are widely tunable and narrow-bandwidth. Most designs in this class are either Littrow or Littman-Metcalf configurations [43, 44] and many of these designs are used for low power laser diodes that are generally characterized by a much narrower free-running bandwidth and often intrinsic single-mode operation. The advantage of using low power laser diodes is that the external cavities can be made very small, which can enhance the single-mode tunability of the laser. When designing these cavities for high power BALs, it is typically the case that the free-running laser is not spectrally narrow and is intrinsically multimode. The challenge of these designs is to simultaneously narrow the bandwidth of the laser while increasing the tunability. Over the past 20 years, there have been many variations of the basic Littrow and Littman- Metcalf designs that address these challenges to varying degrees of success. The degree to which the laser properties need to be altered is dependent on the application. Perhaps the most successful in recent years was a modified Littrow setup designed by Stry et al. for use in creating Bose-Einstein condensates, a very demanding application [45]. They coupled the first order diffraction out of the back facet of a tapered laser diode instead of using the zeroth order output. A clear advantage to this approach is that the high efficiency feedback of gratings at the Littrow angle is fully coupled into the output beam, which remains stationary during tuning. Although it requires access to both facets of the laser diode, which is non-standard with most commercial laser diode mounts. Using an 3

14 output power of 1 W, they achieved continuous tuning of up to 15 GHz with a measured linewidth of several MHz and a side-mode suppression of 57 db. If the application is preparation of spin-polarized noble gases [46], the long term stability and narrow-bandwidth operation is important. By narrowing the bandwidth of the free-running BAL, thus better matching the bandwidth of the Rb absorption band used in the spin-polarization process (c.f. 2.5), Nelson et al. demonstrated near equal polarizations using a free-running W laser and 1.4 W from a frequency-narrowed, Littman-Metcalf ECDL [47]. In more traditional designs, the primary difficulty to overcome is the sensitivity of ECDLs to relative phase changes in the cavity. Synchronous tuning in either design requires a precise location of cavity elements to a common pivot. Some have used rigid cavities [48] and non-mechanical tuning mechanisms [49] to meet this requirement. Merrill et al. designed a hybrid Littman-Metcalf ECDL to get higher coupling efficiencies while keeping good tunability [50]. In their design, the first order output from the grating was redirected through the side rejection port of an intracavity Faraday isolator then back into the front facet of the laser diode. The geometry of this setup for synchronous tuning is somewhat complicated, but without the additional losses from a second grating pass they were able to couple more power into the output beam, at the cost of lower side-mode suppression. They were able to achieve 7 GHz tuning in a low power laser diode. Other groups have focused on controlling the environmental conditions that disrupt pivot alignment [51, 52]. Talvitie et al. provide a complete theoretical and experimental treatment of passive environmental stabilization of external cavity lasers [51]. In their paper, their low power laser diode was set in an air tight laser cavity with all components made from low expansion materials and was driven using low noise current sources. They reported short term fluctuations of less than 40 khz and a long term drift of 3 MHz/hour. Most of the designs discussed so far have been constructed for low power laser diodes. Because of a rapid decrease in spectral quality for increasing power, adapting short cavity ECDLs to high power laser diodes is not trivial. In many cases, the output of a low power diode laser can be collimated with a single lens. As the power output increases, however, the required geometry of the semiconductor active layer leads to a highly astigmatic output that necessitates at least a two lens collimation system. The problem of coupling to an external cavity then becomes a two-dimensional one. The slow axis of the laser typically has a dual-lobed transverse multimode output, making it difficult to collimate with a single lens. Many groups have focused effort to this end. The cavities generally use off-axis feedback to select a single lobe of the high-order transverse structure. The feedback optics act as a spatial filter through which higher order modes cannot pass [53]. An 80% improvement in slow-axis divergence was achieved using this simple mirror feedback in laser diode arrays [54, 55]. Chen et al. and Raab et al. achieved near diffraction limited slow-axis divergence using tunable diffractive feedback with intracavity etalons to narrow the bandwidth to GHz scale with tunable ranges as high as 32 nm [53, 56]. These experiments focused mainly on spatial beam quality improvements while simultaneously improving the bandwidth and tunability with dispersive feedback, though recent work, including our own, suggests these two are intertwined (c.f. Chapter 4). Although these groups achieved near diffraction limited beam quality and narrow bandwidths, the cost is lower output power due to the spatial beam filtering. This sort of laser pre-conditioning is not required for low power ECDLs. This illustrates the problem of simply adapting successful low power designs. Because our design aims to unify all of the best characteristics of high power ECDLs, including narrow-bandwidth, wide coarse and fine tunability, and stability, comparing our results to other works is not necessarily easy. Groups using ECDLs in spin-exchange optical pumping (SEOP) experiments have reported narrowed bandwidths of 70 GHz with 2.5 W of output power and a coarse tunable range of 8 nm [47] and 20.3 GHz with 1 W of output power and a 4-6 nm coarse tunable range [57]. The latter group used the same BAL as in this work. Other groups have just focused on improving the spatial beam quality and spectral bandwidth without regard to tunability. Samsøe et al. reported a novel design utilizing zeroth and first order feedback from a Littman-Metcalf mounted grating that 4

15 yielded 1 W of output power with a 33 GHz bandwidth [58]. A similar bandwidth with 2.3 W from a laser diode array has also been reported [59]. An 8 GHz bandwidth was also observed in a very simple ECDL operating at 1.5 W [60]. There are examples of high power ECDLs that combine narrow-bandwidth operation with high tunability. One such example demonstrated a 14 nm coarse tunable range with a 16 GHz bandwidth using a 1 W BAL [61]. We also examined the modal linewidth of our ECDL. Although true single-mode operation has only been demonstrated with injection locking procedures or with tapered semiconductor lasers, the modal linewidth of high power ECDLs has been investigated. Modal linewidths of 120 MHz [62] and 200 MHz [63] have been reported using such mode-selective elements as a grating and an intracavity etalon respectively. As a final note, successful ECDL designs (regardless of the type of laser used) rely on the absence of stray reflections from intracavity elements other than the primary feedback element. These include reflections from the front facet of the laser diode itself, which can be severe owing to the large difference in refractive index at the interface ( 3.5:1). The presence of these laser chip modes sets up additional wave interference to an external cavity that is trying to lock to a single oscillating mode. Left uncontrolled with moderate feedback, tuning continuously in a single mode becomes more difficult [41]. There are a couple ways around this. Either the phase of the internal chip wave is electronically compensated for external cavity length changes [64], or very weak feedback is used [65]. Both methods add complication by adding parameters that need to be precisely controlled for synchronous tuning. The simplest way to avoid these issues is to use an anti-reflection (AR) coating on the front facet of the BAL. We will explain the differences and similarities between AR coated and uncoated BALs in an ECDL. We aim to design a passively stabilized high power ECDL utilizing the Littman-Metcalf configuration, designing the cavity to have a strict control over the variables that determine the tunable range of the laser while achieving narrow-bandwidth output. Along the way, we will compare our experimental results to the works cited above as well as others, paying careful attention to results of high power BALs applied to spin-polarized noble gases. 1.3 Applications Several areas of active research require lasers with high single-mode tunability and narrow bandwidths. Included among these are high-resolution laser spectroscopy, spin-exchange optical pumping of noble gases, and the production of Bose-Einstein condensates (BEC) in dilute gases. In the past, these research areas were served well by expensive solid-state lasers and gas laser systems. The proliferation of cheap BALs that can achieve similar output power, however, has led these devices to be increasingly desired over their expensive counterparts. In addition to being used to probe the properties of atomic and molecular systems, WTNB lasers are also used in the preparation of quantum and macroscopic systems whose properties can be carefully controlled depending on the resolution of the laser used to prepare the systems. Many free-running BALs can easily resolve the electronic structure of atoms. However, carefully controlled narrow-bandwidth BALs are needed to study fine and hyperfine structure in atomic systems or vibrational-rotational structure in molecular systems. The latter is easily enabled with high power BALs via Raman spectroscopy. The most demanding use of WTNB lasers is in the creation of samples of laser-cooled atoms [45]. In this application, lasers are used to cool atoms by selectively pumping the atoms with circularly polarized light. The tuning properties of the laser are of major importance here, as the lasers need to be tuned slightly off resonance to account for the Doppler shifted energy levels of the moving 5

16 atoms. Selectively pumping the hyperfine transitions confines the atoms to a small region within the laser intersection as the atom slows due to absorption of photon momentum from several directions. In this case, the linewidth of the laser needs to be on the order of khz or MHz, and be tunable across the complete hyperfine spectrum. In the most commonly used atoms for trapping, cesium or rubidium, this means tunability on the order of several GHz. Typically, low power diode lasers are used in place of high power BALs due to the extreme requirements of the linewidth and tunability, but master-slave configurations with BALs have been used [21] as well as the previously described high power Littrow geometry [45]. High power WTNB lasers are desirable because they permit larger beam diameters to be used, which leads to large trapping volumes if used as the trapping beam or possibly less trap loss if used as a repump beam. These may be important in the study of quantum statistics for example. The application that provides the motivation for this work is the creation of systems of noble gas atoms with a high degree of nuclear spin polarization. Such systems are used in place of water to dramatically improve the resolution of magnetic resonance imaging (MRI) instruments [66]. In this case, alkali atoms (typically potassium or cesium) are selectively pumped via circularly polarized light between the 2 S 1/2 and 2 P 1/2 valence electron states. The alkali atoms become spin-polarized and transfer their aligned electron spins to noble gas nuclei with a nuclear spin of 1/2 ( 3 He or 129 Xe) by a hyperfine contact interaction. By matching the alkali absorption bandwidth to the bandwidth of the incident laser, whether through pressure broadening the alkali band or narrowing the laser bandwidth, the intensity that the alkali atoms see can be maximized, yielding maximum polarizations. Details of the basic physics involved and why narrowed-bandwidth lasers are applicable are presented in 2.5. In presenting this work, we will first provide essential background in the basic physics of lasers and semiconductor lasers in particular, while detailing the theory behind our external cavity design. An introduction to the theory behind the primary application of this laser will also be presented to provide a motivation for the experimental design, which will be thoroughly described in Chapter 3. A discussion of laser characteristics and experimental results will follow as well as a prospectus of future research. 6

17 Chapter 2 Essential Background There are a wide variety of lasers in use today. Depending on the type of quantum system that is used as the lasing medium, lasers with different properties in varying spectral regions can be created. Solid-state lasers are often utilized for pulsed applications over a wide range of wavelengths. Semiconductor lasers are often used in continuous wave (cw) applications and are often found in the red and near-infrared (NIR). Other types of lasers in use include gas lasers, of which helium-neon lasers are the most well known, organic dye lasers, which are useful as a tunable source, and eximer lasers, which can access UV wavelengths effectively. Here, we will discuss the basic properties and physics common to all these lasers, and the physics of semiconductor lasers in particular. The theory governing diode laser propagation in an external cavity will be derived from Maxwell s wave equations and the basic physics behind the spin-polarization of noble gases will be presented. 2.1 Laser basics Many of the key properties common to all lasers can be derived from a simple examination of the rates of common transition mechanisms. In addition to the well known spontaneous emission and absorption processes, both emission and absorption can be stimulated to occur, as shown by Einstein in Stimulated emission is the fundamental mechanism driving lasers. Fig. 2.1 shows a 4-level atomic system in which a laser is set up between the second and third energy levels. Quantum systems such as this form the basis of many common lasers including helium-neon, argon ion, and Nd:YAG lasers. The transitions are labelled with the Einstein rate coefficients that represent the type of transition occurring. Einstein s A mn -coefficient has a simple interpretation as being the inverse of the m th excited state lifetime. The B mn -coefficient labels stimulated transitions and is dependent on both the lifetime of the m th excited state and the frequency of the stimulating photon. Because stimulated emission is triggered by an incoming photon, the incoming photon and the generated photon are phase-matched and of the same frequency. This is the origin of the strong spatial and temporal coherence of lasers. The overall rate of stimulated absorption/emission is externally dependent on the photon energy density, u mn in Fig Solid lines indicate transitions with the highest probability and dashed lines indicate less probable transitions. In this system, the ground state electrons are pumped to an energy level (4) that has a short lifetime. These excited electrons quickly decay to level 3 which has a comparatively longer lifetime. Whether by a stimulated or spontaneous process or by non-radiative quenching, the electrons decay to level 2 and quickly relax back to ground. Even though the stimulated rates of absorption and emission are equal, the quick depletion of level 2 7

18 A 43 fast B 14 u 14 A41 A 42 B u A slow A A fast Figure 2.1: 4-level diagram of a quantum system in a state of amplified stimulated emission. Here, a population inversion is achieved between levels 3 and 2. Solid lines indicate the most likely transition paths. The inset shows the phase relationship between photons emitted by the stimulated transition. inhibits the total number of excitations back to level 3. By analyzing the transition rates of electrons in this process, the basic properties of most lasers can be derived. To analyze this system, we will assume that the system is already in a state of amplified stimulated emission, so that a steady-state is reached across the levels. The dashed transitions are also being neglected and the ensemble is assumed to contain mostly a ground state population. The rate equations are summarized below: N t 4 = 0 = B 14 u 14 N 1 N 4 A 43, N t 3 = 0 = A 43 N 4 B 32 u 32 (N 3 N 2 ) N 3 A 32, N t 2 = 0 = B 32 u 32 (N 3 N 2 ) + N 3 A 32 N 2 A 21, N t 1 = 0 = B 14 u 14 N 1 + N 2 A 21, and N 1 N. (2.1) These equations can be simultaneously solved to obtain an expression for the population difference between levels 2 and 3, N 3 N 2, given by N 3 N 2 = B 14u 14 N A 21 [ ] A21 + B 32 u (2.2) A 32 + B 32 u 32 Eq. 2.2 shows that there will be a population inversion for any value of the pump rate (B 14 u 14 ) if the rate of decay from 2 to 1 is greater than the rate of decay from 3 to 2. This is a necessary condition to support laser emission. At first glance, the population inversion should continue unbounded with the pump power. However, once lasing occurs, the stimulated emission rate (B 32 u 32 ) will scale linearly with the pump rate. This forces the population inversion to saturate at a sufficiently high pump rate. With this change, Eq. 2.2 yields the bounded behavior shown in Fig This analysis can be repeated for a 3-level system, but the requirements on the pump rate become much more stringent, and besides the Ruby laser, there are not many lasers that use this pumping scheme. The properties common to all lasers then is that to achieve and maintain a lasing condition, there must exist a population inversion between two excited energy states and the natural lifetimes of these states must be analogous to the system studied in Fig

19 Figure 2.2: Behavior of the population difference between energy levels 3 and 2 (c.f. Fig. 2.1) as a function of pump rate under lasing conditions. Pump rate units are arbitrary. The directionality of lasers as well as the large gain is achieved by placing the lasing medium in an oscillating cavity. This cavity usually consists of a perfectly reflecting mirror, and a partially transmitting mirror. The optical stability of the cavity can be found by multiplying the Jones transformation matrices of the two mirrors, which yields the condition ) ) 0 < (1 (1 dr1 dr2 1, (2.3) where d is the distance between the two mirrors and R n are the radii of curvature. Under this condition, positive spherical mirrors appear to represent the best choice. However, planar mirrors satisfy the right hand equality constraint and thus are critically stable. Other important properties of lasers are the mode structure, bandwidth, and the near and far field spatial intensity distributions, collectively known as the beam quality. Because the laser is formed in an oscillator cavity, a stable oscillation will form a standing wave in the cavity. The key parameter is the spacing between modes in the cavity. This quantity is the free spectral range and in a medium of refractive index n and cavity length L, is given as ν = c 2nL. (2.4) The bandwidth of the laser is dependent on the laser power, the nature of the gain medium (single or multiple lasing modes supported), and can be influenced by the type of cavity it is in. The beam quality is measured by how gaussian the laser intensity cross-section is. As long as the laser is not operating in a high-order transverse mode, the output should be gaussian. For the semiconductor lasers used in this experiment, this condition is partially met. The properties discussed in this section are common to all lasers. In the next section, we will 9

20 discuss semiconductor lasers in detail and elaborate on their unique properties. 2.2 Semiconductor lasers In contrast to the generic laser scheme discussed in the previous section, semiconductor lasers do not rely on an atomic energy level decay scheme as it was discussed in the previous section. Rather, semiconductors use the collective atomic energy levels from planes of atoms in a solid crystal lattice as the basis for setting up a laser. Although solid-state lasers have a similar structure, the difference in semiconductors is that their valence electrons are weakly bound and with sufficient energy can be made to conduct. Solid-state lasers are insulators. The lasing levels in semiconductors are not simple electronic states, but nearly continuous energy bands formed by conduction and valence electrons in the crystal lattice Basic physics The simplest semiconductor device is the light emitting diode (LED). These are constructed from a single semiconducting substrate made by crystallizing semi-metal elements from Groups XIII-XV of the periodic table, with GaAs alloys being the most common [67]. Both halves are alternately doped with impurity atoms that provide an extra bonding site (p-type), or an extra valence electron (ntype). The p-n junction formed by these equal bandgap semiconductors is known as a homojunction. LEDs produce light with an energy corresponding to the bandgap between the valence and conduction bands when conduction electrons recombine with holes in the valence band. Although LEDs are a very clean light source, they cannot easily be made into lasers. Examination of Fig. 2.3 illustrates this. With a sufficient forward voltage bias applied to the p-n homojunction, spontaneous electron-hole recombination occurs with the emission of quasi-monochromatic light. However, when an electron reaches the valence band, or the conduction band for holes, there is no impedance in either band to the minority charge carriers leaking out of the active recombination region. Also, the emitted light is not confined to the active area, as there is no refractive index change across the junction. Lasing is possible, although current densities of A/cm 2 are needed [68]. The single and double heterojunction structures depicted in Fig. 2.3 are much better lasers. The single p-n heterojunction is formed by two different semiconductors, so the bandgaps are not equal. When a forward bias is applied, either the conduction or valence minority carriers have a greater chance of staying in the active area after recombination. This partial confinement eventually allows a partial population inversion to set up and stimulated emission becomes easier. A drawback to single heterojunction structures is that both minority carriers are not confined. The emitted light is partially reflected by the dielectric interface at the p-n heterojunction, but only once, then it will escape. These lasers are better than homojunction lasers, but still require current densities of A/cm 2 [68]. The double heterostructure semiconductor laser represents the state of the art. These are formed by sandwiching a thin p-type, narrow-bandgap semiconductor between heavily doped p-type and n-type semiconductors with similar, but comparatively larger bandgaps. The refractive index of the thin middle layer forming the active region is higher than its surroundings. A schematic of this type of laser is shown in Fig When a forward bias is applied to this laser, holes and conduction electrons are allowed to flow into the active area. However, minority carriers in each band are strongly inhibited from moving out of this region. With a constant current shuttling 1 Adapted from Melles Griot laser diode tutorial. 10

21 p n homojunction p n single heterostructure p p n double heterostructure p n p n p p n electron energy electrons holes unbiased unbiased unbiased forward biased forward biased forward biased p n p n p p n minority carriers allowed to diffuse out of active area _ minority carriers partially confined in valence band _ _ minority carriers confined in both bands Figure 2.3: Energy band diagrams of various types of semiconductor laser. For each type, the case for unbiased and forward biased is shown. Figure 2.4: Schematic of a typical single-stripe GaAs double heterojunction laser. 11

22 Figure 2.5: Schematic of semiconductor laser astigmatism. in holes and electrons, a large population inversion can occur, and stimulated emission will overtake all other transition processes. Not only are the electron-hole pairs well confined, but since the index of refraction of the middle layer is higher than the surroundings, total internal reflection will occur at both interfaces, thus confining the light to the active region. The large dielectric difference at the edge of the chip allows a 30% reflection back into the cavity. With required current densities of only 500 A/cm 2 at room temperature, most semiconductor lasers made today are of this type, or variations of this type Properties of semiconductor lasers Semiconductor lasers have several key properties that set them apart from other lasers. For one, they are extremely small and relatively cheap. The chip size of the laser used in this experiment was only 150x1x1000 µm [69]. Ordinary can-style laser diodes with low output powers, are much smaller than this. Because of the semiconductors typically used, these lasers generally operate in the red and IR regimes, however, within this region, the bandgaps can be carefully tuned to a wide variety of wavelengths. These lasers are also very efficient, with power conversion efficiencies of over 50% in most cases, and can operate with output powers from mw to kw depending on construction. There are some notable disadvantages to semiconductor lasers, however. They cannot easily be pulsed, and they are easily destroyed, either by static discharge, moisture, or improper temperature and current control. The largest problem though is astigmatism, as diagrammed in Fig The reason for this is simple. The nature of the gain medium is such that to achieve enough confinement for high gain, the active layer must be made very thin, but the high level of current required for this gain forces the transverse dimension to be wider to avoid catastrophic optical damage at the output facet. The result is an output beam with an elliptical cross-section diverging faster in one direction (fast axis) than in the other (slow axis). The eccentricity of the output ellipse increases as the geometric aspect ratio increases. This proves to be a major challenge to successfully collimate the output into a usable beam. The details of this process for the current experiment will be discussed in the next chapter. A related disadvantage is that the spatial intensity profile of semiconductor lasers 2 Adapted from Coherent Inc. technical note. 12

23 is at best two-dimensional gaussian because of the astigmatism. Even corrective optics have difficulty restoring a uniform gaussian profile. Coupling the output to a single-mode fiber will alleviate the problem, but at the cost of over half the output power typically. To discuss semiconductor lasers further, we will break them up into two classes: high and low power. These classes are represented by two design types, index-guided and gain-guided lasers Index-guided lasers The double heterostructure laser described in Section is an example of an index-guided laser [70]. In this type of laser, the light is confined by total internal reflection to the active region. The astigmatism is generally small, as the aspect ratios of these lasers are less than 10:1. This level of confinement means index-guided lasers are low power, with outputs no greater than tens of milliwatts, but they often operate in a single longitudinal and transverse mode due to the spatial confinement Gain-guided lasers The main difference with gain-guided double heterostructure lasers is that the refractive indices between the various layers are the same. These lasers still confine the charge carriers well, but rely on the laser itself modifying the refractive index in the active area to confine the light [70]. The weaker confinement requires high injection currents and thus wider active areas. Consequently, the aspect ratios of gain-guided lasers are larger than 10:1. For example, the gain-guided laser used in this experiment has an aspect ratio of 150:1. The large active areas of gain-guided lasers allow them to operate at high output power, on the order of watts. The beam quality suffers though, as the lack of confinement along the width of the chip allows multiple longitudinal and transverse modes to propagate in the waveguide. Indeed, the same physics that yields high gain also leads to nonlinear optical processes such as self-focusing that saturate regions of the active area and fragment the output into filamentous transverse structures [71, 72] 3. These structures can be dynamic [73, 74] and have very important consequences for our ECDL design as we will demonstrate. The bridge between high quality index-guided lasers and high power gain-guided lasers is the tapered semiconductor laser. This type of laser has already been discussed as being used in production of BECs [45]. These lasers couple an index-guided low power waveguide that can only support the fundamental transverse mode into a gain-guided BAL section whose width is tapered to its maximum value at the output facet. High-order modes excited in the BAL section are suppressed because of the tapered structure. These lasers attain higher quality beams than traditional BALs with output powers up to about 2 W. Semiconductor lasers are widely useful, but the astigmatism inherent in every design requires these lasers to be coupled to an external collimating system to be of any use. There are many ways to collimate these lasers [70]; but to analyze the laser beyond the exit facet requires a knowledge of the propagation of the beam in free space. This analysis is critical in properly collimating an elliptical beam and choosing optimal cavity components. 3 This process is known as spatial hole burning. 13

24 2.3 Propagation of lasers The behavior of lasers outside of the gain medium can be analyzed as a propagating electromagnetic wave using the time dependent Maxwell s equations. The inherent assumption that separates lasers from other propagating EM wave solutions is that the transverse intensity profile of ideal laser beams is uniformly gaussian. Although we showed in the previous section that semiconductor lasers are not uniformly gaussian, we will show that this is not a problem as we can apply this assumption to each of the two orthogonal components of the laser beam independently. Maxwell s time dependent equations in free space 4 are E = 4πρ Gauss s Law (2.5) B = 0 (2.6) E = 1 B c t F araday s Law (2.7) B = 1 E c t + 4π J c Ampérè s Law. (2.8) Here, ρ is the total charge density and J is the total current density, both of which are assumed to be zero in this experiment. Equations 2.7 and 2.8 can be combined by taking the curl of each to arrive at Maxwell s wave equations in free space, 2 E = 1 c 2 2 E t 2 (2.9) 2 B = 1 c 2 2 B t 2. (2.10) We take a propagating, non-uniform E-field solution of the form E = E(r)e i(kz ωt), (2.11) and substitute it into Eq The amplitude E(r) is, for now, an arbitrarily varying function of position; k and ω are the wave number and angular frequency of the light wave respectively. The expression obtained after substitution is [ z + 2ik ] E(r)e i(kz ωt) = 0, (2.12) 2 z where the Laplacian operator is with respect to the plane perpendicular to ẑ. In the paraxial limit, the curvature term in Eq varies much slower than the spatial variation and can be ignored 6. The 4 CGS units; ɛ,µ = 1 in free space. 5 A symmetric solution using Eq with the magnetic field component can also be used. 6 For the wavelengths of interest (red and NIR), this is a very good assumption. 14

25 oscillating term cancels, leaving a wave equation dependent only on the amplitude function E(r), [ 2 + 2ik ] E(r) = 0. (2.13) z This is the Paraxial Wave Equation (PWE). It can be used for any propagating wave with varying spatial amplitude. The mathematical form of the PWE is similar to the 2-D Schrödinger equation for a free particle. The purely classical derivation of the characteristics of propagating gaussian beams is somewhat cryptic, while the solution of the quantum mechanical version is straightforward. By analyzing the quantum mechanical free particle, we can infer the characteristics of gaussian beams by making use of Ehrenfest s theorem, which says if a quantum mechanical operator exists for a classical quantity, then quantum mechanical results can be inferred from classical phenomena by replacing the classical quantity with the expectation value of the appropriate quantum operator and vice-versa. For the one-dimensional free particle problem, the particle is unbounded in a zero potential. From knowledge of the energy eigenvalues of the system, the wavefunction of the particle at some later position and time, Ψ(x, t) can be found from the initial wavefunction, Ψ(x, 0) by constructing the appropriate transformation operator. Since we are concerned with gaussian beams, consider a quantum particle with a normalized gaussian wavefunction, Ψ(x, 0) = e ipox / e x 2 /2 2. (2.14) (π 2 ) 1/4 This gaussian wavepacket has an expectation value of zero and has an initial momentum p o in the positive x direction. The constant is related to the statistical width of the wavepacket. At some later time the wavefunction has the form [75] Ψ(x, t) = ( [π 1/2 + i t )] 1/2 [ ( ipo exp x p )] ot m 2m [ ] (x po t/m) 2 exp. (2.15) 2 2 (1 + i t/m 2 ) This is the solution to the gaussian free particle Schrödinger equation. The analogous classical quantity is E(r) which is a solution to the Paraxial Wave Equation (Eq. 2.13). The classical quantity of interest is the gaussian intensity distribution. The analogous quantity for the free particle is the probability distribution, found directly from Eq as P (x, t) = The uncertainty in x is time-dependent and grows as [ ] 1 (x po t/m) 2 exp. (2.16) π 1/2 ( t 2 /m 2 2 ) 1/ t 2 /m 2 2 X(t) = 2 [ t 2 m 2 4 ] 1/2. (2.17) From these results (Eqs ), we can make appropriate substitutions to yield the classical result that we seek. A key difference between the PWE and the free particle Schrödinger is that the latter 15

26 tracks the temporal evolution of the wavepacket, whereas the PWE tracks the spatial evolution. The two are related through the momentum by z = p o t/m. We now define w(z) as the half-width of the gaussian beam along either the x or y axes. Using the spatial representation, Eq is written as ] w(z) = [1 + 2 z 2 1/2. (2.18) p 2 o 4 The factor 1/ 2 was removed because it results from a statistical definition of width, rather than a physical measure. The momentum of the wave is p o = k o, where k o is the wave number (2π/λ o ), and can be substituted into Eq to obtain ] 1/2 w(z) = [1 + z2. (2.19) (k o 2 ) 2 Eq has an absolute minimum at z = 0, where w(0) =, the quantum mechanical width parameter. This is the waist of the laser beam, a point of minimum half-width. The quantity k o 2 has units of length, and is a reference distance. When z = k o 2, w(z) = 2 = 2w(0). This reference distance is known as the Rayleigh length (z R ) and defines the distance on either side of the waist over which the laser beam is well collimated. Using k o = 2π/λ o, the Rayleigh length can be written in its familiar form as z R = πw2 (0) λ o. (2.20) Putting this all together, the width of a gaussian laser beam varies along the propagation axis according to ] 1/2 w(z) = w(0) [1 + z2. (2.21) zr 2 To infer another key property of gaussian laser beams, we will examine the other terms in Eq We drop the pure phase term, and consider the complex exponential [ ] (x po t/m) 2 Ψ (x, t) = exp. (2.22) 2 2 (1 + i t/m 2 ) In the above equation, the quantity x p o t/m can be replaced with x(t) for simplicity. Recall, that the PWE is 3-dimensional whereas the free particle Schrödinger is in 2-d. For a free particle in 3-d, the time-dependent position, r(t), lies in a plane defined by x(t) and y(t). With this change, we separate the real and imaginary parts of Ψ (r, t). Eq becomes [ ] r 2 (t) Ψ (r, t) = exp 2 2 (1 + 2 t 2 /m 2 4 ) [ ] i t r 2 (t) m exp 2. (2.23) 2 2 (1 + 2 t 2 /m 2 4 ) The imaginary exponential describes the shape of the spreading gaussian phase front. Making the same substitutions we made earlier, and using our result in Eq. 2.21, a little algebra simplifies the phase term in Eq to [ ] iko zr 2 (t) Φ (r, t) = exp 2(zR 2 +. (2.24) z2 ) Gaussian waves can be reduced to a geometrical ray picture in the far-field (i.e. far from the focal 16

27 region where the divergence is constant). This was the implicit assumption made in deriving the cavity stability condition in Eq This requires the phase fronts of a gaussian wave to spread as spherical waves for z z R, with a radius of curvature equal to z. Applying this limit to Eq. 2.24, we can identify the quantity z/(zr 2 + z2 ) as being 1/R(z), where R(z) is the radius of curvature. Upon rearranging for R(z) we get [ ] R(z) = z 1 + z2 R. (2.25) z 2 Another useful equation can be found by eliminating z from these equations and solving for w(0): w(0) = w(z) [ 1 + ( ) ] πw 2 2 1/2 (z). (2.26) λr(z) This equation says that if the half-width of the beam and radius of curvature are known at any point along the beam, the waist can be found, and subsequently z can be found. This is useful when determining the effect of thin lenses on a gaussian beam. The lens does not affect the width of the beam, but can change the radius of curvature. This shifts the location of the waist and changes the Rayleigh length as well. The results contained in Eq and Eq are important in laser optics, and we will return to them in describing the setup of the cavity and theory behind the design. These equations are only valid for gaussian beams. In our experiment, the BAL used was gaussian along the fast axis, but not along the slow axis. The parameter used to describe the non-gaussian nature of a beam is the M 2 quality factor defined as M 2 w r(0) θ r w(0) θ o. (2.27) This is the ratio of the experimental product of the beam waist and local divergence to the predicted product. If this factor is considered in the propagation equations (Eq and Eq. 2.25) they can be rewritten as [ ( ) ] M 2 2 1/2 z w r (z) = w(0) 1 + (2.28) and R r (z) = z z R [ ( zr ) ] 2 1 +, (2.29) M 2 z where the subscript r denotes real experimental values. Eq shows that at any point in the beam, an increase in M 2 is accompanied by an increase in phase curvature. This will become an important point when analyzing the data from our experiment. M 2 can be determined experimentally by many methods. In our experiment we indirectly find it by measuring the real half-width of the beam at the Rayleigh length and comparing it to the ideal waist size. Solving Eq in this manner gives M 2 = [ (wr ) ] 2 1/2 (z R ) 1. (2.30) w(0) The analysis just carried out can be continued to infer the full solution to the PWE, but the remaining phase terms are not of consequence in this experiment. 17

28 Figure 2.6: Illustration of basic diffraction. The dashed line indicates the grating normal. 2.4 External cavity diode lasers: theoretical background Having discussed the basic properties of lasers, and the detailed theory behind their propagation, we are now in a position to detail the theory behind the external cavity design being used in this experiment. Classical ECDLs are composed of nothing more than laser diode collimating optics, a dispersive element, and possibly other optics to provide feedback. When designing an external laser cavity, three major issues need to be addressed. These are the bandwidth of the laser, single-mode tuning range, and the coupling efficiency. The bandwidth and coupling efficiency are generally a function of the chosen dispersive element, while the tunability depends on how well the cavity design maintains the modal structure under external changes. In this section, we will explain the physical basis underlying each of these issues. We then discuss two popular ECDL designs, the Littrow and Littman-Metcalf configurations, while emphasizing the latter ECDL physics In discussing the underlying physics common to ECDLs, we only consider designs utilizing reflective diffraction gratings, noting that other designs exist in the literature (c.f. Chapter 1). The basic physics of diffraction gratings can be derived as a generalization of Young s double slit experiment [67]. A simple geometric relation results, which is illustrated in Fig The angle of incidence, θ, is related to the diffraction angle, φ, by the fundamental grating equation mgλ = sinθ + sinφ. (2.31) Here, g is the groove density of the grating, and m is the diffraction order. All ECDLs operate in first order, so we will take m = 1. This equation is the foundation of this section. 18

29 From Eq we can get a simple expression for the output angular dispersion, which is λ φ = g cosφ. (2.32) This, together with Eq. 2.31, says that the dispersion increases as the angle of incidence approaches 90. This grazing-incidence condition is the basis for the Littman-Metcalf design, which utilizes the grating for dispersion and relies on another optical element (usually a mirror mounted in first order) for feedback. Another useful condition arises when the diffraction angle is equal to the angle of incidence. This is known as the Littrow angle (θ L ) and is related to the parameters in Eq by sinθ L = gλ 2. (2.33) This condition defines the second major class of ECDL, which utilizes the grating primarily for feedback and relies on external optics if narrower linewidths are desired (e.g. intracavity etalon). As stated earlier, in classic Littman-Metcalf cavities, the grating determines the bandwidth of the laser coupled to it. Original Littman-Metcalf designs were constructed for use in dye lasers [76]. Here, a suitable pump laser is focused with a cylindrical lens into a dye cell. The optimum dipole fluorescence is directed at 90 where it is coupled to a grating at grazing incidence. In most cases, no additional optics are required to set up these lasers. In their original paper, Littman and Metcalf modelled the cavity as an effective spectrometer with the grating serving as the input side and the active region of the dye cell serving as the exit slit. Modelling the dispersion in this way for a cavity length smaller than the Rayleigh length of the input laser leads to a bandwidth of [44] λ 2λzR πw g (sinθ + sinφ)l g, (2.34) where W g is the width of the grating and L g is the distance from the laser to the grating midpoint. The angles can be eliminated using Eq. 2.31, leaving a very simple expression dependent only on the center wavelength and grating properties. This bandwidth is minimized for cavities at the Rayleigh length of the input laser. Because of the large collimated waist sizes in our cavity, the Rayleigh length of our BAL was about 9 m. Our ECDL cavity lengths were well below this value. For our conditions, this model predicts a narrowed bandwidth of 42 GHz for a cavity length of 30 cm. For astigmatic laser diodes, the original analysis by Littman and Metcalf is further constrained by the small diameter lens used to collimate the fast axis of the laser diode. In this case, the dispersion is limited by the acceptance angle of the lens. Gavrilovic et al. applied these constraints, and extended Eq to include feedback dispersion, to come up with a theoretical upper limit to the bandwidth, given by [77] λ λ gd(1/cosθ + 1/cosφ). (2.35) The extra parameter, D, is the diameter of the fast-axis collimating lens. This equation suggests an upper limit of 1.4 GHz to the bandwidth of our ECDL. Neither model correctly predicted the behavior of BALs in our external cavity. We will discuss the implications of this in Chapter 4. To derive the synchronous tuning conditions for ECDLs, we follow the procedure set forth by McNicholl and Metcalf [78]. The desired condition is defined when tuning the wavelength affects no change in phase in an oscillator defined by the back facet of the laser diode and the feedback mirror, 19

30 Figure 2.7: Littrow geometry for determining the synchronous tuning condition. thereby maintaining the mode structure. McNicholl and Metcalf tracked the overall phase change of a plane wave traced from the laser, through the cavity, and back again. From scalar diffraction theory it can be shown that the diffraction at the grating yields a constant relative phase factor that is independent of the wavelength [79]. The only relative phase difference is accrued by propagation of the beam alone. From the previous section, we know that this also holds true if a gaussian beam profile is assumed. By summing the round trip phase shift (ψ), the conditions necessary for synchronous tuning can be derived for the Littrow and Littman-Metcalf configurations. Fig. 2.7 shows a generic Littrow cavity, with an arbitrary pivot point, P. If the front facet is AR coated, the plane wave is allowed to propagate entirely from the back facet of the laser diode to the grating and back again. The distances d 1 and d 2 are the perpendicular distances to the pivot point from the laser plane and grating plane respectively. They are considered positive if the pivot location is in front of the plane formed by the surface of the optic. The round trip phase shift accrued through displacements of the cavity optics from the pivot point is given by ψ = 2k(d 1 + d 2 cosθ L ). (2.36) For synchronous tuning, this accrued phase needs to be zero, so that the standing wave is stable across the cavity. For a Littrow cavity, this condition is satisfied if the pivot point is located at the intersection of the mirror and grating planes (i.e. where d 1 and d 2 equal zero, indicated as a red X in Fig. 2.7). This condition is necessarily independent of tuning angle, and thus wavelength. The geometry for analyzing the Littman-Metcalf configuration is shown in Fig. 2.8 with the mirror plane displacement (d 3 ) added. Again, starting from the laser diode, the round trip phase shift due 20

31 Figure 2.8: Littman-Metcalf geometry for determining the synchronous tuning conditions. to cavity optic position errors is given by ψ = 2k(d 1 + d 2 (cosφ + cosθ) + d 3 ). (2.37) Inspection of Eq shows an analogous tuning condition to the Littrow cavity, in that synchronous tuning occurs if the pivot point is located at the intersection of the three optical planes. Indeed, this condition is satisfied in general for N cavity optics [78]. Another interesting tuning condition arises if the grating is assumed to be perfectly aligned (i.e. d 2 = 0). Here, if the pivot point is located a similar distance behind the feedback mirror plane as in front of the laser diode plane, or vice-versa, then synchronous tuning is also possible. The existence of a second tuning condition for Littman- Metcalf cavities eases the difficulty of achieving synchronous tuning somewhat. Assuming the grating is well placed, displacements of the feedback mirror from the pivot point can be compensated for by adjusting the laser along the optical axis. Thus, the alignment in our cavity is potentially onedimensional. The tolerance of these synchronous conditions is related to the free spectral range of the desired single-mode scan, ( ) 1 c d <. (2.38) 10 2π ν s Here, d represents the total misalignment from the pivot point by each cavity optic [78]. As the desired scanning range ( ν s ) increases, the tolerance on the pivot point becomes stricter. The factor of 1/10 represents the tolerable phase error, as a multiple of 2π. If longer cavities are desired to give narrower linewidths, the synchronous condition becomes harder to satisfy as small angular displacements of the cavity optics are amplified by the increased distance of the optics from the pivot point. This is the primary tradeoff that needs to be considered when designing ECDLs. If we assume only linear displacements of the cavity optics, the machine tolerance of our ECDL is 38 µm. Eq then predicts a maximum synchronous tuning range of 125 GHz. 21

32 2.4.2 Contrasting Littrow and Littman-Metcalf designs From the previous analysis we can deduce some key advantages and disadvantages to each cavity type. If spectral narrowing is important, the Littman-Metcalf cavity is the one to use. Although it is possible to achieve optimum narrowing with Littrow cavities by using beam expanders to fully illuminate the grating, the same is done without additional optics in the Littman-Metcalf geometry. Conversely, if easier tuning is desired, Littrow cavities can be made very short, making the tolerances easier to satisfy. However, in Littman-Metcalf cavities, the tunability may depend less on the longer cavity lengths due to the less stringent alignment criteria provided by Eq A final consideration is more practical. If the classic Littrow cavity is used, the output angle will change while tuning the wavelength 7. This is often undesirable. However, since the grating is held stationary during tuning in a Littman-Metcalf cavity, this problem is completely avoided. 2.5 Application to spin-exchange optical pumping of noble gases The laser presented in this work was primarily designed for high-resolution spectroscopy and as a pump laser for alkali gases involved in spin-exchange optical pumping of noble gases. The latter is used in high-resolution medical MRI diagnostics, as well as in the production of homogenous spin systems for fundamental nuclear structure experiments. We present a brief summary of the physics involved, and the need for WTNB lasers as efficient pump sources Basic physics For as long as MRI diagnostics have been used in imaging internal tissues such as the brain and lungs, the process has relied on nuclear magnetic resonance (NMR) signals from hydrogen nuclei located in abundance as water in the body. Unfortunately, this is as inefficient as it is easy to implement and limits its use in modern medicine. The proton nucleus is a spin-1/2 fermion. In thermal equilibrium, Boltzmann statistics can be easily applied to examine the polarizations that are detected with conventional MRI systems. The population ratio of spins aligned and anti-aligned to an external biasing field is simply a ratio of the Boltzmann factors, N N = e hνr k B T. (2.39) The energy splitting is given as hν r, where ν r is the MRI resonant frequency. In the limit that hν r k B T the spin-polarization ratio is given by P = hν r 2k B T. (2.40) For typical temperatures and resonant frequencies of hydrogen nuclei bounded in water molecules, 7 This can be avoided if one has access to the back facet of the laser diode [45]. 22

33 Figure 2.9: Optical pumping scheme of alkali gases. the polarization is of order 10 6 [66]. This is incredibly small, and leads to poor resolution images. Conventional MRI systems compensate by broadening the Zeeman energy splitting with strong magnetic fields. By contrast, if a nuclear spin-polarized gas is breathed in and imaged, the polarization ratios are increased a million-fold. Minimal strength biasing fields are needed to achieve order of magnitude increases in resolution and the polarized gas can illuminate air passages in the lungs that are inaccessible by conventional MRI. Noble gases are used in this application due to their inert nature. Furthermore, to reduce spin-relaxation contributions from electric quadrupole interactions, spin-1/2 3 He and 129 Xe are specifically used [46]. Only 3 He can be directly prepared in a spin-polarized state, but requires wavelengths poorly covered by cheap diode lasers [66, 80]. The dominant method uses narrow-bandwidth lasers to optically pump an alkali gas into a spin-polarized ground state. Fig. 2.9 illustrates this using a generic energy level diagram for the ground state and first excited P state. The electric dipole selection rules are dependent on the polarization of the incident radiation field and are given by +1 LCP m s = 1 RCP. (2.41) 0 linear For left circularly polarized light (LCP), electrons are pumped from the m s = 1/2 ground state to the m s = 1/2 sublevel of the 2 P 1/2 excited state. From here, the electron relaxes to either ground state sublevel. To avoid radiational depolarization, this relaxation is forced via collisional quenching from a nitrogen buffer gas [66]. If it relaxes back to the original sublevel, it is simply repumped by the laser. Over time, a substantial population will develop in the spin-up ground state. The spin information is transferred via a hyperfine contact interaction to the noble gas atoms. The interaction Hamiltonian, Ĥ = γ(r) ˆN Ŝ + A(R)Î Ŝ, (2.42) represents contributions from electron spin (Ŝ) - van der Waals molecular rotation ( ˆN) coupling, and electron - nuclear spin (Î) coupling. The functions γ(r) and A(R) help set the spin-exchange cross section and are strong functions of the alkali-noble gas internuclear separation, (R). In practice, only one or the other term is dominant [46]. In either case, expanding the interaction term in the coupled angular momentum eigenbasis will show that there exists an equal probability that the combined system can be found in either a (, ) or (, ) state, which leads to spin exchange. For low pressures, the interacting atoms form a temporarily bound system via van der Waals forces and the first term dominates. At high pressures, binary collisions take over and the second term dominates. The detailed physics of the interaction mechanisms are given in Ref. [46]. Theoretically, after a sufficient pumping time, the noble gas polarization should match the alkali polarization levels, which can be quite high for an adequate beam intensity. However, there are a number of factors that limit the maximum polarization. Atom-atom collisions, wall collisions, thermal relaxation and interactions with an inhomogeneous magnetic field can all affect the net polarization [46, 66]. In general, the spin-exchange rate (denoted as γ se ) is directly proportional to 23

34 Figure 2.10: Spin-exchange and spin-relaxation cross-sections for various combinations of noble gas and alkali atoms [46]. Open symbols represent theoretical estimates, and closed symbols represent experimental values. the density of alkali atoms. Since the alkali atoms are usually evaporated from a liquid or solid state, the spin-exchange rate depends on the temperature of the system as well. Denoting the polarization of alkali gas and noble gas by P a and P n respectively, and grouping all relaxation processes into a single spin-relaxation term, T1 1, a simple first-order rate equation can be solved to yield an exponential charging function [66], P n = P ] aγ se [1 γ se + T1 1 e (γ se+t 1 1 )t. (2.43) The saturated polarization depends solely on the ratio of the spin-exchange rate to the spin-relaxation rate. If this is large, the noble gas will saturate at a high polarization. In many respects the science of SEOP is limited by an understanding of the relaxation processes that can occur in the sample. These complicated processes have been the subject of much research [46, 66, 81, 82]. In contrast, controlling the spin-exchange rate is a better understood problem. Walker et al. carried out a detailed analysis of this problem by examining the spin-exchange and spin-relaxation cross-sections for intramolecular relaxation processes [46]. Their results are highlighted in Fig To maximize the spin-exchange 24

35 Figure 2.11: Theoretical and measured polarization of 129 Xe versus temperature for W of freerunning output from a commercial LDA (open circles) and a narrowed 1.4 W BAL (closed triangles) [47]. rate while minimizing the spin-relaxation rate, polarization of 129 Xe should be carried out with Rb or Cs. Sodium or potassium are better suited to production of spin-polarized 3 He. To directly enhance the spin-exchange rate, the temperature can be increased to increase the density of the alkali vapor. The limit to which this works depends on the supply of pumping photons along the entire length of the cell. High power lasers, and a careful matching of the gain profile with the absorption bandwidth to maximize the pumping efficiency, are crucial to achieving high polarizations The effect of the laser Experimental studies using high power broadband lasers and low power, frequency-narrowed ECDLs have clearly demonstrated the benefits of optimizing the laser gain profile and cell temperature [47]. Fig illustrates this fact. For nearly 10% of the power, a frequency-narrowed laser performs as well as high power, free-running laser diode arrays. Similar results were also demonstrated with the 2 W diode laser used in this experiment, though various cavity inefficiencies and an uncoated laser facet limited its power output [57]. If the laser bandwidth is well-narrowed, the gas cell can be held at a lower pressure. For example, with pressure broadening rates of about 15 GHz/atm in Rb [83] with a nitrogen buffer gas, a wellnarrowed laser would reduce the pressure required to match the laser bandwidth. This would mitigate the side-effect of increased atom-atom relaxation that comes along with broadening the line artificially. The limit to useful bandwidth narrowing is the doppler bandwidth of the alkali, which is typically several hundred MHz. The application of high power ECDLs to SEOP experiments is a robust area of research because they are relatively inexpensive to build. The available literature suggests that ECDL technology has not been fully explored in this application, as most papers on the subject are post-year Mode-stabilized ECDLs that are widely tunable should have a large impact on this field, and it is to that end that we direct this research. 25

36 Chapter 3 Experimental Design We now describe the details of our ECDL design, as well as the instruments and techniques used for analyzing the performance of the laser. Fig. 3.1 shows a schematic of the entire apparatus used for this experiment. The apparatus sits on an air-filled optical bench, isolating it from external vibrations. The drive circuitry and thermoelectric cooler (TEC) driver were mechanically isolated from the experiment. The only known source of vibrational noise on the bench itself was from the scanning Fabry-Perot interferometer and it was isolated from the experiment by a thick styrofoam base. The experiment is best described by splitting Fig. 3.1 into two sections, one containing the ECDL itself, and the other containing the instrumentation for analyzing the beam. The physical separation between these two sections is the Electro-Optics Technology model LD38I780 optical isolator. The isolator utilizes Faraday rotation in a terbium gallium garnet magneto-optical crystal to reduce backreflections into the isolator by up to 35 db [84], allowing up to 80% transmission. Where appropriate, we will point out possible avenues of improvement that have become apparent in the course of this work. 3.1 ECDL design Careful attention was paid to passive suppression of external noise while constructing the cavity. Floating the optical bench dramatically improved the vibration control, as evinced by Fig. 3.2, which shows a voltage signal with and without a floating optical bench from a piezoelectric wafer secured to the base of the cavity. To further damp exterior vibrations, the cavity arms supporting the optics were mounted on a heavy (17 3/4 x 8 3/4 ) steel baseplate, and the whole assembly was affixed to the optical bench via an aluminum plate. The two arms supporting the diffraction grating and feedback mirror were made from 1/2 thick copper. The copper is a low expansion material that thermally isolates the optics. Air currents were suppressed by enclosing the entire cavity in a plexiglas housing. The sealing was not perfect, as there were openings for the actuator and beam exit port. Despite this, the housing showed a noticeable improvement in frequency drifting caused by local index of refraction fluctuations. The interior of the box was covered completely with black flock paper from Thorlabs to reduce stray reflections. The cavity was not kept at a temperature or pressure different from ambient, thus the cavity was allowed to drift with slow changes in ambient conditions. To seal the box completely, an AR coated window would have to be installed on the exit port, which would be expensive for the large size of the exit port. A better solution would be to actively compensate 26

37 Figure 3.1: Overview of our experimental setup. Figure 3.2: Average voltage response from a piezoelectric wafer attached to the base of the cavity s feedback mirror mount. The figure shows the signal a) with and b) without the optical bench floating. 27

38 for ambient drift by using a locking circuit if the laser is to be fixed in frequency over long periods of time. However, for our ECDL, this was not necessary. The passive stabilization techniques described so far protect against environmental noise resulting from vibrations, air currents and thermal conduction. The other primary source of noise in this experiment was electrical. In discussing the cavity design, we will note how this was important The cavity Our Littman-Metcalf external cavity was designed to be a rigid implementation of the synchronous tuning conditions outlined previously. Fig. 3.3 shows a photo of the scissor mount with and without the laser optics. Schematic diagrams are included in Appendix A. We optimized every dimension of the cavity to rigorously satisfy the multiple constraints imposed by synchronous tuning requirements (c.f ) and by practical considerations. The cavity was designed to fit into a box with interior dimensions of 18 7/8 by 9 1/8. The optimization parameters are depicted in Fig In the figure, L is the total cavity length and is a sum of the laser-grating length, L g, and the grating-mirror length, L m. L p and M p represent the pivot-grating and pivot-mirror distance to the respective midpoints. In the laser plane, D L is the pivot-laser distance and M 1 is the projection of M p onto the laser plane. W m and W g are the widths of the feedback mirror and grating respectively, and t g is the distance from the pivot to the edge of the box (a minimum of the thickness of the grating arm). The definitions of the angles are the same as in Fig The box size and required wavelength range fix most of the constraints on the mount. The mount dimension with the most stringent size constraint will set both dimensions. The width of the cavity is constrained principally by M 1 but also by t g. If W is a limiting width (from a box width constraint for example), then schematically L max g must satisfy the inequality W t g + M 1 + x 1. (3.1) The parameter x 1 is included to account for any additional constraints on the width (in our case we used this for extra sidewall clearance). M 1 can be written in terms of the principal angles and L max g in Fig The maximum laser-grating length is found by solving Eq. 3.1 for L max g, giving L max g = (W t g x 1 )sinθ. (3.2) cosφcos(θ φ) The desired operating wavelength range will constrain φ for a given grazing incidence angle. Eq. 3.2 needs to be evaluated at the maximum φ since this will correspond to the scissor mount being open. Not included in the constraint on cavity length is the length required to hold the mounts for the diode laser and collimating optics, which varies with the application. Because L g > W in Littman-Metcalf designs, in a practical sense the length of the available baseplate may actually limit the length before its width does. If the baseplate is not a limitation, then the material chosen for the scissor mount arms may present a limitation. This was the case in our experiment. The steel baseplate was available in house in a size fitting our box dimensions, so the copper arms were our limiting constraint. We chose a 12 x12 x1/2 sheet of copper to fabricate the arms holding the optics. Eq. 3.2 predicted a maximum laser-grating length nearly twice the linear dimension of our copper sheet based on our desired operating conditions. If the width is not a constraining factor, specifying the grating arm length will fix the minimum movable arm length. 28

39 Figure 3.3: The Littman-Metcalf scissor mount a) without and b) with cavity optics. The location of the geometrical pivot is indicated in the figure. 29

40 Figure 3.4: Parameters used in deriving constraint equations for our external cavity mount. This length is parameterized by Mp min, which, in terms of L max p is M min p = L max p cosφ + x 2, (3.3) where x 2 accounts for additional length from the mirror mount to get the total arm length. In terms of the total grating arm length (L) and grating width (W g ), L max p = L W g /2 x 3 (3.4) represents the maximum pivot-grating distance with x 3 providing another fudge factor. Mp min must be evaluated at the minimum φ where cosφ is a maximum. The scissor mount can be completely specified using the conditions above. There are other constraints that we did not formalize, but which effect the final design. The width of the arms, for example, is largely set by the mounts that are used to affix the feedback mirror and grating 1. This width needs to be chosen carefully. Since the laser will lie along the pivot plane, the movable arm cannot extend too far beyond this plane or it will impact the laser mount. Also, when tuning to the smallest working angle, care must be taken so that the movable arm does not impact the grating arm. Appendix A shows AutoCAD drawings of the scissor mount in the fully open (Fig. A.1) and closed (Fig. A.2) position to illustrate how we avoided this. The slot cut into the grating arm illustrated in Appendix A should not be so large as to affect the stability of the grating mount for small cavity lengths. The position of the mounting holes along each arm is also set by the requirements of the optics mounts. Since the pivot-mirror line will lie very close to the back edge of the movable arm, we chose to place the mounting holes 1/2 from the front edge of the movable arm. Because of the slot in the grating arm, the mounting holes here were located 1/2 from the back edge of the arm. The spacing of the mounting holes was also 1/2, but the optics were mounted on slotted mounts that 1 If the width of the baseplate is the limiting constraint on the mount dimensions, then the width of the movable arm may have additional considerations. 30

41 allowed any position to be accessed along the arms. A final consideration in designing the mount arms is providing a means to adjust the movable arm. We countersunk an aluminum tab into the movable arm extending beyond the arm edge to avoid interfering with the mirror mount. This tab should be positioned as far from the pivot as possible to increase the tuning resolution. Using the above prescriptions, we can now specify our cavity mount design. We designed the scissor mount to operate in an angular range from 55 to 70, corresponding to a wavelength coverage from 756 nm to 807 nm. With the proper laser, the mount can potentially access both Rb D bands, and the K D1 band at 770 nm, which covers both transitions principally used in SEOP experiments. With a constraint of 9 1/8 for the width of the baseplate and 18 7/8 for the length, we determined, using Eq. 3.2, that the maximum attainable L max g was larger than the length constraint. With that, our grating arm length of 12 set the dimensions of the rest of the cavity. Our baseplate was sized at 17 3/4 by 8 3/4, allowing a free space of 3/8 for the width and 1 1/8 for the length. The cushion on the length is larger to allow the wires feeding the laser to lay without stress from the walls. We set the pivot point 4 3/4 from the back of the baseplate to allow for the laser and collimating optics mounts. We chose to fix the grating arm at an angle of 5 with respect to the pivot plane normal. The cavity was designed around a nominal 2 grating and feedback mirror, not including the mounts. We will elaborate on this in We set the maximum laser-grating length to be 11 following Eq Using Eq. 3.3, this set the minimum movable arm length to be 6 1/2. Both L max g and Mp min include 1 for the half-widths of the optics on the arms. The arms were designed to work at a minimum L g of 1, but because of the space required for collimating optics, this limit is not always realizable. These dimensions result in a nominal cavity length ranging from 5 cm to 52 cm. To access all the cavity lengths, the laser required a linear translation stage with a movable range of 1. The width of the two arms were chosen to be 2 5/8. This was largely chosen to match the size of the mirror and grating mounts. This required a nearly 1 slot to be cut in the grating arm to accept the movable arm for small angles. With our constraints, the width could not be made too much larger than its nominal value, but even if this is not an issue, it is not advisable to use arbitrarily wide arms. As the width is increased, the weight of the movable arm increases. Depending on the types of mounts used for the mirror and the type of actuator used, this may overload the actuator. We chose a Zaber model T-LA28A actuator to control the motion of the movable arm. This actuator features a large stalling load of 50 N and extends to a maximum of 28 mm. The leadscrew is electromagnetically actuated, allowing for reduced friction and a resolution limit of 0.1 µm. The estimated load on the actuator including the feedback mirror was less than 10 N, well within the stalling limit. The contact friction between the movable arm and the baseplate was reduced to a negligible contribution by slightly elevating the arm and using a teflon screw at the point of contact. Even if the movable arm is not a significant load on the actuator, it is still desirable to use an actuator with a large stalling load versus settling on a smaller model. This is because, at small displacements comparable to the resolution of the actuator, larger actuators will have an easier time overcoming the static friction in the system, resulting in a smoother motion. Fig. 3.5 demonstrates this for a 5 N and 20 N load [85]. The data for the 5 N load closely approximates our operating conditions. The stepsize is 0.1 µm and for the 5 N load, the delay in motion is at most one extra step. The 20 N load is considerably less smooth in its motion. Another important characteristic to consider for long term operation (necessary for 129 Xe polarization experiments) is thermal stability. For Zaber T-LA class actuators using the maximum rated drive current, the measured displacement was 35 µm approached exponentially with a time constant of 20 minutes [85]. For the requirements of our ECDL, this was not a concern, as we only required minimal motion for tuning, and did not need to maintain a drive current to hold the movable arm over an extended period of time. The actuator is secured to an aluminum right-angle mount that cradles the cylindrical actuator and is affixed directly to the baseplate. A rubber boot is fastened to the aluminum tab on the movable arm to reduce vibrations from the leadscrew while in motion. This tab was placed as far 31

42 Figure 3.5: Smoothness of actuator motion characteristic of Zaber T-LA class actuators. The data, taken from T-LA technical notes [85], was taken with a load of 5 N and 20 N on the leadscrew. from the pivot as possible. The frequency resolution achieved by the actuator at this position was estimated to be 57 MHz. The resolution actually realized in the lab was better than this in part because the actuator was not lined up tangent to the pivot. The actuator can be controlled manually or remotely. The advantage of Zaber actuators over others in the marketplace is that it does not require proprietary driver electronics, which dramatically reduces the cost. Our actuator houses the driver hardware internally, and uses an RS-232 serial cable to interface with the computer. We chose to implement the software interface in LabView, although Zaber provides software drivers for many other languages including C and Visual Basic among others. Fig. B.5 in Appendix B shows a screen capture of the interface program that was designed around the driver supplied with the actuator. The details of this program are left to an ECDL user manual supplied as an addendum to this thesis Collimating optics The problem of collimating a BAL is more complex than that of a normal laser diode. We used a Coherent Inc. S C-150-C 2 W single-stripe cw BAL whose transverse dimensions, as previously stated, were 150x1x1000 µm. This large aspect ratio is the root of the problem. Using the results from Gaussian beam propagation theory (c.f. 2.3) we can predict how the beam will be shaped in the collimating lens system. In the active area of the chip, the laser exists in a Fabry-Perot cavity with plane reflecting surfaces. The radius of curvature in both dimensions is infinite, so the chip defines the waist of each laser. The fast axis of our laser had an initial waist size of 0.5 µm while the slow-axis waist was 75 µm. The Rayleigh lengths for the fast and slow axes at the typical center wavelength of 790 nm were 0.9 µm and 2.2 cm respectively. For reasons that will become clear, we decided to use an aspheric lens for the first collimating optic, and a cylindrical lens for the second. The lenses are each anti-reflection coated for optimum reflection in the NIR. The focal length of the aspheric lens is 2.7 mm. Because the focal length is much larger than the fast-axis Rayleigh length, Eq predicts R(z) z. The effective thin lens focal length (f eff ) assumes the spherical phase front emanates from a point source, thus f eff = R(z) [67]. If the aspheric lens is placed one focal length away from the laser diode, it should perfectly collimate the fast axis. In our setup, this was indeed the case. The waist size of the collimated dimension was about 1.5 mm in our cavity, just as predicted from Eq At 790 nm, the new Rayleigh length was about 9 m. We have verified that 32

43 the fast axis is well collimated in this range. The effect of the aspheric lens on the slow axis is a different story though. In this case, Eq predicts that R(z) = 18.2 cm. Thus, f eff for the slow axis is 18.2 cm behind the laser diode. This astigmatism is the direct result of the geometry of the emitter. Since the aspheric lens is located much closer to the laser than f eff, the new slow-axis R(z) just after the lens is equal to the focal length of the aspheric lens. Using Eq. 2.26, we can derive a new Rayleigh length for the beam equal to 0.3 mm. The net effect on the slow axis is to pull the effective focal point back into the laser diode. The cylindrical lens we used has a focal length of 5.0 cm. In an analogous way to the fast-axis collimation, placing the cylindrical lens one focal length away from the laser should now collimate the slow axis, since the effective focal length is no longer different, and leave the fast axis unchanged. Eq also predicts the new waist size to be 1.5 mm. This was not the case in our cavity. It should not be too much of a surprise based on the discussion in 1.2. The transverse multimode structure along the slow axis cannot be collimated with a single thin lens due to its non-gaussian profile. Another common collimation scheme uses two cylindrical lenses to separately collimate each dimension. We experimented with this, but found several disadvantages to it. The first collimating lens would output a diffraction limited beam along the fast axis as before. However, this lens would not have any effect on the slow axis, leaving the effective focal point way behind the laser. Because of the slow divergence angle, if a symmetric beam is desired, the second collimating lens needs to have a long focal length. To limit the amount of space taken up by the optics, the first cylindrical lens should be as small as possible. The large radius of curvature necessary to make small focal length cylindrical lenses constrains the lower limit on the focal length. The smallest focal length lens we could find was still longer than the aspheric lens discussed previously. By this distance, the fast axis diverged too much to be effectively collimated and the resulting beam quality was poor. A solution to this problem that we did not try would be to use a gradient index (GRIN) cylindrical lens to collimate the fast axis. These are available in very short focal lengths, allowing the slow axis to be effectively collimated. The collimation needs to be taken care of in as short a distance as possible not only to increase the operating range of the ECDL, but also to reduce the width of the beam. This reduces the Rayleigh length, thus increasing the bandwidth narrowing capability of the cavity according to the Littman-Metcalf theoretical model. We currently have the collimating optics set on a common mount. The advantage of this is that for a particular laser, once the optics are locked down, they can be moved together, maintaining relative alignment. This makes it easy to make small collimation adjustments. An improvement that should be sought is placing the collimating optics mount and laser on a common translation stage with freedom in the pivot plane. This would greatly facilitate changes to the cavity length, which is not as easy currently Diffraction grating and feedback mirror We used two separate diffraction gratings for this experiment. From our earlier discussion, optimum narrowing of the laser bandwidth should occur if the grating intercepts the entire beam. This is a constraint on the system in the sense that a large illuminated area is desirable, but not with a large area beam. For our operating wavelengths, 2400 grooves/mm gratings were the highest dispersion we could use. We used a holographic grating because of the high groove density. These gratings do not show debilitating effects such as stray light and ghost reflections. The gratings were mounted along the fast axis of the laser, with the grooves parallel to the polarization direction of the BAL. A collimated beam width of 3 mm required a grating size of at least 2 to fully intercept the beam. The first grating used was a standard aluminum coated, 1 holographic grating [62]. This was half the 33

44 Figure 3.6: Typical reflectance curves for aluminum and gold in the visible and NIR. grating needed to efficiently intercept our laser and in our experiment, nearly half the incident beam power was not coupled to the grating and was lost. This helped to hold down the coupling efficiency to around 20%. An even smaller fraction was actually sent back to the laser due to zeroth order diffraction on the return pass. We will show the effect this had on the laser in Chapter 4. This small feedback is still more than sufficient to lock the laser [41,86,87], but we did notice a susceptibility to mode hops caused by external reflections that was reduced when going to a 2 grating. In choosing the second grating, we aimed to address all the deficiencies of the first grating. We chose an Optometrics model holographic grating. The length was increased to 2, sufficient to intercept nearly the entire beam, and the grating was coated in gold. For our wavelength region of interest ( nm) there is a significant improvement in diffraction efficiency over aluminum as shown in Fig These particular gratings were optimized for grazing incidence use. Also, the grating was written on a pyrex substrate to reduce thermal expansion from prolonged laser heating. We immediately noticed an improvement in the laser coupling, as we will discuss in Chapter 4. The coupling efficiency improved to over 50% mainly as a result of coupling the entire beam and using a gold coating. It should be noted again that not all of this feedback makes its way back to the laser, as some is diffracted into a secondary zeroth order. This secondary diffraction can be reduced by rotating the BAL s incident polarization away from vertical with a half-wave plate as long as the feedback is sufficient to keep the BAL locked to the external cavity, though we did not experiment with this. There are less degrees of freedom in choosing the feedback mirror. It need only be large enough, and highly reflective. The latter was satisfied by choosing a common dielectric mirror coated for nearly 100% reflection in the NIR. The size of the mirror can be calculated by finding the projection of the grating surface onto the plane of the mirror. It needs to be large enough to intercept all the light diffracted at the minimum operating angle of the scissor mount (55 ) where the projection is the largest. The maximum projection works out to be a little over 1. Since the rubidium D bands can be accessed at higher angles, a 1 mirror is completely sufficient. It should also be noted that 2 Image is adapted from Optometrics LLC. 34

45 Figure 3.7: Laser and TEC mount. The location of the BAL chip is shown. the grating and mirror were mounted on multiaxis adjustable mounts making fine adjustments easy. We will describe the alignment procedure in more detail in Laser and drive electronics We used two lasers of the same model described earlier in our experiments. One of the lasers was AR coated on the output facet and the other was a bare chip. Fig. 3.7 shows a picture of the laser in the cavity. We will characterize the important properties of both lasers in Chapter 4. The BAL active area is constructed from an InGaAsP semiconductor [88]. The laser chip is mounted onto a copper heat sink. The temperature is controlled by a Peltier effect thermoelectric cooler with thermal feedback provided by a 10 kω thermistor attached to the laser diode mounting block. The room temperature operating wavelength of both lasers lie near 790 nm. For our purposes, there is no need to cool the laser as we are principally interested in the Rb D1 band at nm. Cooling the laser potentially increases thermal drift in the coupled laser wavelength as the TEC sinks most of the extracted heat into the atmosphere. We note this as a consideration if cooling is required (to access the Rb D2 band for example at nm). The laser s position in the cavity can be precisely controlled with the two-axis translation stage to which it is mounted. Each axis can be moved over a 1 span, which is sufficient to cover any cavity length accessible by the scissor mount. The heart of the laser is the electronics used to drive both the BAL injection current and the TEC. The drive electronics were almost completely reconstructed in an effort to fix what ultimately was a major grounding problem. The details of the problem will be left to an auxiliary manual that will be drafted for this laser system so it can be avoided in the future. Fig. 3.8 shows a block diagram of the drive electronics. The entire system was mechanically isolated from the laser cavity. The high power laser diode driver (Wavelength Electronics MPL-2500) drove the laser in a constant current mode. Although a constant power mode is supported, we did not use this feature in a 35

46 Figure 3.8: ECDL drive electronics. 36

47 Figure 3.9: Temperature-voltage calibration for the feedback thermistor attached to the laser diode case. tuning application where the current could not be allowed to drift. Also shown in Fig. 3.8 is the equivalent circuit diagram for our laser. In addition to the laser diode, we used a Schottky-type barrier diode to prevent reverse voltages from damaging the laser. The driver is capable of supplying 2.5 A of continuous current with an RMS noise level <10 µa. Although the driver could be directly modulated, we controlled the current externally. We monitored the voltage across the laser diode and the output current directly. The driver outputted current in a 1:2 ratio with the external modulation voltage that we provided and the output current monitor voltage was in a 1:1 ratio with the actual supplied current. The driver was mounted with thermally conducting adhesive to a heat sink and was electrically isolated from the electronics housing. An additional cooling fan was mounted overtop to further cool the driver. The TEC was separately controlled via a Wavelength LDC-6000 laser diode driver and temperature controller. The laser driver circuitry was not utilized in favor of the low noise MPL-2500 driver. The TEC and laser driver were both supplied with a 12 V floating power supply. The laser temperature was monitored via a voltage reading across the 10 kω thermistor. The calibration plot for this thermistor is shown in Fig The quoted thermal stability of this driver is <0.08 C in the short term, though we have realized considerably better stability in the lab because our thermistor uses only a 10 µa reference current for high sensitivity Alignment procedures The alignment of the optics in the external cavity is essential to seeing a well coupled laser that tunes nicely. Not including the optics needed for analysis of the laser, there are seven points of alignment in the cavity. A secondary aim of the cavity design was to make the alignment of optical components relatively fast. The cavity is modular, so components can be swapped in and out without dramatically affecting the alignment. The entire cavity can be reconstructed in 2-3 hours. Currently, the most difficult alignment in the cavity by far is the collimating optics. It is for 37

48 Figure 3.10: Apparatus used to align the major cavity components to the pivot point. this reason that they are placed on a common mount, so that the relative position and tilt do not change over time. Since the first collimating lens needs to be of a small focal length in order to capture the fast diverging light, this lens needs to have a large numerical aperture (NA). This is simultaneously the source of the alignment issues and a guide to quick and guaranteed alignment. A very slight transverse misalignment of the aspheric lens is noticeable as a distortion or diffraction pattern in the image several meters from the box as the laser divergence angle closely matches the large NA of the aspheric lens. Longitudinal misalignments are easily spotted in the spectrometer data as multimode structure if an AR coated laser is used 3. If the laser is not allowed to warm up (1-2 hours), the collimation can be off in this way. The cylindrical lens is more forgiving, but this alignment cushion can mean misalignments go unnoticed during collimation. Since the AR coating is designed for near normal incidence, this can show up in the laser as characteristic mode hops due to the increased back reflections, which reduces the continuous tuning range. The current mount does not lend itself to fine tilt alignment of the cylindrical lens, so we have tilted the cylindrical lens forward enough to ensure no light is reflected back into the cavity. The three cavity components are also a critical alignment due to the sensitivity of the pivot point. We have developed a procedure that makes a first alignment very accurate, and reduces the degrees of freedom essentially to one. We used a laser plumb bob and a small focal length cylindrical lens, with an iris for stabilizing the plumb bob 4, to project a long straight line that we used to align the cavity components to the pivot. The apparatus is shown in Fig. 3.10, and an image of the alignment of each of the components is shown in Fig Fig In each case, the alignment laser was made to go through the pivot point. The grating was the 3 With an uncoated laser, multimode structure is generally present anyway. Misalignments manifest themselves with a lower than average coupling efficiency. 4 Certainly not a standard use of an iris. 38

49 Figure 3.11: Image of grating alignment. Figure 3.12: Image of feedback mirror alignment. 39

50 Figure 3.13: Image of laser alignment. easiest of the cavity elements to align. The edge of the grating arm was made to line up with the pivot point to within ( 13 µm). We lined the laser plumb bob up to this edge, as shown in Fig. 3.11, and then aligned the shadow of the grating surface to the edge as well. By necessity of the design, the line from feedback mirror to the pivot point had to be put on the back side of the movable arm. Although there was no edge available to directly align the mirror, the front and back edge of the arm were parallel to this line. We used the front edge to first align the cylindrical lens so that the projected line was parallel, then locked the lens in azimuth and moved it straight back to bring it into line with the pivot point. The front surface of the mirror was then aligned as with the grating. This is shown in Fig A quick improvement would be cutting a small groove parallel to the arm edge that goes through the pivot point so alignment of the feedback mirror is easier. The laser itself was perhaps the hardest to align accurately in this scheme. The problem was that there was no fiducial with which to align the laser to. Since the mount holding the laser was made parallel to the dimensions of the baseplate, we adjusted the alignment laser until it was going through the pivot, parallel to the back edge of the baseplate. Because the ECDL reflects off the back facet of the laser chip, this is what needed to be lined up with the pivot. This was a problem because the front facet was the only side of the laser visible to the alignment beam. Once the front facet was reasonably aligned to the pivot, we moved the laser forward roughly 1 mm to complete the alignment of the back facet. This alignment is shown in Fig Here, the back edge of the grating arm should be made parallel to the pivot plane to make this alignment easier. We are most confident in the alignment of the grating, followed by the feedback mirror and the laser using this coarse alignment scheme. Although the initial laser alignment was admittedly less precise than the grating or mirror, it could be corrected. Recalling the discussion of 2.4, if the grating is assumed to be aligned to the pivot point, the synchronous tuning condition can be met if 40

51 the mirror and laser are displaced from the pivot in equal magnitudes but opposite directions. Since the grating could be very accurately aligned in our cavity, offsets in the mirror could be compensated for by adjusting the laser mount. A similar procedure has also been applied to a Littman-Metcalf dye laser, though the feedback mirror in that system did not rigidly hold its alignment during tuning [89]. Having the mirror and grating locked in position during tuning reduced the fine alignment procedure to one dimension by only having to adjust the laser forward or backward until an optimum point was found. In principle, the Fabry-Perot output can be used to find this optimum point. If not properly aligned, the cavity mode structure will be multimode [89, 90] with a secondary mode being present exactly 1 cavity FSR away. If multiple modes are already present, due to poor beam quality as in our case, the continuous single-mode tuning range of the laser can be used to find this optimum point. If an even finer adjustment is desired, the grating can be very finely adjusted after the optimum point is found. The final issue is the vertical alignment of the grating and mirror. We vertically adjusted the grating until its feedback lined up vertically with the incoming beam. The movable arm was tuned so that the feedback returned from the mirror went through the right side of the cylindrical lens. The mirror was adjusted until the feedback again lined up with the incident laser. Viewing the laser image outside the cavity also helped with aligning the coupled laser to the uncoupled, free-running laser. This was easier to do with an AR coated laser, since the internal chip modes were suppressed more than in the uncoated BAL. The contrast between the coupled and uncoupled laser was more noticeable in the output beam. The feedback mirror was adjusted until the coupled laser overlapped the uncoupled, free-running laser output at a distance of 3.5 m. The entire procedure is relatively quick, and is a primary feature of the design. Additional details are provided in Appendix C. 3.2 Data analysis The ECDL was analyzed in a number of ways outside the cavity. We will briefly describe each of the analysis techniques and what they revealed about the laser. Fig. B.2 shows an annotated image of the layout of the analysis optics. The primary instruments for analyzing the ECDL were the Fabry-Perot interferometer and a 1.26 m high-resolution spectrometer. The Burleigh RC-110 adjustable scanning Fabry-Perot interferometer was used to resolve the mode structure of the ECDL and make bandwidth and fine tuning measurements. The interferometer could be adjusted to a minimum free spectral range of 1 GHz. We operated the interferometer here and with an FSR of 15 GHz. The mirrors are plane-parallel, making alignment tricky but precise. Three fine adjustment screws were used to align the movable mirror until the interference maxima were separated as much as possible. The scanning piezos were driven by a Burleigh RC-43 ramp generator. The amplitude of the scan was set to a maximum to image several FSRs of the interferometer. A 100 ms scan was suitable to make the ECDL mode structure well defined. The output was first heavily attenuated, then fed to a 500 MHz HP 54522A oscilloscope by a photodiode mounted behind the interferometer. The spectrometer was used to view the beam structure and get a measure of how well coupled the laser was with respect to the free-running modes. The coarse tuning and mode hops could also be measured. The output was coupled to an Ocean Optics P200-5-VIS-NIR multimode fiber with a 200 µm core size prior to entering the Fabry-Perot via a glass slide beamsplitter. The Spex model 1269 spectrometer is a Czerny-Turner design with a 2400 grooves/mm grating providing a 1.23 nm field of view. The instrumental resolution is about nm/pixel, which was insufficient to resolve fine tuning of the laser. Because of the small field of view, calibrating the instrument at any point across the fairly broad coarse tuning range was very difficult. Because of this, we set the wavelength 41

52 scale using a Coherent Inc. WaveMaster wavemeter to get an absolute wavelength with a nm resolution and an accuracy of ±0.005 nm. The spectrometer was driven by a Spex CD2A calibrated control board 5. As an experimental test of the laser, we have also set up a rubidium cell to which another part of the beam is directed by a glass slide beamsplitter. If the laser is narrow enough, tuning across the D1 band should individually excite the hyperfine transitions. The hyperfine lines occupy a band about 6.5 GHz in width with the largest hyperfine line separation equal to 127 MHz. This band of hyperfine lines is barely resolvable on the spectrometer, but can be visually seen in the cell by use of an IR viewer. Mounted opposite the cell is the wavemeter used to monitor the wavelength of the laser. To avoid saturating the hyperfine levels, the intensity of the input beam is dramatically reduced by use of beamsplitters and neutral density filters. This setup is an important diagnostic for the SEOP experiment and measurements are currently underway. The results reported in this work were derived from the experiment described in this chapter. We will first describe the results pertaining to the ECDL in Chapter 4, then mention the beginning stages of the 129 Xe polarization experiment in Chapter 5. band. 5 The spectrometer drive system was modified beyond specs to allow the grating to tune enough to view the Rb D1 42

53 Chapter 4 Results So far, the design of our high power external cavity diode laser and the theory behind it has been discussed. Because the ECDL described in the previous chapter was designed from scratch, it is prudent to describe the basic characteristics of the ECDL, as well as how each component affected the performance of the laser. In the first section, we will describe the fundamental properties of our design that did not vary with the particular configuration of the cavity. Some of these were specific to the diode laser used in the cavity and some are invariant properties of the ECDL. The second section will focus on how the various cavity elements affected the performance of the ECDL. Much of the results garnered over the course of this work were realizations of how each component worked in the cavity as it was being constructed and improved. The final two sections will show performance results from the ECDL. These will include measurements of the bandwidth and fine tunability as well as variable cavity length data, which to our knowledge has not been studied in an ECDL of this type. Suggestions for improvement will be made whenever appropriate. 4.1 ECDL characteristics The two major components of any ECDL are the diode laser and the cavity elements that provide wavelength-selective feedback. Many of the fundamental characteristics of the ECDL are linked to the laser itself. These include the thermal tunability, free-running bandwidth, the extent of gain that can be accessed by the external cavity, and the spatial quality of the output beam. It will be shown that the performance of the ECDL was very sensitive to the spatial quality of the laser s output. Other characteristics, such as the stability of the cavity, are not related to the cavity elements. We examined both short and long term stability and tested the ECDL s tolerance to normal vibrations Thermal tunability The range of wavelengths accessible by a single laser diode in an external cavity can be greatly extended by varying its temperature. For the non-ar coated laser, the thermal tunability is shown in Fig The wavelength dependence is linear and follows the calibration equation, 1 We were unable to obtain similar data for the AR coated laser because of an unfortunate accident that destroyed the semiconductor chip. 43

54 Figure 4.1: Temperature tuning curve for a 2 W Coherent Inc. single-stripe BAL centered near 790 nm. λ = T. (4.1) The temperature T is in degrees Celsius and the wavelength is in nanometers. The wavelengthtemperature coefficient was in error by only 3% from Coherent Inc. spec sheets [69]. Although the laser could be operated at a minimum temperature of -20 C, we did not take precautions to prevent potentially destructive condensation on the front facet of the laser. When combined with the ECDL tuning, both Rb D bands can be accessed by a single laser without having to take these precautions. The maximum temperature for operating our laser is 30 C. Once our laser was temperature stabilized, the thermistor voltage varied on a scale of 0.1 mv over a long period of time. This corresponds to a variation of C and a change in wavelength of nm. The TEC controller has demonstrated this tolerance for long periods of time and helps contribute to the overall stability of the laser as will be discussed Laser gain profile In an uncoupled, free-running condition, our BAL lases in many modes simultaneously as shown in the inset of Fig The spacing of these modes is set by the FSR of the 1 mm long Fabry-Perot cavity formed by the semiconductor chip. The envelope created by these modes was imaged using a 0.27 m Jarrell Ash spectrometer in a low-resolution mode and is also shown in Fig The typical FWHM of this envelope was about 2.5 nm. When reporting FWHM bandwidths of our coupled BALs, we will generally use frequency units. For a sense of scale in future sections, 1 nm is around 500 GHz. 44

55 Figure 4.2: Low-resolution spectrum of the free-running BAL. The FWHM was 2.5 nm. The inset shows a portion of the free-running mode spectrum taken with the 1.26 m high-resolution spectrometer. There is no relationship between the absolute intensities shown in each image. Figure 4.3: Coarse tunable range of our ECDL with strong coupling. 45

56 Figure 4.4: Typical Fabry-Perot spectra of the 30.5 cm ECDL a) with the grating feedback unblocked and b) with the top half of the feedback blocked. Fig. 4.3 shows the coarse tunable range of the BAL coupled to a well-aligned cavity with a length of 23 cm. The extent of the tuning was 12 nm total and was symmetric about the center wavelength. The intensities roughly mimic the envelope shown in Fig. 4.2 showing that we were accessing the full gain of our laser. The localized intensity variations were caused by a changing transverse mode structure within the laser as we tuned the wavelength. In the current implementation, this structure is not being controlled. It was the result of vertical divergence in the laser caused by its non-gaussian nature in that dimension. We will expand on this point in subsequent sections since it was a very important factor in the performance of this ECDL Spectral narrowing We now examine the extent to which our external cavity design narrows the several hundred gigahertz free-running gain profile. The results presented in this section were taken with 30.5 cm and 23 cm ECDL cavity lengths. We will present results with other cavity lengths later in the chapter. When using high power BALs, the concepts of bandwidth and linewidth have to be distinguished. Because of the high-order transverse mode structure and the low finesse of BAL cavities, many longitudinal modes are excited simultaneously in the free-running case. Each lasing mode has a characteristic linewidth that is affected by the traditional broadening mechanisms. This modal linewidth is expected to follow the theory presented in Chapter 2. The combination of many simultaneously lasing modes also leads to an effective bandwidth. This effective bandwidth actually determines how the laser will interact with an absorbing medium. We will make this distinction as we proceed. Fig. 4.4 shows typical Fabry-Perot spectra of our ECDL at a 30.5 cm cavity length. The 1 GHz Fabry-Perot free spectral range is noted in the figure. The typical pattern shows multimode structure. For this cavity, the two modes were separated by 495±10 MHz, characteristic of this cavity length. Fig. 4.4 clearly shows that the multiple ECDL longitudinal modes were caused by high-order transverse structure in the BAL. With an injection current above threshold, the BAL lased in a filamentous pattern along the slow axis, which was dual-lobed in the far-field. These filaments acted as separate lasers when being coupled to the external cavity, and as such could lase in different longitudinal modes. When the top half of the feedback was blocked from returning to the laser chip, one of the modes dropped out. This process of obtaining a single spatial mode in a high power BAL is similar to that described in Ref. [53], although our approach was more ad hoc, and worked best 46

57 Figure 4.5: Fabry-Perot spectra of the ECDL arranged with a 23 cm cavity length showing evidence of a superposition of transverse modes with the BAL operating below threshold. when the BAL was operated near or below threshold. The linewidth shown in Fig. 4.4 is 169 MHz. The average linewidth at this cavity length was found to be 173±6 MHz. It is important to note that the linewidth data presented in this chapter was all taken near or below threshold. The reason for this was that with injection currents greater than threshold, additional transverse modes began to overlap as the FSR of the Fabry-Perot was smaller than the spectral distribution of modes. This increased the linewidth to about 250 MHz. This overlap decreased with lower output powers as the outer parts of the laser chip containing the high order transverse structure turned off. For every cavity length tested, a similar pattern was observed. We also saw evidence that even the linewidth data taken below threshold may still be a superposition of transverse modes as shown in Fig In the figure, there appears to be two overlapping modes. The linewidth shown in the figure resembles our initial measurement of the average linewidth with the ECDL in this configuration. This suggests that even below threshold, the measured linewidths may not be as large as we are currently reporting and further narrowing is possible. We will detail the results of the short cavity length, along with others in It is important to note that Fig. 4.5 was abnormal when compared to the large number of measurements used to pin down the linewidths at each cavity length. The only difference is that this data was taken at the shortest accessible cavity length where the slow-axis divergence of the beam was at a minimum. When coupled with other lines of evidence that we will soon present, this suggests that the slow-axis divergence was the chief reason for multiple mode ECDL output. When this ECDL is brought to bear on an absorbing medium, such as rubidium vapor, it will interact with an effective bandwidth that is a collection of the transverse modes that we resolved using the Fabry-Perot interferometer with a 1GHz FSR. The high-resolution spectrometer can resolve this bandwidth to a precision of ±1 GHz. The measured effective bandwidth of the short cavity ECDL even below threshold was 4 GHz, which seems to support the reasoning given for Fig This result was confirmed in Fig. 4.6 using the Fabry-Perot configured with a 15 GHz FSR, showing that the spectrometer can be a good measure of effective bandwidths. When varying the cavity length of the ECDL, we noticed changes in the individual mode linewidths, but we did not notice a significant 47

58 Figure 4.6: Fabry-Perot spectra of a short cavity ECDL taken with an FSR of 15 GHz. The average bandwidth is noted. difference in the effective bandwidth. We will elaborate on this in Fine tunability Besides the bandwidth, the fine tunability is just as important a characteristic of the ECDL. One of the primary goals of this work, as an extension of Ref. [62], was to improve the tunability of the ECDL without mode hopping. When we discuss the affects of the cavity optics and their alignments on the ECDL, we will show how we extended the tunable range to its present value of 3.5±1 GHz. In this section we describe the nature of the mode hops that limit the tunability and discuss general tuning characteristics. We measured the fine tunable range by first moving the feedback mirror to obtain an arbitrary wavelength, then stepping the actuator in increments of 1-2 µm to slowly tune the ECDL. We monitored the progress of tuning with the Fabry-Perot until a mode hop occurred. The tunable range could be read by tracking the pattern on the oscilloscope. The mode hops were seen as a gradual motion of the Fabry-Perot signal without tuning the ECDL, followed by a sudden intensity fluctuation and locking into a new mode. Fig. 4.7 is representative of a normal tuning data run. The most obvious feature is the variability in the tuning range as the wavelength is tuned. This is a puzzling characteristic of the ECDL. Regardless of where the feedback mirror was initially moved to, the tunable range prior to the first mode hop was always the largest 2. Subsequent tuning of the ECDL yielded smaller tuning ranges each time until it reached an equilibrium value, usually around 1 GHz. Unless there was a large coarse tuning of the laser to a new wavelength, the original tunability was never recovered. There was however an expected correlation between the magnitude 2 This was true for all but a few exceptional cases. Prior to a realignment of the cylindrical collimating lens, the tunable range was relatively constant, albeit small. This was ultimately attributed to reflections from the cylindrical lens and has not been seen since it was realigned. 48

59 Normalized Intensity Wavelength (nm) Figure 4.7: A composite of high-resolution snapshots of the ECDL after each mode hop. The variable nature was characteristic of our cavity. of the hop and the distance covered by the actuator prior to the hop. This relationship is shown for the data in Fig. 4.7, and other data taken the same day in Fig This shows the linear nature of the tuning arm. We also note that although the magnitude of the mode hop generally increases with the fine tunable range, as shown in Fig. 4.9, the relationship is not precisely linear, as it was with the actuator tuning. This discrepancy is curious since the laser wavelength should tune in step with the actuator. This may be related to the nature of these mode hops. If the ECDL was moved to a new wavelength, the fine tunability repeated the patterns shown in Figs We have seen evidence on several occasions that these hops were not purely longitudinal in nature. In such hops, the interferometer signal clearly jumped into a new mode, but there was no corresponding jump in wavelength. The reason is that the mode hops that defined our tunable range were accompanied each time by a transverse mode hop. This could be seen directly by looking at the secondary diffraction of the grating feedback. The key point is that the transverse mode hops that were always seen were not always accompanied by the longitudinal mode hops that changed the ECDL wavelength. This inconsistency is evidence that the limiting factor in fine tunability was the spatial quality of the beam. The cavity was well designed to maintain the longitudinal mode structure. However, as the laser was tuned, the vertical angle of the return beam was changed slightly each time. This transverse motion, we believe, eventually destabilized the laser in much the same way the longitudinal mode structure is destabilized if the cavity optics are misaligned from the pivot point. It is not the variation in intensity 3, but the nonuniform variation in phase that likely triggers these hops. The small perturbations caused by this variation tend to destabilize the transverse mode structure in the BAL [73, 91]. Another key point is that the fine tunability of the ECDL was not observed to be a function of cavity length. The average tunability quoted in this section included measurements taken in a variety of cavity configurations. This may attest to one of two things. For one, the FSR of the ECDL decreases with increasing cavity length, which increases the difficulty of satisfying the tolerance of 3 Changing the injection current over its entire range does not induce mode hops, even though the slow-axis beam quality changes dramatically (c.f ). 49

60 Figure 4.8: Magnitude of mode hops in nm versus distance covered by actuator in mm. Figure 4.9: Data from two separate runs showing the relationship between the magnitude of the mode hop (in nm) and the fine tunable range (in GHz). In the general case, the tunable range reaches a stable value after tuning across several hops. 50

61 the pivot alignment. If our alignment strategy was accurate to within the accessible tolerances of the ECDL, then the tunable range should not be a function of the cavity length. The other possibility is that the transverse mode hopping was the factor limiting tunability. If the latter is true, then carefully controlling the slow-axis divergence of the laser could result in larger tunable ranges. We have evidence that this may be the case. On two occasions we noted tuning ranges greater than 5 GHz, and on one occasion a tuning range of GHz. These were substantially larger than the average, and came with no special adjustments of the cavity. Also, the predicted tolerance of our alignment with an average tunability of 3.5 GHz is only about 1 mm. This seems large compared to the precision alignment afforded by our cavity design. Using a laser with higher spatial quality, such as a tapered BAL or even a low power, single-mode diode laser, would clear up this issue. Although the fine tunability is not a major benefit for SEOP experiments, aside from initial tuning to the absorption band, improving this aspect of the ECDL leads to greater stability since the tuning ranges are much larger than most transient effects and even slow instabilities such as thermal changes in the laser and environment ECDL stability This subsection summarizes the properties of the ECDL that do not change with changes in optical elements or laser (unless the TEC and controller are switched to ones with different noise characteristics than already described). For best performance in a SEOP experiment, the ECDL needs to provide a stable output for many hours. Conditions disrupting this stability arise chiefly from thermal or electrical noise in the laser itself, and from mechanical vibrations and environmental disturbances. In our case, the latter was the dominant source of short term instability while the former affected long term operation. The laser was carefully controlled with low noise drivers (c.f ) and represents the limit of our passive stabilization measures. The major source of short term fluctuations was easily mitigated by operating the ECDL on a floating optical bench. This eliminated a strong 60 Hz electromechanical vibration detected with a piezoelectric wafer. The only remaining source of vibrational noise was from the scanning Fabry- Perot interferometer mounted on the same optical bench. In addition to its rigid housing, we further isolated it from the bench surface by using styrofoam and aluminum as a base. If present as a noise source, we should have seen a 10 Hz signal and we did not. The triple layer construction of the ECDL base has already been described in 3.1. This alone drastically reduced ambient mechanical noise. Even stronger impulses (taps on the bench or falling tools), though visible to our piezoelectric sensor, often did not disturb the laser. Fig illustrates this mechanical isolation. The figure directly shows the vibration damping of the cavity as a function of impulse amplitude and distance from the impulse source (i.e. the actuator). In the course of fine tuning, where the actuator was only moved one or two microns per step, the vibration was not detectable, even near the actuator. The 1.0 mm and 0.1 mm stepsizes are impractical for fine tuning, but illustrate the cavity s ability to damp strong vibrations before they reach the nearest cavity optics. These runs were carried out with a rubber boot placed on the actuator contact tab to separate it from the actuator leadscrew. Without this, the ECDL had a tendency to hop to an adjacent longitudinal mode. The largest remaining source of noise was from environmental fluctuations. The most significant of these were air currents that changed the index of refraction along the beam. This caused the laser to hop between adjacent longitudinal modes erratically. Addition of a closed, light-tight box dramatically reduced this erratic behavior. This box was not sealed. Openings were made to output the laser beam and admit communication and power cables. Sealing the cavity can eliminate noise caused by pressure variations [51], but this was not seen as a significant source of instability in our 51

62 Figure 4.10: Impulse from movable arm actuator. Left-right: Amplitude of impulse with varying distance from the actuator contact tab. The sensor was placed a) on the aluminum contact tab, b) on the copper arm opposite the contact tab (almost 3 ) and c) on the feedback mirror mount. The stepsize was constant at 1.0 mm. Top-bottom: Amplitude of impulse with varying actuator stepsize, measured on the actuator contact tab. From the top, a) a 1.0 mm, b) a 0.1 mm and c) a 1 µm stepsize. 52

63 1.15 Intensity (arb. units) Time (s) Figure 4.11: Fabry-Perot spectra taken three hours apart to demonstrate the stability of the ECDL. Note the change in mode structure reflecting a change in the transverse profile. experiment. All of these noise sources contributed to the short and long term stability of the ECDL. In the short term, the stability of the ECDL was seen to depend largely on the strength of the coupling. If mode competition was present (resulting either from a low coupling efficiency or poor spatial quality in the vertical direction), the laser was sometimes unstable. For a sufficiently coupled laser, the short term stability was largely dependent on electrical noise in the laser, and from external vibrations and residual air currents. These combined to yield fluctuations of the modal linewidth within 1 FWHM visible from the Fabry-Perot at an FSR of 1 GHz. In the long term, the dominant source of instability was self-tuning of the laser due to slow temperature drift and instabilities in the transverse mode structure of the BAL. However, this was not a significant effect as shown in Figs Fig and Fig. 4.12, respectively showing the interference signals and high-resolution spectra with the ECDL outputting 0.25 W, were taken three hours apart. Neither measure showed a significant difference. The spectra were separated by 1.4 GHz, which is essentially the resolution limit of our spectrometer. The Fabry-Perot signal seems to suggest that this motion may just be a shifting of the transverse mode structure. On the spectrometer, this may be seen as a shift in the wavelength as another part of the chip, lasing in a different transverse and longitudinal mode, becomes more dominant. Fig shows spectrometer data taken over a 12-hour period with a full output power near 1 W. The laser needed about 2 hours to come to an equilibrium temperature when at full power. Once it did equilibrate, the wavelength was stable for several hours, only fluctuating at 780 MHz. The small hop that is visible after several hours was about 4.7 GHz. This was likely a redistribution of intensity in the vertical transverse structure and not an actual mode hop as this hop was not confirmed by either the wavemeter or Fabry-Perot interferometer. Also, even with this hop the ECDL stayed within the bandwidth of the laser at that time, which was measured to be between 6 and 7 GHz throughout the 12-hour span. Thus, the ECDL shows exceptional long term stability once it reaches equilibrium. This stabilization was completely passive; no active feedback was used at any point because it just was not necessary. If this laser were adapted to laser cooling experiments, however, further testing would be warranted and some additional stabilization features may need to 53

64 Intensity (arb. units) Wavelength (nm) Figure 4.12: Spectra of the ECDL taken three hours apart. The wavelengths were separated by the resolution limit of the spectrometer Wavelength (nm) MHz 4.7GHz Elapsed time (hrs) Figure 4.13: Spectra of ECDL taken over a 12-hour period with an output power near 1 W. 54

65 be added. In the course of analyzing the stability of the laser, we did notice a weak point in the design that should be addressed in any future redesign. Copper was used for both arms in part to thermally isolate the cavity optics. Because the laser and TEC module needed to be shifted along the laser-pivot plane with changes in cavity length, we used commercially ubiquitous translation stages. If the lab was near room temperature, where the laser was operated most of the time, the TEC could not dump the heat from the laser to the environment quick enough, and the anodized aluminum stage acted as an insulator. In several hours the stage and the region surrounding the TEC would heat up. This has the potential of destabilizing the laser, and in fact this was seen on a couple occasions. Keeping the lab cool reduced this effect, but this issue may be significant if the laser needs to be cooled to tune to the Rb D2 band for example. 4.2 ECDL dynamics In the previous section, we explained how the performance of our ECDL was strongly affected by the poor spatial beam quality of BALs. In this section we examine the sensitivity of the ECDL to alignment of the cavity elements, and to stray reflections. Because our ECDL is designed to be modular, we also explain the effects of changing certain cavity elements External elements Besides the major cavity optics, there were external elements that had an impact on the performance. The most important was the Faraday effect optical isolator that blocked external reflections from reaching inside the cavity. Beyond our cavity, the major source of disruptive back-reflections was from the Fabry-Perot interferometer set up to analyze the ECDL bandwidth and fine tunability. By nature of its critical alignment, light from the Fabry-Perot cavity was sent directly back along the incident beam. Because the cavity lengths of the ECDL and the Fabry-Perot are comparable, significant interference is possible. We did not notice severe interference from the Fabry-Perot, but back-reflections were present as structure in the spectra. Fig shows characteristic spectra before and after inserting the isolator. The fact that there was not a single peak was not due to the isolator; its presence will be discussed later. Without the isolator (c.f. Fig. 4.14a), there generally was additional structure present in the spectra as other nearby longitudinal modes could be excited by the Fabry-Perot feedback. This feedback was at least comparable to that from the external cavity itself and maybe more so because of the high reflectivity of the Fabry-Perot mirrors. This structure did not reappear after the isolator was placed (c.f. Fig. 4.14b). 55

66 Figure 4.14: Characteristic spectra from ECDL a) before and b) after insertion of a Faraday isolator. 56

67 Figure 4.15: Fabry-Perot spectra characteristic of data taken with a) a 1 grating, and b) a 2 grating Grating and feedback mirror The diffraction grating is the key element in the external cavity. We used two different gratings as described in The most important difference between the two was the size. The newest grating had the same groove density, but was twice as long as the original grating. For a 3 mm beam waist, at least a 2 grating was needed at the 85 angle of incidence to capture the full beam. The 1 grating only coupled about half of the incident beam. This difference is illustrated in the characteristic Fabry-Perot spectra taken with each grating, shown in Fig The effect of the larger grating in our cavity was to better resolve the mode structure. If the entire beam was not coupled to the grating, the uncoupled free half, with a continuum of laser modes, acted as a DC offset that is clearly visible in Fig The longer grating improved the coupling of the external cavity laser over the free-running modes. This had important qualitative effects on the rest of the experiment. Because the transverse structure of the BAL was now being completely determined by the external feedback, it began to influence the fine tunability of the ECDL as described in the previous section. The feedback mirror did not have many notable effects beyond obvious alignment issues. Of these, the vertical tilt of the mirror was the most interesting. The lost light from secondary zeroth order diffraction was an important visual image of the transverse structure of the BAL and could be 57

68 Figure 4.16: Variation in effective bandwidth as the feedback is directed to a) the top, b) middle, and c) the bottom of the BAL. The injection current was A. used to accurately align the feedback mirror. The BAL could be selectively coupled by adjusting the vertical tilt of the mirror [61, 92]. The laser scanned the entire face of the BAL until the full chip lased, indicating a perfectly aligned feedback mirror. Perfect alignment brings a well coupled, high intensity beam. However, it is also generally multimode, with several filaments lasing simultaneously. If the feedback was directed to the top or bottom of the BAL by tilting the vertical mirror, the BAL could be forced into lasing with a low-order transverse structure. The effect on the bandwidth was fairly dramatic as can be seen in Fig 4.16, taken at near full output of our BAL. We saw similar behavior near threshold, but not quite as dramatic as the low power BAL tended to emit with loworder transverse structure anyway. This is one of multiple lines of evidence presented in this chapter that support controlling the vertical divergence, thereby forcing the BAL into a low-order or even single-mode emission Collimating lenses The two lenses used in collimating the laser affected the ECDL performance in very different ways. The aspheric lens collimating the fast axis, as already noted, was incredibly sensitive to misalignment as the fast diverging light nearly filled its numerical aperture. Even slight misalignments in either direction showed up as knife-edge diffraction at a large distance from the cavity. Relative tilt showed up as distortions in the beam shape. In order to get a stable ECDL with reasonable beam quality, the aspheric lens had to be perfectly aligned, thus it did not have the ability to affect the ECDL greatly. In contrast, the cylindrical lens, collimating the slow axis, had very noticeable effects on the ECDL. Fig shows ECDL spectra with the cylindrical lens tilted about a vertical axis, and set perpendicular to the BAL. The tilted lens distorted the beam enough so that additional modes were allowed to lase due to the imperfect coupling of the dominant external cavity mode. Similar effects could be seen for tilting the lens about its horizontal axis, though tilting about this axis had a lesser effect for an equal angle due to the asymmetric curvature of the lens. The most critical alignment in the entire cavity proved to be the axial alignment of the cylindrical lens. A tilt about this axis allowed focusing along the fast and slow axis of the BAL, which distorted the beam and dramatically reduced the coupling efficiency. Because the collimating optics mount was separate from the laser mount, changing the cavity length proved to be more difficult a task because of this critical alignment. Affixing the collimating optics to a mount on the laser translation stage should reduce a several hour realignment to under an hour, the time it takes to align the grating and feedback mirror. Even though the cylindrical lens is AR coated, it is very sensitive to alignment normal to the 58

69 Figure 4.17: ECDL spectra with the cylindrical lens a) tilted about its vertical axis and b) perpendicular to the incident beam. 59

70 beam. We had no means of precisely controlling this alignment. When we were using the AR coated BAL (see next subsection), the effect of this critical alignment became apparent. Because the free-running component was almost completely suppressed, the BAL was now enslaved by external reflections. Unlike the aspheric lens, which has strong curvature in the plane of the laser, the front face of the cylindrical lens is planar. If not mounted precisely, the AR-coating had no effect and normal Fresnel reflection was sent directly back to the laser. Until the AR coated laser was installed, we were operating with no tilt in the cylindrical lens and were consistently not seeing fine tuning much greater than 1 GHz. Once installed, the beam appeared filamentous a good distance from the cavity and not so when the lens was tilted. We tilted the lens forward for the reasons described above. After this adjustment, we noticed an increase in fine tunability to between 2-3 GHz on average. The tradeoff in tilting the lens to improve tunability was that the laser was not collimated as well vertically. For larger angles, this starts to affect the coupling efficiency. This is another line of evidence suggesting the importance of the vertical beam divergence in ECDL performance The laser We were fortunate to have both an anti-reflection coated and an uncoated BAL on hand to test in the external cavity. The difference between these different types of high power laser is not as well distributed in the literature as it is for low power laser diodes (c.f. Chapter 1). The reason being that the processes for applying the AR coating are not the same since high power BALs are attached directly to a thermoelectrically cooled heatsink and operated in open air. The process of AR coating BALs is usually handled within the lab group using them, and not commercially. Fig shows characteristic spectra of each type of laser. The ECDL was tuned to be inside the central gain of the BAL. The difference between the two is clear. In the uncoated laser, the free-running modes were not well suppressed. At times we noticed strong coupling, but it was not consistent. The figure shows the structure when the ECDL was tuned across the strongest of the freerunning modes. If tuned off resonance, the free-running modes were still present, though attenuated, for the uncoated laser. This was not the case for the AR coated laser. The free-running modes were strongly suppressed, even when significantly detuned from resonance. The additional structure seen in the AR coated laser spectra was attributed to transverse structure in the BAL. This structure was visible regardless of the type of laser used. This free-running suppression had notable effects on the performance of the ECDL. The most obvious was that the coupling efficiency was dramatically improved. This was most noticeable far off-resonance and was clear by visual inspection of the laser. For BALs centered far from the Rb D1 band, this improved off-resonance coupling efficiency is important. This improvement made the overall cavity less sensitive to the alignments discussed above. What may be most important though is what was not different when using either laser. The key parameters of laser bandwidth and fine tunability were not noticeably different. The Fabry-Perot signals were more stable with the AR coated laser, but had similar bandwidths. From previous discussion, this means that the transverse mode structure was still present. The fact that the fine tunability was also independent of laser type suggests that the limits of bandwidth and single-mode tunability were being set in our implementation by the vertical collimation, and not by the cavity itself. This is further supported by the periodic observation of much larger tunability and much narrower bandwidths reported in an earlier section. It should be noted that the largest tuning range reported, GHz without a mode hop, was achieved with the uncoated BAL. 60

71 Figure 4.18: Characteristic spectra for a) a non-ar coated laser and b) an AR coated laser both tuned to the center of their respective gain profiles. 61

72 4.2.5 Laser position When laying out the theory behind the Littman-Metcalf cavity, a nice feature of its design is the ability of the laser to compensate for misalignment of the feedback mirror. Since the grating could be precisely aligned in our cavity, we could take full advantage of this feature. When moving the laser perpendicular to its pivot plane, the best way to align it was to watch the tunability. This is a slow alignment process, but only has to be done once, as long as the laser mount is not changed. Recall that changing the alignment of the cylindrical lens improved the average fine tunability to between 2-3 GHz. After adjusting the laser position, the fine tunability increased to between 3.5 and 4 GHz on average. Because the collimating optics and laser were not on a common mount, this may not be the most optimum location for the laser. At each step, the collimating lens system would be brought back into alignment. Even though this was simple to do because of the sensitivity of the aspheric lens to position, a single common mount would ensure no relative change between the collimating optics and laser and thus eliminate this as a source of error in determining the optimum alignment of the BAL. The improvements to the ECDL discussed so far were carried out with the AR coated laser because it was easier to see the differences in the output beam when making these changes. These characteristics were retained when switching back to the uncoated BAL Laser current It is well known that changing the current in a laser will tune its wavelength (for our BAL this amounts to 0.02 nm over its full operating range). This is not as dramatic as temperature tuning, but is still present. We focused on measuring the spectral bandwidth, rather than the wavelength, as a function of current. The additional structure apparent in Fig at higher current shows that neighboring longitudinal modes were being excited. This source of broadening was likely related to the increasing slow-axis divergence of the beam as the current was increased. This divergence is characterized by the M 2 quality factor (c.f. 2.3). Its relationship to injection current for our ECDL is shown in Fig Superimposed on this data are typical results of the effective bandwidth of the ECDL as a function of current. There is clearly a correlation in the data. As the injection current was increased, higher-order transverse structure was excited along the wide dimension of the gain-guided BAL due to the low spatial confinement. This increased the slow-axis divergence as the beam became less gaussian. As the divergent feedback spread across the chip with increasing intensity, different parts of the chip did not necessarily lase in a common mode because of small pathlength differences in the feedback across the chip. Thus, the effective bandwidth was broadened as the BAL was powered up and the beam quality degraded. Controlling this broadening is not easy because of this circular relationship. If the feedback were structured to selectively excite only loworder transverse modes, the divergence, and subsequently the bandwidth, would improve [93]. Plots of M 2 versus injection current have been taken with tapered BALs. The dependence on increasing injection current is the opposite as that shown in Fig. 4.20, with a constant M 2 for low injection currents, rising sharply for higher currents as the BAL s preference for high-order transverse modes prevails. Successful control of the slow-axis divergence in our ECDL should show a similar trend to that of tapered BALs. 62

73 Figure 4.19: ECDL spectral broadening with the injection current a) just above threshold at 0.50 A and b) at 1.15 A. 63

74 M Injection current (A) Effective bandwidth (GHz) Figure 4.20: Slow-axis beam quality (black circles) and typical ECDL bandwidth versus injection current (red triangles). The bandwidth data was taken with the Fabry-Perot spectrometer at an FSR of 15 GHz. Outliers indicate transitions to higher order transverse structure, and tended to occur at lower currents Variable cavity length One of the primary features of this ECDL is that its cavity length may be adjusted relatively easily. We have already seen however, that this does not have much of an affect on the effective bandwidth and fine tunability of the ECDL. We have shown that, because of slow-axis beam divergence, shorter cavity lengths tended to exhibit stronger coupling and larger coarse tuning ranges. For the application of SEOP, which is sensitive to the effective ECDL bandwidth rather than the linewidths of the individual laser modes, this suggests that a shorter cavity length should be used. The variability of the cavity length is still potentially useful, however. As stated earlier, high power ECDLs could be used in optical trapping experiments that would use the variable cavity length as an optimization mechanism for improving the efficiency of the process. We tested four different cavity lengths in the course of this experiment. Data from short and middle cavity lengths (23 cm and 30.5 cm respectively) have already been introduced. We also tested the ECDL in a long (50 cm) and mid-long (43 cm) configuration. The cavity lengths were gleaned from the average mode spacing and are precise to ±0.5 cm. We focused on determining the functional dependence of the modal linewidth and effective bandwidth on the ECDL cavity length. There is no literature of which we are aware that characterizes external cavity lasers in this way at different cavity lengths. To do this, we averaged linewidths from multiple datasets at each cavity length. The current results are shown in Fig The data trends with the inverse square root of the cavity length. This result is surprising in light of the theoretical model presented by Littman and Metcalf [44]. Recall that they modelled the ECDL as a spectrometer with appropriately defined entrance and exit slits (c.f ). This model has been generally accepted even though it was designed for dye lasers and not multimode semiconductor lasers. Despite the error in the datapoints, the linewidths clearly do not follow a 1/L dependence as is expected by the theory for L less than the Rayleigh length of the laser (9 m in our case, making this limit well satisfied). 64

75 Modal linewidth (MHz) Cavity length (m) Figure 4.21: Modal linewidth as a function of cavity length fit with an inverse square root power law. These results are preliminary, and need to be confirmed. When we first took measurements at the short cavity length, we noticed a variability in the linewidth over a single scan of the Fabry-Perot (100 ms) as shown in Fig The linewidth varied between MHz. Variability in the linewidths on this scale was not seen with the other cavity lengths (evident from the error bars in Fig. 4.21). This prompted us to retake the short cavity linewidth data again. Great care was taken to precisely align the cavity optics. The first time data was taken at the short cavity length was also the first time we attempted to change the cavity length. The second time at 23 cm was after all the other cavity lengths were tested, so the alignment process was improved. Fig shows that the actual linewidth was clearly not 202 MHz. The variability in the linewidth was still present though. The >200 MHz lines were the result of superpositioning of transverse modes. Because of the smaller slow-axis divergence at this short cavity length, the extra mode structure was not stable, leading to the short timescale variability. We believe that the BAL was lasing nearer to a single transverse mode than at the other cavity lengths. The average dominant linewidth was measured to be 124±12 MHz the second time around. The large standard deviation reflects the variability. This result is smaller than the linewidth measured at the longest cavity length and suggests the other measured linewidths may also be superpositioned transverse modes. This linewidth resembles results obtained from the predecessor to this experiment, though their result of 120 MHz was for a cavity length of 44 cm [62]. This also suggests that further narrowing is possible. These measurements need to be retaken when the slow-axis beam divergence has been corrected to confirm the dependence shown in Fig Although there was a clear dependence of modal linewidth on cavity length, the same was not true for the effective bandwidth. The averages for three of the cavities are shown, together with the average modal linewidths for each cavity, in Table 4.1. The standard deviations show that the effective bandwidths are statistically equal. The larger standard deviation of the long cavity result and the smaller value of the short cavity bandwidth support our general conclusion that the effective bandwidth is determined more by spatial beam quality and collimation than by the resolving power of the grating. This confirms recent work done by Mandre et al. [73]. In their work, the spatial and temporal profile of the front facet of their BAL was monitored. They showed a very complicated free- 65

76 Figure 4.22: Fabry-Perot data from the first run at a 23 cm cavity length. Figure 4.23: Fabry-Perot data from the second run at a 23 cm cavity length. 66

77 Cavity size Modal linewidth Effective bandwidth Short cavity (23 cm) 206±18 MHz 6±1 GHz Middle cavity (30.5 cm) 173±6 MHz 7±1 GHz Mid-long cavity (43 cm) 151±7 MHz N/A Long cavity (50 cm) 134±7 MHz 6±2 GHz Table 4.1: Summary of results at various cavity lengths. An insufficient number of measurements were made of the mid-long cavity s effective bandwidth to give a good statistical average. running profile consisting of multiple longitudinal modes within which several high-order transverse modes were supported. Using only a high-frequency spatial filter they were able to significantly reduce the mode structure. They concluded that the effective bandwidth was directly related to how well the BAL internal emission characteristics were controlled, and not by external dispersion. This result has interesting consequences. Standard dispersion equations suggest operating the grating with the highest incident angle and minimum grating period possible. Higher incident angles mean larger and more expensive gratings are needed to couple all the light. This work suggests that those considerations are invalid when using high power BALs in the external cavity unless the BAL can be operated in a single transverse mode. Any model of cavities of this type can only be considered valid for the modal linewidths, as the effective bandwidths were not influenced by the external cavity. We have highlighted unexpected behavior when using BALs in an external variable length cavity. The results detailed in the previous two sections deserve further experimentation as both a confirmation and exploration of the physics of externally coupled BALs. No other group to our knowledge has carried out such investigations with a variable external cavity length. The general performance of our laser compares favorably to work already done in this area. The average effective bandwidth of our ECDL at full output power was 8±1 GHz. At nearly 1 W of output power, this is over a factor of two better than comparable ECDLs used for SEOP experiments. Some groups have reported comparable bandwidths, while some have reported higher tunable ranges (c.f. 1.2). In most cases, the same groups did not report both and those that did were spatially filtering the output to achieve high beam quality, thus dumping a lot of the total output power. Our ECDL strikes a unique balance by combining high output power, WTNB operation with short and long term stability, and the ability to access multiple spectral features with a single ECDL mount. 67

78 Chapter 5 Conclusions and Future Work In the course of this work, we have designed and thoroughly tested a high power, variable cavity length external cavity diode laser that is widely tunable and narrow-bandwidth. We designed the ECDL to be easily aligned, modular, and robust in its applications. The analysis of the laser showed that the ECDL was very stable, both in the short and long term. The detailed and refined alignment procedures developed have led to relatively quick and precise adjustment of the cavity. The largest coarse tuning range obtained was 12 nm, which is larger than most ECDLs using similar BALs. This range depends on the alignment and the beam quality. This wide tunable range allows a single laser to access both Rb D bands with a small amount of temperature tuning. With the proper laser, the cavity is also designed to access the K D1 band. We have also improved the fine tunability to 3.5±1 GHz. This is important for stability against mode competition and also for tuning very closely spaced hyperfine transitions. We examined the dynamics of the ECDL under every conceivable change. The most important cavity elements were shown to be the collimating optics, and specifically the cylindrical lens, whose alignment greatly influenced the coupling efficiency and fine tunability of the ECDL. Two lasers were used in this experiment, one with a front facet anti-reflection coating and one without. A surprising result was that the tunable ranges, both fine and coarse, seemed to be unaffected by which laser was used. Indeed the maximum ranges in both categories were achieved with the uncoated laser. The primary advantage of the AR coated laser was the suppression of side modes resulting from the BAL itself. The beam was more spectrally pure in that the wavelength components were determined more by the external cavity than by the BAL. Although there was a drop in output power for an equivalent injection current, the simultaneous improvement in monochromaticity offsets this. The effective bandwidth of our laser running at full power was an average of 8 GHz. This result is better per Watt of output power than other lasers designed for SEOP. The narrow bandwidth complements the large coarse tuning range and fine tunability of our ECDL. Neither the effective bandwidth nor the fine tunability were a function of the cavity length. These results did not agree with either model presented in This suggests that those models are incomplete for BALs. We were not even able to verify the inverse dependence on cavity length that is characteristic of the Littman-Metcalf model. Judging from the complex emission of BALs, this failure may not be surprising. The theory behind the Littman-Metcalf cavity was designed for dye lasers, which supply a true broadband profile to the grating. Free-running BALs are really a collection of several comparatively narrowband longitudinal modes spaced out in wavelength according to the dimensions of the chip. The interaction of a collection of laser modes on the grating may be more complex. This may also be why the latter model fails. In our results, the effective bandwidth does not satisfy the upper limit of 1.4 GHz. Their model does not appear to take into account the simultaneous existence 68

79 of several laser modes (each of which satisfies the limit) and does not fit other experiments with BALs. We are in the process of rigorously deriving the single-pass dispersion from diffraction theory in an attempt to explain our results and the inconsistencies with the other models. The results of this experiment suggest two major strategies for improvement. The first is a redesign of the collimating optics mount. Currently, this mount is separate from the two-axis translation stage holding the BAL. The collimating optics are on a common mount, which is beneficial in maintaining the relative separation, but when the cavity length is changed, the collimating optics have to be independently realigned. Constructing a mount that can be attached to the same translation system as the BAL would mean the entire system could be aligned once (for each laser used). This would cut the alignment time in changing cavity lengths from several hours to just under one hour. In addition to making the ECDL user-friendly, this improvement will increase the consistency and reliability of results. This will allow us to measure the modal linewidth at many other points in the cavity, which should be done to confirm the dependence seen in this work. The second major improvement may potentially come from improving the slow-axis collimation. This is the bane of high power BALs because of the large active area volumes that are necessary to achieve high powers in gain-guided lasers. Our BAL, like many others, was dual-lobed in the free-running state along this axis, but single-mode along the fast axis (which is spatially confined in comparison). When coupled to an external cavity, the slow-axis divergence allowed the BAL to emit nonuniformly across the face of the chip leading to several simultaneously lasing external cavity modes, and an effective bandwidth that was larger than the modal linewidth. The results presented in the previous chapter suggest that controlling the feedback more carefully in this dimension may dramatically improve the performance of the ECDL. The easiest way to do this would be to change the feedback mirror from planar to curved about the fast axis of the laser to match the curvature of the phase front. Because the beam quality varies with power, laser type, collimation, and cavity length, a fixed focal length mirror may be insufficient. We are currently contemplating a design for a curved mirror with an adaptive focal length. Such designs have been theoretically suggested [93 95] and experimentally carried out in a short cavity regime [96]. Work done on semiconductor lasers under delayed optical feedback have shown the existence of two dynamical regimes defined by the transit time of feedback being shorter (short cavity regime) and longer (long cavity regime) than the timescale for dynamical processes in the BAL itself [97]. Experiments are currently underway vigorously in the short cavity regime utilizing a variety of spatial filters in controlling the emission of BALs [73,98,99]. Because of the interesting dynamical phenomena in the short cavity regime, interest is turning away from the long cavity regime, where we are currently operating. Current experiments with curved mirrors use convex concavities to spatially filter the high-order transverse structure that lies off-axis [96]. This type of filter may work with a longer cavity with less curvature, saving some of the power loss. With a variable mirror, we can test either convex or concave geometries. Since the instabilities appear to result from the difference in phase across the chip, there may exist a concave geometry that optimizes this. Continuing the experiment along this line is interesting enough as a fundamental experiment in broad-area laser physics. It is true that this may not be necessary for a SEOP experiment beyond improving the spatial distribution of light in the cell and possibly the fine tunability. The effective bandwidths reported in this thesis are an improvement over similar designs, and can be used in such experiments with minimal pressure broadening of the Rb D1 band. However, improving the cavity in this way may allow high power BALs to be used in laser cooling experiments as well. The narrow-bandwidth output could be utilized as a repumping beam in a magneto-optical trap. Current repumping beams are not high power, and are focused on repumping atoms along a single hyperfine transition. The larger bandwidth and higher power of an externally coupled BAL, versus a low power narrow-linewidth trapping laser, would mean that atoms falling into any hyperfine level could be repumped to allow the trapping beams to cool them. For this application, the BAL may have to be single-mode. Further improvement of the bandwidth to a true single mode would also allow direct 69

80 trapping with externally coupled BALs. The higher power would increase the efficiency of the laser cooling process, meaning less trap loss and potentially larger and more stable atom clouds. Using tapered semiconductor lasers in place of BALs would dramatically improve the spatial beam quality, which should improve the viability of this mount for the laser cooling experiments. These lasers, or even low power laser diodes, would also be a good test of the conclusions derived here for BALs in an external variable length cavity. At present, we are designing the SEOP experiment to test our ECDL. We have constructed a low-frequency NMR apparatus that will be used to measure the polarization of 129 Xe. One of the advantages of our design over others is that our ECDL s effective bandwidth is much smaller for equivalent output powers. Therefore, we expect to perform SEOP experiments with minimal pressure broadening of the Rb D1 band to yield a high polarization of 129 Xe. This is necessary to improve MRI imaging of biological tissues [57,66]. Because of our narrow bandwidth, we may also be able to probe the structure of the D1 band. Spin-polarized noble gases have also found use in many novel imaging experiments besides MRI body tissue imaging. They are being used to study phenomena ranging from granular flow to fundamental particle physics. There are many directions in which to go, but our immediate priority is to first test and optimize the performance of the ECDL in a SEOP experiment. Redesigning the ECDL as suggested earlier has the potential of allowing two completely different experiments to be undertaken with a single laser. Switching experiments could be as easy as swapping feedback mirrors. With the established popularity of optical trapping experiments, and the rising popularity and diversity of spin-exchanged optical pumping experiments, the need for this type of laser is plausible. The design presented in this work is superior in stability, configurability and wavelength tunability. We look forward to directly applying it to the experiments described above and continuing to explore the dynamics of a BAL in a variable external cavity. 70

81 Appendix A ECDL Schematics The figures in this appendix are detailed schematics of our ECDL cavity design. The schematics were designed according to calculations presented in 3.1. AutoCAD was used to render the design. 71

82 Figure A.1: Overhead schematic of the scissor mount in the fully open position. The open region behind the scissor mount contains the translation stages for the laser and collimating optics. The actuator interfaces with the movable arm at a contact tab affixed to the two holes on the left side of the figure. The size of the actuator prevents the mount from achieving this configuration in the current implementation, but this is not important since there are currently no spectral features of interest beyond the Rb D1 band. 72

83 Figure A.2: Overhead schematic of the scissor mount in the fully closed position. In the current implementation, this position is not attainable because a resistive spring is mounted between the movable arm and the fixed arm. For accessing the Rb D1 band this is not a problem. If the D2 band needs to be accessed, the hex screw holding the spring in place may be shaved down. If the K D1 band is needed, the spring will need to be repositioned. 73

84 Figure A.3: Depiction of the scissor mount in its current rest configuration with the actuator mount shown. In operation, the rest angle is a little smaller than 67 because of a rubber boot placed on the tab to attenuate vibrational noise from the actuator. This sets the laser wavelength near 796 nm at rest, just red of the Rb D1 band. 74

85 Appendix B Experiment Photos We are including annotated photos of our current experimental setup. Many of the analysis techniques used in the initial testing of this laser should continue to be used to monitor the ECDL performance in future experiments. When changing optics and instrumentation, the photos provided here should be a good reference as to what things looked like when the experiment was in a known working condition. 75

86 Figure B.1: An outside view of our ECDL. The surrounding box is not air tight, though this does not significantly affect the stability of the coupled laser. A detailed image of the mount itself is shown in Fig

87 Figure B.2: Image showing instrumentation for analyzing the performance of the ECDL. Shown are the scanning Fabry-Perot interferometer and fiber optic inputs for the nm resolution Coherent Inc. wavemeter and nm resolution Czerny-Turner spectrometer. We are currently applying the ECDL to high-resolution absorption spectroscopy of a Rb vapor to be used in a 129 Xe spin-exchange optical pumping experiment. 77

88 Figure B.3: 1.26 m Czerny-Turner spectrometer used for monitoring the output of the ECDL. The optics in front of the entrance slit reduce and collimate the fiber optic output and allow for near instrumental resolution at the CCD. 78

89 Figure B.4: Drive electronics for the BAL. The TEC and laser current drivers are separate, but are commonly powered and grounded. Great care was taken to isolate each component from the chassis ground to properly power the laser. Not shown is a regulated 5 V reference used by the current modulation circuitry. 79

90 Figure B.5: Screen capture of the scissor mount control interface (SMCI) program developed in LabView to communicate with the actuator mounted on the movable arm of the ECDL mount. A more detailed overview of the program will be provided in an addendum to this thesis. 80

91 Appendix C Detailed Alignment Procedure In this appendix, we present a complete alignment procedure assuming the ECDL is being set up for the first time. This is useful if the optics need realigned as a reality check or if the ECDL is placed into a new experiment. Here, only alignment procedures relative to the ECDL itself are discussed. Alignment of common analysis instrumentation is left to a manual provided as an addendum to this thesis. C.1 Laser rough alignment The best place to start aligning the ECDL is with the laser itself. When mounting the C-block copper mount containing the BAL chip to the TEC module, there is enough play in the mounting screw that the laser may not sit perfectly level in either plane. Tilts about either axis can be corrected with the collimating optics, though this should be minimized as the mount is not designed for large off-axis tilts of the lenses. Before placing any optics, make sure the beam is level in each direction by measuring the horizontal and vertical displacement of the center of the beam at varying distances from the laser. The center of the beam should be 7.5 cm above the baseplate. The horizontal position will vary with cavity length. In our case, the front of the TEC module had to be raised slightly with pieces of aluminum foil to make the uncollimated beam level. The 2 W Coherent Inc. BALs are expected to be dual-lobed along the vertical axis. The laser should be moved close to its final position along the pivot plane before the collimating optics are placed. 81

92 Figure C.1: Diagrams of the BAL image with various horizontal axis tilts of the aspheric lens. The lens mount is shown for orientation. C.2 Collimating optics rough alignment The first collimating optic to be placed should be the small focal length aspheric lens collimating the fast (horizontal) axis. Whether the current mounting system is used or whether the integrated mount design discussed in Chapter 5 is used, the procedure will not change. The aspheric lens is closely matched to the fast-axis divergence of the laser. This is good because this restricts the alignment tolerance, permitting very precise alignment of this optic. Any tilt or displacement is clearly seen in the laser image it renders. Adjustments should first be made to get the aspheric lens roughly into position, centered on the BAL. To do this, the laser image should be monitored. It may be helpful to place a target card at the position used to level the uncollimated laser as a reference. To center the beam, move the aspheric lens in the direction that the image needs to be moved to reach the target position. The resulting image will be a thin slice that diverges rapidly in the uncollimated slow (vertical) direction. If the beam is observed at a position where the vertical extent is about an inch or so, the image can be used to align the tilt about the horizontal axis. Fig. C.1 shows how the rectangular beam looks with different tilts about this axis. The degree of curvature is related to the magnitude of the tilt. This should be observed with the aspheric lens slightly out of collimation. This exaggerates the size of the image making it somewhat easier to see the curvature. Perfect placement will have equal top and bottom curvatures and be vertically level. Small vertical translations will also show this curvature error. If the curvature is equal, but the beam itself is not level, it means that the lens is tilted in such a way that the vertical translation error is compensated for. This simultaneous alignment can be tricky, but in the end is very accurate. This is good for a rough alignment. The laser will have to be collimated with the cylindrical lens to make further improvements. Move the aspheric lens with the translation stage to collimate the beam in the horizontal direction. The cylindrical lens should be placed one focal length from the aspheric lens with the curved side facing away from the laser. When placed into the beam with the aspheric lens, the laser will assume its collimated form. Slowly adjust the position of the cylindrical lens along the common collimating optics arm until the beam is optimally collimated at a far distance from the laser (3-4 82

93 m is good to notice small changes in position). Because of the non-gaussian beam quality in this dimension, optimum collimation means with minimum divergence. Unless the lenses themselves are replaced, the relative position between the two has been determined and locked and should not be changed. That being the case, the cylindrical lens still has one more translational degree of freedom along the vertical axis. The lens should be aligned along this axis just like the aspheric lens was, so that the image is centered on the target position at the opposite end of the ECDL box 1. Before proceeding, watch how the laser focuses just beyond the cylindrical lens when adjusting the entire lens assembly into collimation. The laser should focus symmetrically. If it appears to focus from the right, the laser is misaligned to the right of the aspheric lens. Since the beam should be centered, this misalignment is likely small. In this case, it is better to adjust the position of the laser since it is on a two-axis translation stage. If the beam appears to focus from the left, move the laser in the opposite direction to correct it. One final thing to consider is an error in the vertical-axis tilt of the aspheric lens. This is difficult to detect. If the laser is symmetrically collimating, but is directed to the right or left of the target center, then there is likely a tilt error in the collimating lens about its vertical axis. Tilting the entire optics assembly is the easiest way to fix this, though the cylindrical lens may have to be adjusted slightly. C.3 Collimating optics fine alignment Once both collimating lenses are placed, the laser image can be used to tune this alignment very precisely. In this section, the beam should again be monitored at a distance of about 3-4 m. Because the common collimating optics mount is designed to lock the relative separation of the two lenses, fine collimation is reduced to one dimension. The fast axis can be collimated to a diffraction limited width. Calculations with the optics used in this experiment give ideal waist sizes just after the cylindrical lens (c.f ). The non-gaussian slow axis will be larger than its ideal value and will continue to diverge with distance. The collimated fast axis will remain 3 mm in total width in the near field, increasing to 4.25 mm at 9 m. It is important to note how many mirrors are used to steer the beam to the distant screen. An odd number of mirrors will flip the image about the vertical axis. We assume either no steering mirrors or an even number of them when discussing the cylindrical lens alignment. The vertical translation and horizontal axis tilt of the aspheric lens should already be in good alignment. If this is not the case, it will result in coma that is clearly visible at a large distance. Fig. C.2 relates the image to the possible error that occurred. The coma results from off-axis illumination of the lens. Whether by vertical displacement or angled incidence from a tilted lens, the focal distance becomes nonuniform along the vertical extent of the beam. The degree of the coma is directly proportional to the magnitude of the error. Assuming the aspheric lens is aligned as previously described, the first major problem that will likely be apparent is a relative tilt error between the cylindrical lens and the aspheric lens. We break this alignment into tilts about two axes. One is about the vertical axis, and the other is about the optical axis of the cylindrical lens. Because the cylindrical lens acts only along a single axis, an imperfect alignment will break the beam into image components. At a far distance, small tilts about the optical axis will yield two images, one that is properly vertical, and another that is tilted at the angle of the error. For larger tilts, the image will become severely distorted. Fig. C.3 shows what this looks like. The distorted image will reflect the appearance of the front face of the cylindrical lens looking down the optical axis from the laser. Tilt errors of this nature would be eliminated if an 1 Note that the laser can hit any point along the horizontal axis of the cylindrical lens without changing the image alignment. 83

94 Figure C.2: Diagrams of the collimated BAL image at a distance of 3-4m from the output facet showing errors in either the vertical translation of the aspheric lens or the horizontal axis tilt. The orientation of the tilt is the same as in Fig. C.1. Figure C.3: Distortions caused by cylindrical lens tilt about the optical axis. The effect is more pronounced due to the asymmetry in the beam. The magnitude of the tilts are exaggerated. 84

95 Figure C.4: Effect of vertical axis tilt of the cylindrical lens. Looking down the vertical axis of the cylindrical lens, the aberrations result from a) counterclockwise tilt and b) clockwise tilt. A collimated HeNe laser was used to acquire the images. integrated optics mount were used instead of the current separated setup, saving a lot of alignment time since this error is typically the hardest to correct. If the cylindrical lens is tilted about the vertical axis, a curved aberration will result. Fig. C.4 uses a collimated HeNe laser to demonstrate this error. The aberrations described above follow the assumptions made prior to this discussion. If an odd number of steering mirrors are used, the effects will be opposite those diagrammed in Figs. C.3-C.5. When the tilt errors in the cylindrical lens have been corrected, the laser should have a nice vertical rectangular structure beyond the cavity. The last fine adjustment to be made is to correct very minor horizontal displacements of the laser with respect to the aspheric lens. This was already addressed at the end of the previous section, but very small displacements are only noticeable at a far distance when the laser is collimated. If present, the image will be flanked by a knife-edge diffraction pattern pointing in the direction the laser needs to move to correct it. Fig. C.5 shows this effect for our ECDL. This type of misalignment, along with small collimation errors, is the most common type of misalignment because the other errors should all be permanently corrected as long as no changes are made to the relative alignment of the collimating optics. The collimating lens system should now be accurately aligned. It should be noted that the tilt errors described above will be more forgiving with the cylindrical lens because of its large NA compared to the relatively small slow-axis divergence. Even a visibly tilted lens may not show image aberrations if tilted small enough. This can be utilized to prevent reflective feedback from the cylindrical lens from entering the laser and is a good idea even for an AR-coated lens due to its sensitivity to angle of incidence. The lens should only be tilted about its inactive axis (horizontal in our case) because small tilts about the vertical axis are noticed in the spectra of the coupled ECDL (c.f ). Tilting about the horizontal axis does not distort the beam shape, but will increase the 85