Optimized Second-Harmonic Generation in Quantum Cascade Lasers

Transcription

1 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 11, NOVEMBER Optimized Second-Harmonic Generation in Quantum Cascade Lasers Claire Gmachl, Senior Member, IEEE, Alexey Belyanin, Deborah L. Sivco, Member, IEEE, Milton L. Peabody, Nina Owschimikow, A. Michael Sergent, Federico Capasso, Fellow, IEEE, and Alfred Y. Cho, Fellow, IEEE Abstract Optimized second-harmonic generation (SHG) in quantum cascade (QC) lasers with specially designed active regions is reported. Nonlinear optical cascades of resonantly coupled intersubband transitions with giant second-order nonlinearities were integrated with each QC-laser active region. QC lasers with three-coupled quantum-well (QW) active regions showed up to 2 W of SHG light at 3.75 m wavelength at a fundamental peak power and wavelength of 1 W and 7.5 m, respectively. These lasers resulted in an external linear-to-nonlinear conversion efficiency of up to 1 W/W 2. An improved 2-QW active region design at fundamental and SHG wavelengths of 9.1 and 4.55 m, respectively, resulted in a 100-fold improved external linear-to-nonlinear power conversion efficiency, i.e. up to 100 W/W 2. Full theoretical treatment of nonlinear light generation in QC lasers is given, and excellent agreement with the experimental results is obtained. For the best structure, a second-order nonlinear susceptibility of ( pm/v) is calculated, about two orders of magnitude above conventional nonlinear optical materials and bulk III V semiconductors. Index Terms Intersubband transitions, mid-infrared, multiple-wavelength emission, nonlinear optics, quantum cascade laser, quantum wells, second-harmonic generation. I. INTRODUCTION ONE-PHOTON intersubband transitions in semiconductor quantum wells (QWs) such as in linear absorption or emission are the basic building blocks of quantum-well infrared photodetectors (QWIPs) [1] or Quantum Cascade (QC) lasers [2], respectively. In these devices, intersubband optical transitions are engineered by the choice of QW and barrier thicknesses to provide the appropriate energy levels, optical dipole matrix elements, and electron scattering rates amongst other parameters. Aside from their linear optical properties, resonant intersubband transitions in coupled QWs can how- Manuscript received June 6, 2003; revised July 8, This work was supported in part by DARPA/US ARO under Contract DAAD19-00-C The work of A. Belyanin was supported by Texas Advanced Research and Technology Program and the Office of Naval Research. C. Gmachl was with Bell Laboratories, Lucent Technologies, Murray Hill, NJ USA. She is now with the Department of Electrical Engineering, Princeton University, Princeton, NJ USA ( cgmachl@ princeton.edu). D. L. Sivco, M. L. Peabody, A. M. Sergent, and A. Y. Cho are with Bell Laboratories, Lucent Technologies, Murray Hill, NJ USA. A. Belyanin is with the Department of Physics, Texas A&M University, College Station, TX USA ( belyanin@jewel.tamu.edu). N. Owschimikow was Bell Laboratories, Lucent Technologies, Murray Hill, NJ USA. She is now with the Technical University of Darmstadt, Darmstadt, Germany. F. Capasso is with the Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA USA. Digital Object Identifier /JQE ever also be designed as strongly nonlinear oscillators, thus providing for giant nonlinear optical susceptibilities [3] [6]. The latter have first been demonstrated in the early 1990s, but their usefulness in nonlinear frequency conversion was limited due to difficulties in efficiently coupling the pump radiation to the intersubband optical transitions. Besides, even with good coupling, there are fundamental problems of resonant absorption of the external pump radiation and the lack of a suitable phase-matching scheme in most III V semiconductors. A monolithic and guided wave approach of integrating the nonlinear optical transitions with the pump light source would provide the best solution for efficient coupling and allows overcoming the difficulties indicated above. In the integrated device, laser radiation generated by carrier injection into the active region serves as an intracavity optical pump for the nonlinear frequency conversion. All fields participating in the nonlinear interaction can be at resonance with the corresponding intersubband transitions, maximizing the nonlinear optical response. True phase matching can be achieved by using optical modes of different transverse order. Such integration was earlier suggested for diode lasers [7]. Recently we have demonstrated the first integration of nonlinear optical intersubband transitions with QC lasers. We monolithically integrated a two-stack two-wavelength QC laser and coupled QWs with strong second-order nonlinear susceptibilities, resulting in sum-frequency and second-harmonic generation (SHG) [8]. In this latter work, we identified two different methods of integrating the optical nonlinearity with the QC laser, one being the addition of a separate section of specially designed QWs into the laser waveguide core. The second approach simultaneously uses the QWs in the active region of the QC laser itself for nonlinear light generation. This latter approach has clear advantages as it assures a strong overlap and efficient in-plane coupling of fundamental and nonlinear guided modes; it furthermore allows for an automatic resonance of the pump light with one leg of the nonlinear optical transition cascade and finally suggests full use of the laser cavity for QC-laser active regions and injectors, thus increasing the power of the fundamental pump light. Since the QWs of such a laser design not only have to function well as QC lasers but also need to provide a large optical nonlinearity, a tradeoff may exist between laser performance and linear-to-nonlinear power conversion efficiency. In this paper, we present optimized SHG in QC lasers, in which the QWs of the active regions simultaneously function as nonlinear oscillators. We discuss three generations of QC laser designs. The first generation is exactly modeled after the /03$ IEEE

2 1346 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 11, NOVEMBER 2003 one reported first in [8], where several 10 milliwatts of fundamental power were converted into about 10 nw of SHG light. The second-generation design improved upon this baseline by keeping essentially the same energy level structure, but maximizing the essential parameters for laser performance and SHG, such as resonance conditions, optical dipole matrix elements, and carrier density. Up to 1 W of pump power at mwas then converted into up to W of SHG at mwavelength; the linear-to-nonlinear power conversion efficiency was improved by about a factor of five over the original design. In third-generation devices, operating at 9.1- and m wavelength, the electronic level structure was optimized for SHG, resulting in a power conversion efficiency that is enhanced up to 100 times. It is important to note that this optimization for SHG in coupled QWs is not a global one, as was described by Khurgin [9], but is performed under the condition that the resulting structure must also be a reasonably high-performing QC laser. In fact, we have tested another active region design with a nominally (by another factor of 100) increased linear-to-nonlinear power conversion efficiency. However, this particular structure did not display laser action. This paper is focused on the optimization of SHG in QC lasers by proper design of the electronic level structure. We would, however, also like to note that by analogy our assertions are similarly applicable to sum-frequency and higher harmonics generation as well as to difference frequency generation. In addition, work on phase matching of the waveguides is currently in progress and will be presented elsewhere. This paper is organized as follows. Section II describes the quantum design, layer structure, and device layout of our samples. Section III provides the theoretical framework needed to calculate the condition for and efficiency of SHG and related nonlinear optical effects. In this section, we also estimate the nonlinear optical susceptibilities for our samples and external linear to nonlinear power conversion efficiency. In Section IV, we report and evaluate the experimental data. Section V presents a short conclusion and outlook. II. SAMPLE DESIGN, STRUCTURE, AND LAYOUT In [8], we had focused on sum-frequency generation in QC lasers. The intersubband transitions in the regions with large optical nonlinearities were near resonant for sum-frequency generation of 7.1 and 9.5 m wavelength light. However, due to the (intrinsic and extrinsic) broadening of the intersubband transitions [10], which easily can reach mev full-width at halfmaximum (FWHM) for transitions in the mid-infrared wavelength range, the intersubband transitions also supported SHG. In the following, we will focus on optimizing QC lasers for SHG, and we will use the layer design of the structure of [8] as a baseline. QC-laser active regions up to now have been designed starting from a single QW to active regions containing ten coupled QWs or superlattices.[2] Some of the most successful active region designs contain a minimum of three consecutive energy levels, termed 3, 2, and 1, with the laser transition being from level 3 to level 2, and level 2 being depleted of electrons quickly by resonant longitudinal optical (LO) phonon scattering into level 1. Under operation, electrons are injected into level 3 by resonant tunneling from the ground state termed g of the preceding injector region, and tunnel resonantly out of levels 2 and 1 into the following electron downstream injector region. High-performance QC-laser active regions are then characterized by a large optical dipole matrix element for the laser transition, fast tunneling times into and out of the active region, a long lifetime of the upper laser level 3, and a short lifetime of the lower laser level 2. With the appropriate design of scattering rates, the only energy levels with significant electron population are levels 3 and g, which share a common quasi-fermi level. We can adopt the gain coefficient as a good figure of merit for the quantum design of the QC laser. It is given as [1], [2] where is the LO-phonon scattering time between levels 3 and 2, is the electron charge, the laser wavelength, is the modal effective refractive index at, the thickness of one pair of active region and injector, and the FWHM of the transition. An intersubband structure capable of SHG, on the other hand, contains yet another triplet of energy levels (i, ii, iii) in the conduction band of coupled QWs. An optimized structure is in near resonance with the pump radiation at frequency and SHG at and the product of the three optical dipole matrix elements,, and between all three levels is large. We adopt the absolute value of the second-order nonlinear susceptibility as the figure of merit of our design; the latter is approximately given as [6] (2) where is the electron density in the active region, and are the energy difference and transition broadenings between levels and, respectively. To be an efficient nonlinear converter, at least one energy level of the nonlinear cascade (i, ii, iii) has to be populated with free electrons. This latter requirement guides the design of viable QC-laser active regions with integrated nonlinear optical cascades, as the upper QC-laser level (levels 3 and g) the only one significantly populated with electrons under laser operation must coincide with one level of the nonlinear cascade. A. SHG in QC-Lasers With Three-QW Active Regions In Fig. 1(a), the conduction band structure of one active region with its preceding and subsequent injector region is shown. The QWs are InGaAs and the barrier material is AlInAs, both lattice matched to InP substrate. We use a conduction band offset of 520 mev and an applied electric field of 58 kv/cm. Fig. 1(a) also shows the moduli squared of the essential wavefunctions, the baselines of which coincide with their respective energy levels. This QC-laser active region contains three coupled QWs: a thin first QW followed by two wider ones. The latter are the essential QWs sustaining the laser transition, between levels 3 and 2. The center QW is furthermore the main origin for energy level 5, and the thin first QW mainly supports level 4. The (1)

3 GMACHL et al.: OPTIMIZED SECOND-HARMONIC GENERATION IN QUANTUM CASCADE LASERS 1347 spatial asymmetry of the QWs assures sizable optical dipole matrix elements. Both the original design of a QC laser with integrated nonlinear optical cascade (designs D2616, D2882, and [8]) as well as its successor optimized for SHG [design D2886 shown in Fig. 1(a)] followed this design idea. The design parameters for both designs are given in Table I. B. SHG in QC-Lasers With Two-QW Active Regions (a) (b) Fig. 1. A portion of the conduction band diagram, one active region sandwiched between two injector regions, and the moduli squared of the essential wavefuntions of designs (a) D2886 and (b) D2912. The significant energy levels are labeled 1 to 5 inside the active region and g for the ground state of the injector. The dashed lines indicate the extent of the minibands inside the injector regions. The laser transition (3! 2) is marked by a wavy arrow. The thicknesses in nanometers of the QWs and barriers of one period of active region and injector of D2886 (top) are from left to right (i.e., electron down-stream) and starting with the injection barrier I : 4:3=1:4=1:3=6:8=1:1=5:1=2:6=3:6=2:2=3:4=2:1=3:3=2:1=3:3=2:5=3:2, the barriers are indicated by bold font, and the underlined layers are doped to 4: cm. The analogous layer sequence of D2912 (bottom) is: 4:1=8:3=1:3=5:2=2:6=4:1=2:1=3:9=2:3=3:7=2:5=3:5=2:6=3:3; the doping density was 3: cm. The conduction band structure of wafers D2616 and D2882 is similar to that of D2886; the thicknesses of the QWs and barriers are as follows: 4:5=1:5=1:5=6:7=1:4=5:3=2:6=3:5=2:0=2:9=1:8=3:0=1:8=3:2=2:3=3:1; the underlined layers were doped to 3: cm [14]. pump radiation at the fundamental frequency is generated between levels 3 and 2. Nonlinear cascades can be found for the level triplets and As the energy positions of levels 3 and 5 are mainly governed by the center QW, and level 4 by the thin first QW, variations in relative thicknesses of the two QWs quickly allow optimization of the resonance condition, and the A closer examination of the structure of Fig. 1(a), however, reveals some shortcomings. First of all, the two nonlinear cascades are in fact contributing to the total second-order nonlinear susceptibility with opposite sign and similar magnitude, thus diminishing the overall effect. Second, the very choice of a three-qw design also results in another energy level situated between levels 3 and 4. While out of resonance with any radiation inside the cavity, and thus not severely impeding the process, it still leads to smaller than possible dipole matrix elements for the other transitions. Such an argument follows from a sum-rule of the oscillator strength for intersubband transitions [11]. Therefore, we adopted a new design of the QC-laser active region with nonlinear cascade with only two QWs. The conduction band structure and moduli squared of the essential wavefunctions of one active region as well as of its preceeding and following injector region are shown in Fig. 1(b). The structure has been calculated for an applied electric field of 38 kv/cm. QC-laser action again takes place between levels 3 and 2. As the first leg of the nonlinear cascade coincides with the laser transition, i.e., the fundamental pump light, their remaining in resonance is trivial. Resonance of the second leg can be achieved by relative thickness variations of the two QWs and the barrier between them. It is worth noting that, in this design of the nonlinear cascade, resonant absorption of the SHG radiation is negligible, as the free electron population is in level 3 rather than in level 2. The full set of device parameters for this type of design [D2912, numbering of the energy levels follows Fig. 1(b)] are also given in Table I. C. Waveguide Designs and Device Layout Four different wafers are being compared in this paper. The nominally identical wafers D2616 and D2882 contain the same active regions and injectors as the structure of [8]. The active regions and injectors of wafers D2886 and D2912 are shown in Fig. 1(a) and (b), respectively. The thicknesses of the individual QWs and barriers are given in the caption of Fig. 1; in the following we will give the waveguide parameters. For wafers D2616 and D2882, 32 QC-laser active regions interleaved with injector regions were grown sandwiched between two layers of low-doped InGaAs cm, 500 nm below, and 300 nm above. All these layers together constitute the waveguide core. The bottom waveguide cladding coincides with the low-doped cm InP substrate. The top cladding is made of an inner 1.5- m and outer 0.8- m thick AlInAs layer, doped cm and cm, respectively, followed by a highly doped

4 1348 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 11, NOVEMBER 2003 TABLE I DESIGN AND DEVICE PARAMETERS OF SAMPLES D2616/D2882, D2886, AND D2912 (a) (b) Fig. 2. Conduction band diagrams and moduli squared of the essential wavefunctions of the active regions of designs (a) D2886 and (b) D2912; the SHG nonlinear cascades are indicated to the right of each active region. Cascades I. and II. span the levels and 3-4-5, respectively. The thick dashed line denotes the energy level with the highest electron density. The higher performance of design (b), D2912, can in part be attributed to the absence of the energy level indicated in gray and by the star in (a), which is present in designs D2616/D2882 and D2886. cm, 350-nm-thick InGaAs layer [12]. Between all bulk-like layers, 25-nm-thin digital transition layers are grown. In wafer D2886, 31 periods of active regions and injectors were bounded on the bottom by an inner, 800-nm-thick AlInAs layer cm, followed by a 1.1- m-thick In- GaAs layer cm, and the InP substrate. The top-cladding consisted of an 800-nm-thick AlInAs layer cm, followed by 1.1- m InGaAs cm, 1.8- m AlInAs cm, and, finally, capped by 350-nm-thick highly doped InGaAs cm. This waveguide was intended for potential phase matching, but as later experiments showed did not achieve it, likely due to a sizable discrepancy between theoretical and experimentally obtained modal refractive indices. Wafer D2912 again has a conventional QC-laser waveguide similar to that of D2616 and D2882. Fifty periods of active regions and injectors are sandwiched between two layers of In- GaAs, a 600-nm-thick one below and a 400-nm-thick one above, both doped to cm. The bottom cladding is provided by the InP substrate and the top cladding is made from an inner 2.1- m-thick AlInAs layer doped to cm an outer AlInAs layer, 400 nm thick and doped to cm, which are also capped by a 350-nm-thick highly doped cm layer of InGaAs. The calculated modal refractive indices and waveguide attenuation coefficients of all waveguides at both the fundamental ( and, respectively) and SHG ( and, respectively) wavelengths are summarized in Table I. All wafers were grown by molecular beam epitaxy (MBE) using In Ga As and l In As. The devices were processed as deep-etched ridge waveguide lasers with widths varying from 8 to 16 m. The side-walls are coated with 300-nm-thick SiN, and a Ti/Au contact is supplied to the top of the ridges; it also coats the electrically insulated sidewalls. Ge/Au/Ag/Au is applied to the substrate side as back-contact metalliziation following the thinning (lapping) of the wafer material to m. Laser bars with lengths ranging from 1.5 to 3 mm were cleaved from the processed chips, In-solder bonded to copper heat sinks, and wire-bonded. III. THEORY AND MODELING RESULTS Fig. 2(a) and (b) shows the close-up details of the conduction band diagrams of the structures in Fig. 1(a) and (b), respectively. To calculate the resonant nonlinear optical response of such a multistate system, we solve the coupled density matrix equations and Maxwell s equations. For the reader s convenience, we outline the derivation details here. Equations for the density

5 GMACHL et al.: OPTIMIZED SECOND-HARMONIC GENERATION IN QUANTUM CASCADE LASERS 1349 matrix elements form [13]: can be written in the following general (3) of the field amplitudes and arrive at the following expression for the amplitude of nonlinear polarization in the -approximation: (4) (10) Here is the relaxation rate of the off-diagonal element of the density matrix, the transition frequency, the dipole moment of the transition, and denotes all relaxation and pumping terms that determine the population of the th state in the absence of radiation field. The electric component of the radiation field inside the laser cavity can be represented in our case as a sum over quasi-monochromatic components with slowly varying amplitudes and frequencies nearly resonant to the transition frequencies As is evident from Fig. 2,,, and, where is the fundamental frequency of a laser. Similarly,,, and. Off-diagonal elements of the density matrix can be written as where the amplitude is a slowly varying function of time. For the diagonal elements,. Using the above expressions in (3), (4), we arrive at the truncated density matrix equations Here. Note that,, and. The nonlinear polarization at the second harmonic can be calculated from (7) and (8) as where is the volume density of electrons in the active mixing region. This polarization serves as a source for the electromagnetic field at the second harmonic. In this paper, we consider the operation in the CW regime or with current pulses much longer than all relaxation times. In this case, we can neglect all time derivatives in the above equations, and solving for and is reduced to algebra. In principle, the expression for the nonlinear polarization defined by (9) is valid for arbitrarily strong field amplitudes and includes such resonant nonlinear effects as saturation and power broadening. However, in the present study, the field intensities were well below their saturation values most of the time, except for the measurements of devices made from D2886 at the highest current, when the fundamental pump power reached 1W.For sufficiently weak fields, we can expand the solution in powers (5) (6) (7) (8) (9) where is the component of the electric field at fundamental frequency, is the coordinate in the growth direction [001], and is along the waveguide axis in the direction. One can clearly see from (10) the interference between the cascades and If the electrons are mainly in state 3,,,, this interference tends to decrease the overall value of. Therefore, the active regions were designed to have the SHG dominated by only one cascade. Increasing the field intensity beyond the saturation value leads to the decrease in the population differences and broadening of the linewidths,, so that the value of decreases. The saturation intensity is of the order of 1, assuming exact resonance, and increases with detuning. In the same weak-field approximation, the nonlinear polarization amplitude at the third harmonic is given by (11) To calculate the power of the nonlinear signal, we adopt the usual assumption that the transverse distribution of the electromagnetic field is determined by a cold waveguide and constitutes orthogonal sets of transverse electric (TE) and transverse magnetic (TM) modes. Only TM modes are excited efficiently since the polarization associated with electronic intersubband transitions contains only the component. In fact, there is also an excitation of TE modes at a second-harmonic frequency due to nonresonant lattice nonlinearity of a structure. However, this process is inefficient with the present waveguide orientation since it is proportional to a small longitudinal component of the electric field of the TM laser mode at a fundamental frequency. Furthermore, the magnetic field amplitude of a given TM mode with frequency and longitudinal wavenumber can be represented as a product of function, where the complex function varies slowly with coordinate along the waveguide direction, and the transverse distribution, which satisfies the transverse Helmholtz equation for the cold waveguide (12) The component of the electric field is related to as. For time-dependent processes, is also a slow function of time.

6 1350 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 11, NOVEMBER 2003 Substituting the above expression for into the wave equation for the second harmonic, using the orthogonality of functions for modes of different order, and solving the resulting equation for the amplitude, we finally arrive at the following expression for the nonlinear signal power: (13) where stands for the total losses of a given cavity mode at wavelength of the second harmonic, is the cavity length, and are reflection factors of a cavity and effective refractive indices of modes at wavelengths, respectively,, and is the power in the fundamental mode. The nonlinear overlap factor, which defines an effective interaction cross section of two TM modes, is given by (14) where and are dielectric permittivities of a waveguide at frequencies and, respectively. The values of are between m for the devices made from D2616/D2882 and D2886 and around 1000 m for the devices made from D2912. Using (10), (13), and (14), we can now estimate the expected second-order optical susceptibility and the nonlinear conversion efficiency for all three generations of devices. The estimations for are uncertain within a factor of 2 or 3, mainly because of differences between the designed and actual transition frequencies and the doping levels. Applying (10) with parameters taken from Table I, we obtain (170 pm/v), (340 pm/v), and pm/v, for structures D2616/D2882, D2886, and D2912, respectively. Note the large nonlinear coefficient for D2912, which is two orders of magnitude higher than in standard nonlinear optical crystals and bulk III V semiconductors. In D2616/D2882, the main contribution to comes from the cascade In the case of D2886 and D2912, the contributions from and cascades turn out to be comparable, which can lead to some negative interference and reduction in by up to 30%. In estimations of the conversion efficiency, the largest uncertainty comes from, and there are additional sources of uncertainty: the phase mismatch and overlap factor. Variations of these parameters also cause the spread of between different devices of the same structure. Using the design parameters from Table I, for the devices of effective lateral width of the waveguide L m we obtain W/W for D2616/D2882, W/W for D2886, and W/W for D2912. The first two numbers are consistent with experimental values shown in Fig. 4. The calculated efficiency for D2912 is larger than the highest measured value by a factor of 3. The most probable reason for discrepancy is overestimation of by a factor of 2 due to deviation of the actual electron density and detunings from the calculated values. As is evident from the structure of (13), the main avenue for increasing efficiency is to improve the phase matching. The mismatch factor in the structures under study is between cm, which is 100 times larger than the modal losses. Therefore, we could obtain an increase in efficiency of three to four orders of magnitude by making the mismatch factor comparable to the optical losses. However, even in mismatched waveguides, there is still room for improving the efficiency by decreasing the effective interaction area in devices with a D2912-type active region. This could boost the efficiency to the value of 1 mw/w. IV. EXPERIMENTAL RESULTS The laser bars mounted to copper heat-sinks and with selective devices wire-bonded were attached to the temperature-controlled cold-finger of an He-flow cryostat. Most measurements discussed in this paper were taken at cryogenic temperature, close to 10 K. However, as we will discuss in a companion paper on the temperature performance and single-mode tunability of the laser structures discussed here, SHG was observed up to thermo-electric cooler temperature with good efficiency. [14] The lasers were operated in pulsed mode with ns current pulse widths at repetition rates ranging from 4 to 84 khz. The cryostat was fitted with a doubly antireflection (AR)-coated ZnSe window, yet control measurements have also been made using a quartz window; lenses with large numerical aperture, made either from AR-coated ZnSe, Ge, or uncoated CaF, were used to collimate and refocus the highly divergent light emission from the cleaved facets. Quartz, silica glass, sapphire, and an undoped InP flat were used as optical filters to discriminate between fundamental pump and SHG light. The spectra were taken using a Fourier transform infrared spectrometer fitted with cooled HgCdTe and InSb detectors for the pump and SHG light, respectively. When measuring the laser light at the fundamental frequency, attenuation screens were used to avoid saturation of the detector and detection electronics. The light output versus current ( ) measurements were taken with a calibrated, fast HgCdTe photovoltaic detector for the fundamental light and a calibrated, cooled InSb photovoltaic detector for the SHG light. In these measurements, light was collected with near unity collection efficiency from one facet. After measuring the linear and nonlinear characteristics, we deduce the external linear-to-nonlinear power conversion efficiency by graphing the nonlinear power versus the square value of the linear power. A linear fit to this curve (where suggested) results in the external power conversion efficiency. This value is closely related to the second-order nonlinear susceptibility and allows us to compare our theoretical and experimental results.

7 GMACHL et al.: OPTIMIZED SECOND-HARMONIC GENERATION IN QUANTUM CASCADE LASERS 1351 (a) Fig. 4. Scatter plot of the external linear-to-nonlinear power conversion efficiency values of several devices of D2616, D2886, and D2912. All data were obtained in pulsed mode and at 10 K heat sink temperature. (b) Fig. 3. Linear (P, dashed line) and nonlinear (P, solid line) light output versus current characteristics of two representative devices of (a) D2886 and (b) D2912. The insets show the respective graphs of external linear-to-nonlinear conversion efficiency. The numerical values inside the inset graphs have been extracted from least square fits to near linear portions of the data graphs. All data were taken in pulsed current mode at 10 K heat sink temperature. The device of (a) was 12 m wide and 3.04 mm long; the dimensions of the device of (b) were 13 m and 2.25 mm, respectively. A. Linear and Nonlinear Light Output Versus Current Characteristics Fig. 3(a) shows the linear and nonlinear characteristics of a representative device of D2886; approximately 0.5 W of fundamental peak power results in about 200 nw of SHG light. The inset reports the external linear to nonlinear power conversion efficiency, which is close to W/W. The laser threshold of about 1 A corresponds to a threshold current density of 2.74 ka/cm, which is a reasonable value for this type of active region [2], supporting the notion that the added feature of simultaneously integrated nonlinear cascade does not significantly interfere with the laser performance of the active region. The kink at about 2.4 A in the linear curve is a frequent occurrence with QC lasers. It is mostly attributed to the onset of higher order transverse modes, i.e., the laser ridges are wide enough to support two, sometimes even three, transverse modes in lateral direction. The kink is also reproduced in the nonlinear - curve and the external conversion efficiency curve. As different transverse modes have different modal effective indices and attenuation coefficients, it is not surprising that the external efficiency can change noticeably at such a kink. However, no clear trend has been seen on the magnitude or even the sign of the change of the external conversion efficiency with the nature of the kink. This is understandable from the fact that, aside from the variability in the transverse mode patterns, the external efficiency is affected by a much larger range of factors, e.g., the resonance condition depending on the applied electric field, the carrier density in level 3, and more. Fig. 3(b) shows the linear and nonlinear curves for a characteristic device of D2912. Here, about only 100 mw of fundamental peak output power are transformed into nearly 550 nw of SHG light. The external power conversion efficiency is accordingly much higher than that of the device of Fig. 3(a), between a factor of higher. Fig. 4 summarizes this improvement in external linear-tononlinear power conversion efficiency. The efficiencies for several devices of three wafers are shown. Devices of wafers D2616 and D2882 resulted in values clearly below 1 W/W, with the nonlinear curves often too noisy for a clear extraction of the efficiency from graphs of the nonlinear versus linear power squared. Lasers of D2886 performed significantly better, showing values up to W/W. Devices of D2912 finally achieved greatly increased external conversion efficiencies of up to 100 W/W. We notice a strong spread in the values of the external conversion efficiency, which can span almost a decade. However, we did not find a clear correlation with any significant device parameter, such as the ridge width or cavity length two possibilities that were explicitly explored. The spread of the data may still be explained by the simultaneous presence of various lateral transverse modes inside the laser waveguide during operation. Depending on the fraction of power attributed to each mode, the conversion efficiency, which in our measurements is averaged over all modes simultaneously collected on the detector and averaged over many ( 500) consecutive current pulses, can attain a wide number of values. Nevertheless, the improvement in external linear-to-nonlinear conversion efficiency between each generation of wafers D2616/D2882, D2886, and D2912 was significant.

8 1352 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 11, NOVEMBER 2003 Fig. 5. Linear (dashed line) and nonlinear (solid line) light output and voltage (solid line with separate y axis) versus current characteristics of a 10-m-wide and 3.04-mm-long laser device of D2886. The laser was operated with 60-ns-long current pulses at a 4.16-kHz repetition rate and at 10 K heat sink temperature. This device resulted in the highest measured absolute SHG power, i.e., 2 W, of the devices of this work. The external power conversion efficiencies are given in two regions. B. High-Performance ( - W SHG) Nonlinear Light Generation in QC-Lasers Fig. 5 reports the linear and nonlinear light output and voltage versus current ( ) characteristics of the one device of D2886, which gave us the highest absolute value of nonlinear optical power. We obtained 2 W of SHG light at 1 W of fundamental peak output power. Aside from displaying generally very high laser performance as manifested in a low laser threshold density ka/cm, a high slope efficiency (0.24 W/A), and an emission spectrum that remained well defined and spectrally narrow up to high current levels, this device was not remarkable in other aspects. Similarly, its neighbors on the same laser bar (each separated by 500 m) showed just average performance, well in agreement with the data shown in Fig. 4. Therefore, such high-performing outliers give us reason to believe that still considerable nonlinear power gains can be made by greater knowledge about and control over the critical device parameters in QC lasers with integrated nonlinear optical cascades. Fig. 6. Emission spectra of QC lasers with integrated second-order nonlinear cascades. (a) Long-range spectra of a characteristic laser of D2912. The spectrum on top has been taken in step-scan mode with an InSb detector fitted with a sapphire window and additional quartz/silica glass filter. The bottom spectrum is taken with a HgCdTe detector; the laser radiation has been reduced with a metal screen to avoid saturation of the detector and detector electronics. (b), (c) Short-range, high-resolution spectra of representative laser devices of D2886 and D2912, respectively. The SHG (bottom) and fundamental (top) light emission are shown for both devices. The star in (c) marks a portion of the spectrum, where the overlap of two Fabry Perot combs with different transverse mode order can be seen in the data. C. Spectral Measurements of SHG Fig. (6a) (c) reports spectral data obtained from our lasers. Fig. 6(a) displays large-spectral range power versus wavelength data obtained with the InSb (top) and HgCdTe (bottom) detectors. These spectra demonstrate the absence of spurious signals in the power measurements of the two detectors, each targeted for its own specific (the fundamental or SHG) wavelength range. Fig. 6(b) and (c) shows high-resolution spectra of representative devices of D2886 and D2912, respectively. Both spectra in the region of the fundamental as well as the SHG emission are shown. The expected direct correspondence between the respective spectra is observed in the data. Small disturbances [one being marked by a star in Fig. 6(c)] in the otherwise regular Fig. 7. Emission spectrum of a representative device of D2912 (the same as in Fig. 6(a)) in the very short wavelength range. A small THG signal is measured. The energy of the fundamental light is 136 mev (9.1 m wavelength), and SHG and THG are at 271 mev (4.55 m) and 407 mev (3.05 m), respectively. Fabry Perot spectra indicate regions where the overlap of at least two spectral combs of various transverse modes can clearly be seen.

9 GMACHL et al.: OPTIMIZED SECOND-HARMONIC GENERATION IN QUANTUM CASCADE LASERS 1353 D. Third-Harmonic Generation (THG) in QC Lasers This paper is mostly concerned with the optimization of SHG in QC lasers. As was shown in Figs. 1 and 2, both optimized designs of active regions contained two interleaved nonlinear cascades for SHG. As a result, the general possibility exists for a nonlinear cascade for third-harmonic generation (THG) in the same QC lasers. At resonance, the ratio of the third-order to second-order nonlinear susceptibility and the ratio of powers is of the order of. It can be of the order of 0.01 if the pump field intensity is about 1 MW/cm and the dipole moment is of order 10. In fact, while the third-order nonlinear susceptibility is very small in designs D2616/D2882 and D2886, the design of D2912 has nonnegligible, though in no way optimized,. Fig. 7 thus reports the high-energy emission spectrum of a representative device of D2912; a small signal at (at m wavelength) is indeed observed. In future work, we will attempt optimization of THG in a similar structure. V. CONCLUSION In summary, we have demonstrated optimized SHG in QC lasers, in which the resonant optical nonlinearity was directly integrated into the laser active regions. We achieved very high absolute SHG power levels of up to 2 W and large linear-to-nonlinear power conversion efficiency of around W/W. These values have been achieved for QC lasers and integrated nonlinear optical cascades still without phase-matching of the fundamental pump and SHG guided modes. We estimate that with the optimized active regions and frequency converters shown here and a phase-matching waveguide SHG power levels close to 1 mw can be achieved. Therefore, SHG has clear potential as an alternative way to produce very short wavelength m light in QC lasers. Such short wavelengths are of importance for, e.g., trace gas sensing of lightweight molecules. Furthermore, many of the concepts discussed here are similarly valid for a wider range of nonlinear optical effects, such as sum-frequency, difference-frequency, and higher harmonics generation, which in their entirety will significantly broaden the wavelength range accessible to QC lasers. Finally, the demonstrated success of SHG allows us also to assess the feasibility of more complex schemes of parametric light generation, such as monolithic semiconductor parametric amplifiers and oscillators or Raman lasers. ACKNOWLEDGMENT The authors would like to thank Dr. R. Colombelli and Dr. A. Soibel for their contributions and stimulating discussions. REFERENCES [1] H. C. Liu and F.Federico Capasso, Eds., Intersubband transitions in quantum wells: physics and device applications I & II, in Semiconductors and Semimetals. San Diego, CA: Academic, 2000, vol. 62 & 64. [2] C. Gmachl, F. Capasso, D. L. Sivco, and A. Y. Cho, Recent progress in quantum cascade lasers and applications, Rep. on Progress in Physics, vol. 64, pp , [3] M. K. Gurnick and T. A. De Temple, Synthetic nonlinear semiconductors, IEEE J. Quantum Electron., vol. QE-19, pp , [4] M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, and J. S. Harris, Observation of extremely large quadratic susceptibility at m in electric field biased AlGaAs/GaAs quantum wells, Phys. Rev. Lett., vol. 62, pp , [5] E. Rosencher, A. Fiore, B. Vinter, V. Berger, P.Ph. Bois, and J. Nagle, Quantum engineering of optical nonlinearities, Science, vol. 271, pp , [6] F. Capasso, C. Sirtori, and A. Y. Cho, Coupled quantum well semiconductors with giant electric field tunable nonlinear optical properties in the infrared, IEEE J. Quantum Electron., vol. 30, pp , [7] A. A. Belyanin, F. Capasso, V. Kocharovsky, and M. O. Scully, Infrared generation in low-dimensional semiconductor heterostructures via quantum coherence, Phys. Rev. A, vol. 63, [8] N. Owschimikow, C. Gmachl, A. Belyanin, V. Kocharovsky, D. L. Sivco, R. Colombelli, F. Capasso, and A. Y. Cho, Resonant second-order nonlinear optical processes in quantum cascade lasers, Phys. Rev. Lett., vol. 90, p , [9] J. Khurgin, Second-order intersubband nonlinear-optical susceptibilities of asymmetric quantum-well structures, J. Opt. Soc. Amer. B, vol. 6, pp , [10] J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, A. L. Hutchinson, S. N. G. Chu, and A. Y. Cho, Narrowing of the intersubband electroluminescent spectrum in coupled-quantum-well heterostructures, Appl. Phys. Lett., vol. 65, pp , [11] C. Sirtori, F. Capasso, J. Faist, and S. Scandolo, Nonparabolicity and a sum-rule associated with bound-to-bound and bound-to-continuum intersubband transitions in quantum wells, Phys. Rev. B, vol. 50, pp , [12] C. Sirtori, J. Faist, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, Quantum cascade laser with plasmon-enhanced waveguide operating at 8.4 m wavelength, Appl. Phys. Lett., vol. 66, pp , [13] Y. I.Y. I. Khanin, Principles of Laser Dynamics. Amsterdam, The Netherlands: Elsevier, [14] C. Gmachl, N. Owschimikow, A. Belyanin, A. M. Sergent, D. L. Sivco, M. L. Peabody, F. Capasso, and A. Y. Cho, Temperature dependence and single-mode tuning behavior of second harmonic generation in quantum cascade lasers, Appl. Phys. Lett., to be published. Claire Gmachl (S 94 A 95 SM 00) received the M.Sc. degree in physics from the University of Innsbruck, Austria, and the Ph.D. degree (sub auspicies praesidentis) in electrical engineering from the Technical University of Vienna, Austria, in Her studies focused on integrated optical modulators and tunable surface- emitting lasers in the near infrared. In 1996, she joined Bell Laboratories, Lucent Technologies, Murray Hill, NJ, as a Post-Doctoral Member of Technical Staff in the Quantum Phenomena and Device Research Department, to work on quantum cascade laser devices and microcavity lasers. In March 1998, she became a Member of Technical Staff in the Semiconductor Physics Research Department, working on quantum cascade laser devices and applications and on intersubband photonic devices, and has been named a Distinguished Member of Staff in In September 2003, she joined Princeton University, Princeton, NJ, as an Associate Professor in the Department of Electrical Engineering. She has coauthored more than 125 papers, has given more than 30 invited talks at international meetings, and holds 15 patents. Dr. Gmachl is a member of the 2002 TR100 and is a 2002/03 IEEE/LEOS Distinguished Lecturer. She is also a co-recipient of the "The Snell Premium" award of the IEE, U.K., (2003) and the 2000 NASA Group Achievement Award, and a recipient of the 1996 Solid State Physics Award of the Austrian Physical Society and the 1995 Christian Doppler Award for engineering sciences including environmental sciences, Austria. She is a Senior Member of the IEEE Laser and Electro-Optics Society and a Member of the American Association for the Advancement of Science, the American Physical Society, the Austrian Physical Society, the New York Academy of Science, the Optical Society of America, the SPIE-International Society for Optical Engineering, and the Materials Research Society.

10 1354 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 39, NO. 11, NOVEMBER 2003 Alexey Belyanin received the Ph.D. degree in physics in 1995 from the Institute of Applied Physics of the Russian Academy of Sciences. His studies focused on ultrafast coherent optical processes in semiconductors, quantum optics, QED processes in magnetized plasma, and high-energy astrophysics. In 1999 he joined the Department of Physics and the Institute for Quantum Studies at Texas A&M University, where he is currently an Assistant Professor. He has co-authored over 100 scientific papers. His current interests are in coherent nonlinear optics of semiconductor nanostructures and novel materials and schemes for quantum information processing. Dr. Belyanin is a recipient of the 1996 President of Russian Federation Award for Outstanding Young Scientists. He is a member of the Optical Society of America, European Astronomical Society, and International Committee on Space Research (COSPAR). A. Michael Sergent has been employed at Bell Laboratories, Murray Hill, NJ, since July He has been in the Semiconductor Research area since the latter part of He has worked on the luminescence properties of the CdS and ZnSe materials systems and has also performed C-V, C-T, and Deep Level Transient Spectroscopy measurements on GaAs. Since the early 1990s, he has been involved in semiconductor laser research, working on the electroabsorption modulated laser and most recently with the quantum cascade laser. Most of his work in this endeavor revolved around the cleaving and mounting of the devices. Deborah L. Sivco received the B.A. degree in chemistry from Rutgers University, New Brunswick, NJ, in 1980 and the M.S. degree in materials science from Stevens Institute of Technology, Hoboken, NJ, in In 1981, she joined Bell Laboratories, Lucent Technologies, Murray Hill, NJ, where she is currently a Member of Technical Staff in the Semiconductor Research Laboratory. She has been involved with MBE growth of III-V compounds since 1981 and has performed the crystal growth of GaAs AlGaAs and InGaAs InAlAs heterostructures for field-effect transistors, resonant tunneling transistors, bipolar transistors, double-heterostructure lasers, and detectors. She recently prepared the world s first quantum-cascade laser, designed by Faist et al., using bandgap engineering. She has coauthored more than 170 journal papers and holds 15 patents. Ms. Sivco was co-recipient of the Newcomb Cleveland Prize AAAS in 1994, the British Electronics Letters Premium Award in 1995, and a Technology of the Year Award from Industry Week magazine in Milton L. Peabody received the B.S. degree from the University of Maine, Orono. He has been employed at Bell Laboratories, Murray Hill, NJ, since February 1980, where he has been with the Advanced Lithography Research area. He has worked on the Electron Beam Exposure System IV for opticial photomask lithography and was a member of the Photomask Development Shop in the inspection, repair, and metrology areas. In the 1990s, he was a member of the SCALPEL project, electron beam lithography system, involved in wet silicon deep etching and thin metal low-stress films for the electron beam membrane mask. In 2000, he joined the Tuned Frequency Resonator group to do trench etching for the membrane release in this device. Since 2002, he has been involved in semiconductor laser research, working on the processing of the quantum cascade laser devices. Federico Capasso (M 79 SM 85 F 87) received the Ph.D. degree in physics (summa cum laude) from the University of Rome, Rome, Italy, in He joined Bell Laboratories first as a Visiting Scientist in 1976, and then as Member of Technical Staff in He is a Bell Labs Fellow and was Physical Research Vice President at Bell Laboratories, Lucent Technologies, Murray Hill, NJ, from 2000 until From 1997 to 2000, he headed the Semiconductor Physics Research department and from 1987 to 1997 he was Head of the Quantum Phenomena and Device Research department. He is currently the Gordon McKay Professor of Applied Physics and Vinton Hayes Senior Research Fellow in Electrical Engineering, Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA. He is internationally recognized for his basic and applied research on bandgap engineering and on atomically engineered semiconductor materials and devices and he is a co-inventor of the quantum-cascade laser. His work has opened up new areas of investigation in semiconductor science, mesoscopic physics, nonlinear optics, electronics, and photonics. He has coauthored over 300 papers, edited four volumes, and given over 150 invited talks at conferences. He holds over 35 U.S. patents and over 50 foreign patents. He is a member of the editorial boards of the Proceedings of the National Academy of Sciences and was previously on the editorial boards of Semiconductor Science and Technology, Il Nuovo Cimento, and Applied Physics Letters. Dr. Capasso is a Member of the National Academy of Sciences and the National Academy of Engineering and a Fellow of the American Academy of Arts and Sciences. He is a recipient of the R. Wood Prize of the Optical Society of America, the Duddell Medal of the Institute of Physics, the Willis Lamb Medal for Quantum Optics and Laser Physics, the John Price Wetherill Medal of the Franklin Institute, the Rank Prize for Optoelectronics, the W. Streifer IEEE LEOS Award, the Materials Research Society Medal, the Newcomb Cleveland Prize of the American Association for the Advancement of Science, the LMVH Vinci of Excellence Prize, the Heinrich Welker Memorial Medal, the Gallium Arsenide Symposium Award, the New York Academy of Sciences Award, the IEEE David Sarnoff Award in Electronics, the Capitolium Prize, the Alessandro Volta Medal from the University of Pavia, the Seal of the University of Bari, a Popular Science Award, an Electronics Letter Best Paper Prize, the AT&T Bell Laboratories Distinguished Member of Technical Staff Award, and the Award of Excellence of the Society for Technical Communications. He is an honorary member of the Franklin Institute and a Fellow of the Optical Society of America, the American Physical Society, the Institute of Physics (London), the American Association for the Advancement of Science, and SPIE. He is listed in the database of the most cited scientists of the Institute for Scientific Information (ISI). Nina Owschimikow received the M.S. degree from Darmstadt University of Technology in During her master s thesis at Lucent Technologies, Bell Laboratories, she studied nonlinear frequency mixing in quantum cascade lasers. Since 2003, she has been employed at Fresenius Medical Care, Germany, developing sensors for blood gas analysis. Alfred Y. Cho (F 81) was born in Beijing, China, in He received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign in 1960, 1961, and 1968, respectively. In 1968, he joined Bell Laboratories, Murray Hill, NJ, as a Member of Technical Staff and was promoted to Department Head in He was named Director of the Materials Processing Research Laboratory in 1987 and assumed his present position as Semiconductor Research Vice President in He is also an Adjunct Professor at the University of Illinois at Urbana-Champaign and is on the Board of Directors of Riber, Inc., and on the Board of Trustees of the College of New Jersey at Trenton. He has made seminal contributions to materials science and physical electronics through his pioneering development of the