CASCADED ORIENTATION-PATTERNED GALLIUM ARSENIDE OPTICAL PARAMETRIC OSCILLATOR FOR IMPROVED LONGWAVE INFRARED CONVERSION EFFICIENCY.

Transcription

1 CASCADED ORIENTATION-PATTERNED GALLIUM ARSENIDE OPTICAL PARAMETRIC OSCILLATOR FOR IMPROVED LONGWAVE INFRARED CONVERSION EFFICIENCY Dissertation Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree of Doctor of Philosohy in Electro-Otics By Ryan K. Feaver UNIVERSITY OF DAYTON Dayton, Ohio May 17

2 CASCADED ORIENTATION-PATTERNED GALLIUM ARSENIDE OPTICAL PARAMETRIC OSCILLATOR FOR IMPROVED LONGWAVE INFRARED CONVERSION EFFICIENCY Name: Feaver, Ryan K. APPROVED BY: Rita D. Peterson, Ph.D. Advisory Committee Chairman Senior Research Physicist Sensors Directorate Air Force Research Labs Joseh W. Haus, Ph.D. Committee Member Professor Deartment of Electro-Otics and Photonics Partha P. Banerjee, Ph.D. Committee Member Director and Professor Deartment of Electro-Otics and Photonics Monish R. Chatterjee, Ph.D. Committee Member Professor Deartment of Electrical and Comuter Engineering Robert J. Wilkens, Ph.D., P.E. Associate Dean for Research and Innovation Professor School of Engineering Eddy M. Rojas, Ph.D., M.A., P.E. Dean School of Engineering ii

3 Coyright by Ryan K. Feaver All rights reserved 17 iii

4 ABSTRACT CASCADED ORIENTATION-PATTERNED GALLIUM ARSENIDE OPTICAL PARAMETRIC OSCILLATOR FOR IMPROVED LONGWAVE INFRARED CONVERSION EFFICIENCY Name: Feaver, Ryan K. University of Dayton Advisor: Dr. Rita Peterson Otical arametric oscillators (OPOs) utilizing quasi-hase matched materials offer an aealing alternative to direct laser sources. Quasi-hase matched materials rovide a useful alternative to traditional birefringent nonlinear otical materials and through material engineering, higher nonlinear coefficients can now be accessed. Orientation atterned gallium arsenide (OPGaAs) is an ideal material because of its broad IR transmission and large nonlinear coefficient. In contrast to ferroelectric materials, such as lithium niobate, where the attern is fabricated through electric oling, zincblende materials, like OPGaAs, are grown eitaxially with the designed attern. Generating longwave outut from a much shorter um wavelength, however, is relatively inefficiency due to the large quantum defect when comared to similar devices oerating in the 3 5 µm regime. iv

5 One method to increase um to idler conversion efficiency is to recycle the undesired and higher energy signal hotons into additional idler hotons via a second nonlinear stage. An external amlifier stage can be utilized, where the signal and idler from the OPO are sent to a second nonlinear crystal in which the idler is amlified at the exense of the signal. Alternatively, the second crystal can be laced within the original OPO cavity where the signal from the first-stage acts as the um for the second crystal and the resonant intensity of the signal is higher. Puming the second crystal within the OPO should lead to higher conversion efficiency into the longwave idler. The grating eriod needed for the second crystal to use the signal from the first crystal to roduce additional idler has the fortuitous advantage that it will not hase match to the original um wavelength, avoiding unwanted nonlinear interactions. Therefore, a simle linear cavity can be utilized where the um from the first-stage will simly roagate through the second crystal without undesired results. Without this feature, the um would need to be couled out of the cavity before it enters the second crystal. Initial numerical simulations using a custom model, imlemented in MATLAB, for the roosed linear, two-stage, cascaded, OPGaAs nanosecond OPO suggest a significant imrovement in conversion efficiency over a single-stage device can be obtained. The numerical model includes diffraction, crystal loss, hase mismatch, um deletion, and back conversion, it assumes monochromatic waves and neglects grou velocity disersion. For a singly resonant oscillator (SRO) umed by a.5 µm Tm:Ho,YLF laser with 45 ns ulse width, the addition of the second crystal in the cavity increases idler generation by a factor of two and exceeds the quantum defect limit. v

6 Exerimentally, the cascaded OPGaAs OPO demonstrated a ~3% sloe efficiency. Limited outut may be the result of imroer hase matching, given that two distinct idlers wavelengths were observed. Tuning the OPGaAs crystals to generate identical idlers should imrove efficiency. The linewidth of the signal serving to um the second-stage likely reduced efficiency as well. To our knowledge, this is the first cascaded OPO using OPGaAs, and the first cascaded OPO oerating in the longwave infrared where the same longwave idler was generated in the both crystals. vi

7 ACKNOWLEDGEMENTS There are a few individuals whom deserve considerable areciation and whom I owe a great amount of gratitude. First and foremost, I would like to thank Dr. Rita Peterson for her invaluable advice, encouragement, insight, finger-whittling and overall guidance. Next, I would like to thank Dr. Peter Powers. His assion for science was infectious and the academic and general well-being of his students was always his to riority. He is deely missed. Without their guidance and tireless suort this dissertation would not have been ossible. Additionally, I would thank Dr. Joseh Haus for all of his hel with χ () and χ (3) nonlinear modeling. The reliminary OPA code he rovided served as the starting oint for construction of the single-stage OPO and cascaded OPO model. I would also like to thank my other committee members, Dr. Partha Banerjee and Dr. Monish Chatterjee, for their invaluable advice. I would like to thank my family, esecially my wife Emily for her continuous and endless suort and encouragement, esecially through the lengthy and taxing asects of graduate school. I would like to thank my arents for their ersistent suort and instilling the imortance of educational diligence at an early age. I would like to thank my brother Tyler and my sister Abbe, whom are also ursing their graduate degrees and whom I also have the umost admiration for. vii

8 Finally, I would like to thank my friends in the members of the Otoelectronics Technology Branch in the Sensors Directorate at Air Force Research Lab, and the Deartment Electro-Otics and Photonics at the University of Dayton for all of their suort. viii

9 TABLE OF CONTENTS ABSTRACT... iv ACKNOWLEDGEMENTS... vii LIST OF FIGURES... xii LIST OF TABLES... xvi CHAPTER 1 INTRODUCTION Motivation Current Infrared Sources Nonlinear Frequency Conversion Quasi-Phase Matching in GaAs Midwave Infrared Zincblende QPM Exerimentation Longwave Infrared Nonlinear Exerimentation Cascaded Nonlinear Devices Previous LWIR OPGaAs OPO Results Dissertation Overview CHAPTER NONLINEAR OPTICS BACKGROUND Parametric Process Nonlinear Suscetibility....3 Couled Amlitude Equations Poynting Vector and Phase Matching Quasi-Phase Matching Manley Rowe Otical Parametric Amlification Otical Parametric Generation Otical Parametric Oscillator Cascaded Otical Parametric Oscillator Polarization and Nonlinear Coefficient in OPGaAs ix

10 CHAPTER 3 NUMERICAL MODELING Slit-Ste Linear Ste: Beam Proagation Nonlinear Ste: Couled Amlitude Equations Model Parameters Inut Seed Energy... 5 CHAPTER 4 MODELING RESULTS Comarison to SNLO Cascaded OPO Intracavity Intensities Cascaded OPO Mirror Reflectivities Energy Scaling Cascaded OPO Limitations and Concerns CHAPTER 5 EXPERIMENTAL SET-UP Pum Laser OPGaAs Crystals Mirror Coating Reflectivities Polarization... 8 CHAPTER 6 EXPERIMENTAL RESULTS OPO Cascaded OPO Sectra CHAPTER 7 DISCUSSIONS AND NEAR-FUTURE EXPERIMENTATION Crystal Damage Crystal Transmission Temerature and Pum Tuning OPO Linewidth and Line Narrowing Additional OPGaAs Crystals OPO Pumed OPA... 1 CHAPTER 8 CONCLUSIONS REFERENCES APPENDIX A MODELING OPO FEATURES AND CHARACTERISTICS... 1 A.1 OPO Mirror Reflectivities A. Crystal Length A.3 Pulse Width x

11 A.4 Pum Sot Size A.5 Summary APPENDIX B SINGLE-STAGE OPO AND CASCADED OPO CODE OPO.m Grid.m GaAsSell.m Field.m Lens.m CavityBeamSize.m NormInBeam.m FSPro.m CrystalPro.m NLO4mix.m CascadedOPO.m CavityBeamSizeCascaded.m CascadedNLOmix1.m CascadedNLOmix.m xi

12 LIST OF FIGURES Figure 1: Atmosheric transmission.... Figure : Diagram of otical arametric generation Figure 3: Nikon microscoe image of OPGaAs domains (left) and image of bulk OPGaAs (right) Figure 4: All-eitaxial growth rocess of OPGaAs Figure 5: OPO erformance for SRO cavity showing both idler and combined outut (Samle number is in arentheses and sloe efficiency is listed in lot) Figure 6: OPO erformance for asymmetric cavity showing both idler and combined outut (Samle number is in arentheses and sloe efficiency is listed in lot) Figure 7: OPO erformance for SRO cavity showing both idler and combined outut (Samle number is in arentheses and sloe efficiency is listed in lot) Figure 8: OPO erformance for DRO showing both idler and combined outut (Samle number is in arentheses and sloe efficiency is listed in lot) Figure 9: Phase sliage between electric field and nonlinear olarization Figure 1: Time averaged intensity as field and induced olarization roagate along crystal Figure 11: Comarison between 1st and 3rd order QPM vs. no QPM Figure 1: Diagram of cascaded difference frequency generation where the signal from the first-stage is used as a um for a second interaction Figure 13: Illustration of OPA where the signal is amlified and an idler is generated in a QPM material Figure 14: Illustration of otical arametric generation where the signal and idler are generated in a QPM material Figure 15: Illustration of an otical arametric oscillator Figure 16: Normalized OPO temoral outut ulse Figure 17: Illustration of a linear cascaded otical arametric oscillator xii

13 Figure 18: Pum roagation with resect to OPGaAs crystal geometry (left); olarization directions of inut um and resulting signal field (right) Figure 19: Theoretical effective nonlinear coefficient deff as a function of the angle between the um beam olarization vector and the OPGaAs [11] direction Figure : Boundary conditions of the OPO Figure 1: Linear cascaded OPGaAs OPO Figure : Illustration of temoral lots of OPO outut from SNLO (left) and MATLAB (right) Figure 3: Comarison of temoral lots of OPO outut from SNLO (left) and MATLAB (right) Figure 4: Internal intensities of cascaded OPO Figure 5: Idler energy deendence on M reflectivity at λs and λi % loss Figure 6: Idler energy deendence on M reflectivity at λs and λi 1% loss Figure 7: Idler energy deendence on M reflectivity at λs and λi % loss Figure 8: Idler energy deendence on M reflectivity at λs and λi 1% loss Figure 9: Idler energy deendence on M reflectivity at λs1 and λi % loss Figure 3: Idler energy deendence on M reflectivity at λs1 and λi 1% loss Figure 31: Idler energy deendence on M1 and M reflectivity at λs % loss (% R of λi at M) Figure 3: Idler energy deendence on M1 and M reflectivity at λs 1% loss (% R of λi at M) Figure 33: Idler energy deendence on M1 and M reflectivity at λs % loss (6% R of λi at M) Figure 34: Idler energy deendence on M1 and M reflectivity at λs 1% loss (6% R of λi at M) Figure 35: Temoral structure of the fields at wavelengths λ, λs1, λs, and λi; the cavity outut is lotted from M Figure 36: Temoral structure of the fields at wavelengths λ, λs1, λs, and λi; the cavity outut is lotted from M Figure 37: Numerical comarison in idler erformance between OPGaAs SR- COPO and SRO Figure 38: Numerical comarison in idler conversion efficiency OPGaAs SR- COPO and SRO Figure 39: Numerical comarison in idler erformance between OPGaAs DR- COPO and DRO xiii

14 Figure 4: Numerical comarison in idler conversion efficiency of OPGaAs DR-COPO and DRO Figure 41: Conversion efficiency lot of DR- and SR-COPO Figure 4: Pum Sectra Figure 43: Cascaded turning curves Figure 44: Cascaded OPGaAs OPO Figure 45: Cascaded OPGaAs OPO M1 mirror transmission Figure 46: Cascaded OPGaAs OPO M mirror transmission Figure 47: Longwave OPGaAs OPO M1 mirror transmission... 8 Figure 48: Sloe efficiency of samles Figure 49: Sloe efficiency lots of first-stage crystals in OPO Figure 5: Idler sloe efficiency comarison Figure 51: Sloe efficiencies cascaded OPGAs OPO with samle 46 along with the three different secondary crystals Figure 5: Sloe efficiencies cascaded OPGAs OPO with samle 5 along with the three different secondary crystals Figure 53: Image of idler (left) and signal (right) Figure 54: Signal 1 from cascaded OPO with Λ1=76.6 µm Figure 55: Signal from cascaded OPO with Λ1=76.6 µm Figure 56: Idler from cascaded OPO with Λ1=76.6 µm Figure 57: Signal 1 from cascaded OPO with Λ1=76. µm Figure 58: Signal from cascaded OPO with Λ1=76. µm Figure 59: Idler from cascaded OPO with Λ1=76. µm Figure 6: Damage on LWIR OPGaAs samle Figure 61: Theoretical outut of the two OPGaAs crystals as a function of um wavelength using Λ1=76. µm Figure 6: Theoretical outut of the two OPGaAs crystals as a function of um wavelength using Λ1=76.6 µm Figure 63: Theoretical oututs of the two OPGaAs crystals as only Λ1=76.6 µm is heated while Λ=15 µm temerature remains (Note: as the figure shows a temerature deendence on Λ, the temerature deendence originates in the hase matching conditions altered by the first crystal) Figure 64: Theoretical oututs of the two OPGaAs crystals as only Λ=15 µm is heated while Λ1=76.6 µm temerature remains Figure 65: Theoretical oututs of the two OPGaAs crystals as Λ1=76.6 µm and Λ=15 µm are heated simultaneously xiv

15 Figure 66: Theoretical oututs of the two OPGaAs crystals as only Λ1=76. µm is heated while Λ=15 µm temerature remains Figure 67: Theoretical oututs of the two OPGaAs crystals as only Λ=15 µm is heated while Λ1=76. µm temerature remains Figure 68: Theoretical oututs of the two OPGaAs crystals as Λ1=76. µm and Λ=15 µm are heated simultaneously Figure 69: Brewster cut cascaded monolithic OPGaAs crystal OPO Figure 7: Signal outut from a single-stage OPO uming an external OPA to amlify the idler Figure 71: Combined signal and idler outut as a function of outut mirror reflectivities. The inut um ulse energy is 75 µj inut Figure 7: Combined signal and idler outut as a function of outut mirror reflectivities. The inut um ulse energy is 1 µj inut Figure 73: Combined signal and idler outut as a function of outut mirror reflectivities. The inut um ulse energy is 3 µj Figure 74: Normalized lot of SRO at 3 µj inut Figure 75: Normalized lot of DRO configuration at 3 µj inut Figure 76: Combined signal and idler outut as a function of outut mirror reflectivities. The inut um ulse energy is 75 µj Figure 77: Normalized temoral structures of the um, signal, and idler in a SRO configuration with inut ulse energy of 75 µj Figure 78: Normalized temoral structures of the um, signal, and idler in a DRO configuration with inut ulse energy of 75 µj Figure 79: Combined signal and idler outut as a function of outut mirror reflectivities. The inut um ulse energy is OPO 3 µj inut energy Figure 8: Signal and idler energies with resect to crystal length (with changing cavity length: Solid line is at an inut of 4 µj and the dashed line is at an inut of µj) Figure 81: Signal and idler energies with resect to crystal length (with constant 5 cm cavity length: Solid line is at an inut of 4 µj and the dashed line is at an inut of µj) Figure 8: Signal and idler OPO outut vs ulse width for a DRO configuration (Solid line inut energy of 4 µj and dashed line, inut of µj) Figure 83: Signal and idler OPO outut vs ulse width for a SRO configuration (Solid line inut energy of 4 µj and dashed line, inut of µj) Figure 84: Signal and Idler outut deendence of um sot size for a DRO and SRO configuration xv

16 LIST OF TABLES Table 1: Table of commonly used nonlinear crystals (QPM materials have their effective nonlinear coefficients reduced by a factor of /π. LiNbO3 use QPM only when oled (PPLN); un-oled it uses BPM) Table : Summary of grating eriods and associated wavelengths involved in the cascaded rocess Table 3: Outut energy comarison between SNLO and MATLAB Table 4: Outut energy comarison between SNLO and MATLAB Table 5: Modeled mirror reflectivities, varying reflectivity of λs and λi at M Table 6: Modeled mirror reflectivities, varying reflectivity of λs and λi at M Table 7: Modeled mirror reflectivities, varying reflectivity of λs1 and λi at M Table 8: Modeled mirror reflectivities, varying reflectivity of λs at M1 and λs at M Table 9: Modeled mirror reflectivities, varying reflectivity of λs at M1 and λs at M Table 1: Samle list of cascaded OPO samles Table 11: Pum transmission through samles with eriod s Λ1 and Λ xvi

17 CHAPTER 1 INTRODUCTION 1.1 Motivation Broadly tunable, coherent infrared laser sources, articularly in the midwave ( 5 μm) and longwave sectral regimes (8 1 μm), corresonding to the atmosheric transmission windows shown in Figure 1 [1], are in high demand for various military and commercial alications. Desite a growing demand for sources, unfortunately few laser materials exist with the required roerties to oerate directly in these regions. Through the broad field of nonlinear otics, frequency conversion devices, such as otical arametric oscillators (OPOs), have been develoed as an alternative for generating tunable sources in the mid- and longwave IR. One widely used aroach to cover the infrared sectral range is based on the down conversion of mature, well-develoed solid-state lasers. Due to a laser's high temoral and satial coherence they serve as excellent um sources for nonlinear rocesses. While OPOs can generate broadly tunable radiation, the outut wavelengths are constrained by the hase matching conditions and the transarency range of the nonlinear crystal in use. 1

18 Figure 1: Atmosheric transmission. 1. Current Infrared Sources Throughout the entire mid infrared sectral region, there are numerous gas where laser sources are either scarce or nonexistent. Notable and well-develoed infrared sources include solid-state lasers, gas lasers and semiconductor lasers. Crystals and glasses doed with rare-earth ions, such as neodymium (Nd 3+ ), erbium (Er 3+ ), thulium (Tm 3+ ), raseodymium (Pr 3+ ) and holmium (Ho 3+ ) [], are excellent candidates for visible and near infrared lasers due to their narrow fluorescent transitions in these regions. Due to their trivalent nature, the electronic transition occurs in the 4f shell and their otical roerties are largely shielded from the host lattice. Rare earth doed lasers are commercially available but their emission wavelengths are limited to 1 3 μm. Transition metal ion doed crystals, such as zinc chalcogenides doed with divalent chromium (Cr + ) [3] and iron (Fe + ) [4], have large absortion and transmission bands that lead to large gain bandwidths and broadly tunable outut. In zinc selenide, chromium will lase between.4.7 µm and iron between 4 5 μm. Additionally, there are gas lasers oerating in these regions, articularly the carbon dioxide (CO) laser which emits around 9. μm and 1.8 μm and can roduce large outut

19 owers but these systems are often large, fragile, and lack continuous tunability. Helium neon (HeNe) gas lasers tyically oerate at 63.8 nm but also have a transition which emits at 3.38 µm, though the outut owers are relatively low. Quantum cascade lasers (QCLs) [5, 6], and rior to that lead-salt lasers [7], offer a large variety of infrared laser oututs through engineered semiconductors. QCLs utilize intersubband transitions in series of quantum wells and can be designed to oerate in the 8 1 µm regime [8]. While all of these laser sources have their articular advantages and limitations, nonlinear arametric frequency conversion offers an alluring alternative to current laser sources, articularly in tunability and the ability to engineering articular interactions. 1.3 Nonlinear Frequency Conversion Since Franken et al. first demonstrated second harmonic generation in quartz [9] and Giordmaine and Miller [1] first demonstrated the OPO in 1961, the field of nonlinear otics has been raidly exanding. One key feature of nonlinear otics is the generation of light at new frequencies as an intense field roagates through a material. Unlike in a laser, instead of exloiting the atomic energy structures of a material, these new frequencies are generated through the materials induced nonlinear olarization. Frequency down conversion occurs where the energy in a given hoton, named the um, is slit into two lower-energy, lower frequency hotons, hence the term down conversion. By convention, the higher energy outut hoton is labeled the signal and the lower energy hoton is labeled the idler. This otical henomenon is the basis for what is called three-wave mixing and it is fundamental in such nonlinear interactions as second harmonic generation (SHG), difference frequency generation (DFG) and sum frequency generation (SFG). One of the 3

20 constraints on nonlinear frequency conversion is conservation of energy where the sum of the signal and idler hoton energies must equal the energy of the um. A visual reresentation of this rocess is given in Figure. (The theory of difference frequency generation is resented in Chater ). Figure : Diagram of otical arametric generation. A second constraint on nonlinear otical rocesses is the conservation of momentum, or hase matching, where the sum of the wave vectors of the signal and idler must equal that of the um. This condition is ordinarily not satisfied in isotroic material, where normal disersion alies. Therefore, nonlinear otical frequency conversion was long dominated by birefringent hase matching (BPM) where the index of refraction of the nonlinear crystal varies with roagation direction and olarization. Imressive results have been obtained from birefringent nonlinear crystals such as zinc germanium hoshide (ZnGeP or ZGP) [11], silver gallium selenide (AgGaSe or AGS) [1], lithium niobate (LiNbO3) [1], and more recently cadmium silicon hoshide (CdSiP or CSP) [13]. The reliance on birefringent hase matching limits the oerating range of these devices and also introduces comlicating factors, such as electric field walk-off. Walk-off 4

21 degrades the erformance of nonlinear devices given that the beams lose their satial overla during roagation, limiting both the interaction length and conversion efficiency. It is ossible to comensate for walk-off using two successive nonlinear crystals where the second crystal reverses the walk-off roduced by the first crystal [14], but this adds to the comlexity of the overall system. Another drawback is that only certain combinations of crystal orientation and electric field olarization will suort hase matching, and while there are numerous materials that allow this, a material s largest nonlinearity may not be accessible. The most notable case is that of LiNbO3 where its d33 nonlinear coefficient cannot be exloited through BPM but it can be accessed through an alternative aroach called quasi-hase matching (QPM). The efficiency of the nonlinear rocess is related to the magnitude of the material s nonlinear coefficient, which is directly roortional to the induced nonlinear olarization and the material s electronic suscetibility. In isotroic materials, or birefringent materials where it is not ossible to achieve hase matching, the nonlinear conversion results in eriodic transfers of energy between the um and the converted fields which yields no areciable buildu of the signal and idler. In QPM the nonlinear material is eriodically inverted, essentially reversing the nonlinear coefficient, to ensure a continual buildu of the converted field, as was first roosed by Armstrong et al. in 196 [15]. QPM is a very advantageous technique because not only is birefringence no longer a requirement for hase matching, but now a secific desired interaction can be achieved by engineering the aroriate eriodic inversion in the material. This is exlained in more detail in Chater. QPM has seen a large degree of success in the midwave and historically has been dominated by ferroelectric materials including eriodically oled lithium tantalite (PPLT) 5

22 [16], otassium titanyl hoshate (PPKTP) [17], and most notably lithium niobate (PPLN) [18]. QPM structures can be fabricated in ferroelectric materials via electric field oling. By alying a large electric field using atterned electrodes, a ermanent reversal of the crystal structure in alternating domains can be engineered. The use of these ferroelectric materials as nonlinear crystals is limited to wavelengths below ~4 μm due to strong multihonon absortion at longer wavelengths. Zincblende semiconductors, such as gallium arsenide (GaAs) [19], gallium hoshide (GaP) [], and zinc selenide (ZnSe) [1], on the other hand, are known to have large infrared transmission ranges and relatively large nonlinear coefficients. Additionally, the highly symmetric nature of the cubic class of zincblende semiconductors allows for arametric conversion without being inhibited to articular inut olarizations states. Orientation atterned gallium arsenide (OPGaAs), shown in Figure 3, has been used in numerous nonlinear devices in both the midwave [ 4] and the longwave-ir [5 7] sectral regions. Devices have been demonstrated in almost every time domain ranging from continuous-wave (cw) [8, 9] to the nanosecond (ns) regime [ 7] to the ultrafast [3 3]. Its broad transarency (.9 17 µm), high second-order nonlinearity (d14~94 m/v), high thermal conductivity (.5 W cm -1 K -1 ) [19], and ability to be atterned through a mature eitaxial growth rocess make it a rime candidate for QPM-based nonlinear devices. A concise summary of various nonlinear materials is resent in Table 1 comaring OPGaAs with other currently imlemented nonlinear crystals. One limitation, however, is the material s strong two-hoton absortion, which restricts OPGaAs-based devices to um sources with wavelengths longer than ~1.8 μm. Direct μm solid-state laser um 6

23 sources, like Tm,Ho:YLF, are favored for their maturity, relative simlicity, and intrinsically narrow linewidth. Figure 3: Nikon microscoe image of OPGaAs domains (left) and image of bulk OPGaAs (right). Table 1: Table of commonly used nonlinear crystals (QPM materials have their effective nonlinear coefficients reduced by a factor of /π. LiNbO3 use QPM only when oled (PPLN); un-oled it uses BPM). GaAs PPLN GaP ZnSe GaN ZGP AGS CSP Effective Nonlinear coefficient (m/v) Transarency Range (µm) Phase matching tye Thermal Conductivity (W/m K) Damage Threshold (J/cm ) References 19, 33, QPM QPM QPM QPM QPM BPM BPM BPM > 3* , 35, 36, 34, 58, 59 11, 14, 1, 37 38, 39, 4, 56, 14, 41, 4, 43 44, 45 13, 46, 47 *Damage threshold is unublished and gathered from ersonal conversations with Dr. Kent Averett 1.4 Quasi-Phase Matching in GaAs One of the first methods used to quasi-hase match GaAs involved lacing a series of GaAs lates with alternating orientations at Brewster s angle [48]. Later methods included diffusion bonding stacks of alternating GaAs wafers, thinned to the required 7

24 thickness, to create a single monolithic structure and to eliminate the losses from the airsemiconductor interfaces during the bonding rocess [49]. Both aroaches demonstrated the feasibility of QPM in GaAs, but were too lossy to suort a ractical device. Achieving QPM in GaAs through wave vector reversal via total internal reflection also roved to be fairly difficult [5]. Imroving uon these techniques, an all-eitaxial rocess was eventually develoed to fabricate OPGaAs [51, 5], relacing the tedious rocess of olishing and stacking GaAs lates. The eitaxial rocess starts with a temlate on which the bulk atterned material can then be grown. The OPGaAs temlate is grown through molecular beam eitaxy (MBE), while the bulk of the atterned material is grown by hydride vaor hase eitaxy (HVPE). The temlate is created by growing an inverted layer of GaAs, where the sign of the nonlinear coefficient is reversed, on a <1> GaAs substrate cut off-axis by 4 toward <111B>. In order to roduce the inverted layer, a thin layer of Ge is included, which is grown on an intermediate GaAs/AlGaAs suerlattice to minimize strain from the lattice mismatch. GaAs has a face-centered cubic lattice with 43 crystal symmetry. Since the <1> axes have a 4 symmetry, a 9 rotation about any of the [1] axis is equivalent to inversion. The combination of the substrate miscut and the Ge layer creates a vicinal surface that favors the growth of a single-domain layer whose orientation is inverted relative to that of the substrate. Lithograhy and etching are then used to remove the to layer of GaAs at the roer intervals resulting in the desired QPM eriod. The samle is then laced back in the MBE chamber for a thin regrowth layer. The exosed GaAs substrate 8

25 and the thin layer of inverted GaAs both reserve their oosite domain orientations as they grow. The MBE growth results in a 3 μm thick layer of atterned GaAs. After the OPGaAs temlate has been grown, the bulk of the atterned material is grown by HVPE. HVPE will grow the material on the order of 1x faster than MBE, to thicknesses of ~1 mm or more. The OPGaAs fabrication rocess is summarized in Figure 4 [5]. While 1 mm thick samles are more than enough for resonant modes of a tyical OPO, aerture sizes much larger have not been systematically roduced and ower scaling is more readily achieved by increasing reetition rate than by increasing beam sizes [53 55]. Figure 4: All-eitaxial growth rocess of OPGaAs. Gallium arsenide (GaAs) was the first zincblende semiconductor used to demonstrate QPM. Material develoment efforts are now aimed at gallium nitride (GaN), gallium hoshide (GaP), and zinc selenide (ZnSe). GaN is of interest for some alications due its large damage threshold, due to its large band-ga in the UV, but its otential for nonlinear devices is limited due to a relatively small nonlinear coefficient, 17 m/v, and its mid-ir transarency extends only to ~6 µm [56, 57]. 9

26 GaP and ZnSe have lower nonlinearities, comared to GaAs, but they have the advantage of negligible two-hoton absortion (TPA) at 1 µm and 1.5 µm where mature, commercially-available um lasers based on Nd, Yb, and Er oerate. As mentioned before, due to its strong TPA, GaAs is limited to um sources oerating > 1.8 µm. Orientation atterned GaP (OPGaP) can be grown using a rocedure similar to that used for growing OPGaAs. Promising OPGaP growth results have been demonstrated on both OPGaAs [58] and OPGaP temlates [59]. So far, no native temlate technology has been develoed for orientation atterned ZnSe (OPZnSe). OPZnSe films grown on OPGaAs temlated via hysical vaor transort were limited in both thickness and frequency conversion erformance [1]. 1.4 Midwave Infrared Zincblende QPM Exerimentation Notable OPGaAs and OPGaP-based devices oerating in the midwave infrared regime are reviewed below. Vodoyanov et al. demonstrated a successful OPO using eitaxially grown OPGaAs with a eriod of 61. µm, umed with a PPLN OPO umed by a Nd:YAG laser, and temerature tuned between 1.8 and μm. The exeriment studied the um tuning versus signal and idler outut wavelengths while the SRO design achieved a sloe efficiency of 54% and a threshold of 16 μj for the 6 ns um ulses []. In 5 Schunemann et al. reorted an OPGaAs OPO using a 6 μm eriod [3]. Peterson et al. reort similar results in their OPGaAs OPO [4] with sloe efficiencies > 6%. Kieleck et al. demonstrated u to.9 W at a khz reetition rate, 3.9 W at 4 khz and 4.9 W at 5 khz, using a.9 μm Q-switched Ho:YAG laser um source [53]. OPGaAs was comared to ZGP and CSP under identical uming conditions with a Tm:YAP laser. Both 1

27 ZGP and OPGaAs outerformed CSP [47]. Later, in 1, Pomeranz et al. demonstrated the first cw OPGaAs OPO [8]. The maximum combined signal and idler conversion efficiency was 3.6% and at an inut ower of 5 W, the 4.7 µm idler was over 4 W. The first Cr:ZnSe umed OPO was demonstrated, using a synchronously umed resonator to roduce a frequency comb [9]. The first OPGaP OPO was demonstrated in 15, generating 35 mw with a sloe efficiency of 16% [6] and a 1 µm umed OPGaP OPO has also been demonstrated [61]. 1.5 Longwave Infrared Nonlinear Exerimentation Longwave (8 µm) idlers were demonstrated in OPGaAs by DFG of two diode lasers at 1.3 and 1.55 µm [6]. Vodoyonov et al. demonstrated continuous infrared tuning from a singly resonant ZGP OPO that was umed by a.93 µm erbium laser and yielded outut that was continuously tunable from 3.8 µm 1.4 µm (tye I hase matching) and from 4 to 1 µm (tye II hase matching) [63]. Similar tunability was observed from a 3-µmumed OPGaAs OPO where continuous signal and idler tuning was observed from 4 µm 14. µm [64]. More recently, Maidment et al. demonstrated tunability from 5 µm 1 µm in a femtosecond OPGaP OPO [65]. An OPGaAs OPO was recently demonstrated with a quantum conversion efficiency of 36% at 1.6 µm [5] and Clement et al. reorted on a single frequency OPGaAs OPO at 1.4 µm [6]. 1.6 Cascaded Nonlinear Devices As the um hoton is slit between the signal and idler, most of the converted energy will reside in the shorter wavelength signal. When converting a µm um source 11

28 into the longwave IR, in articular, this yields large a quantum defect, but it is ossible to recycle the energetic signal hotons into more idler. This can be accomlished by means of a second nonlinear crystal in which the signal will be used as the um for a second nonlinear interaction designed to roduce more of the same idler, thus imroving overall conversion efficiency into the idler. This cascaded or tandem nonlinear interaction can occur in an external amlifier stage as demonstrated by Powers and Haus [66, 67] where a three-fold increase in idler generation was observed by using two external otical arametric amlifiers (OPAs) to amlify a PPLN otical arametric generator (OPG). Additionally, the cascaded nonlinear interaction can occur with the OPO cavity itself, where the resonant intensities are tyically large. This second aroach is the focus of this thesis. Previous investigations of the dynamics of cascaded OPOs have included the extensive theoretical and exerimental develoment by Moore and Koch [66 73] of singly resonant OPOs with various additional intracavity stages including DFG [71], SFG [7], and SHG [73]. Further theoretical develoment of ulsed otical arametric oscillators with intracavity otical arametric amlifiers in the lane-wave regime was comleted by Melkonian [74]. With a high Q-cavity at the resonant signal field and the roer choice of couling arameters, conversion efficiencies at the idler wavelength in a PPLN OPO were modeled at 197% [71]. An idler hoton conversion efficiency of 11% was demonstrated exerimentally with the secondary crystal roerly hase matched [75]. Through a similar OPO and cascaded DFG rocess, a continuous-wave, tunable idler from µm was generated in a PPLN OPO [76] and in a synchronously umed PPLN OPO where tunable idlers were generated from μm [77]. Intracavity amlification of the 1

29 idler from a PPLN cascaded OPO utilizing a single dual-grating PPLN crystal lead to 6% increase of the 4 μm idler ower [78]. Naraniya [79] and Porat [8] rovided numerical modeling of a similar cascaded technique, but instead of using dual nonlinear crystals, they imlemented a quasi-eriodic MgO:PPLN cascaded OPO that simultaneously hase matches to the OPO and DFG rocess within the same crystal for efficient idler generation. It has been roosed that increased idler generation in LWIR OPGaAs can be achieved by quasi-eriodic gratings that hase match both an OPO and a DFG rocess simultaneously in the same crystal [81]. Other schemes to achieve longwave idlers include 1 µm umed cascaded OPOs where midwave oututs from the first-stage are used to um a second-stage crystal to yield longwave outut. These include a 1-µm-umed couled tandem OPO where a KTP OPO umed a ZGP OPO, both of which were contained within the same cavity [8], a 1-µm-umed PPKTP-umed-AGS intracavity OPO [83], and a 1-µm-umed PPKTP-umed-BaGa4Se7 intracavity OPO [84]. 1.7 Previous LWIR OPGaAs OPO Results We reviously demonstrated LWIR generation from µm in a single-stage OPGaAs OPO [6] using three different grating eriods (Λ=76, 8, and 84 µm). Overall sloe efficiencies reached ~6% with a good beam quality, M ~1., but the maximum idler sloe efficiency obtained was only ~8%. In the singly resonant OPO (SRO) ~35 µj of idler was extracted for 7 μj of inut ower, resulting in a conversion efficiency of 5.% and a um-to-idler hoton conversion of only 1.4% at 8.8 µm. Efficiencies for the 1.7 µm and 11.5 µm idlers were even lower. 13

30 A different set of mirrors was borrowed from BAE Systems, forming a cavity which outcouled the signal and idler at the inut and outut mirrors resectively. This low-q, asymmetric, cavity was originally designed for a system where back conversion was a roblem, and by reventing either the signal or idler from building u a strong resonance in the cavity, the onset of back conversion was delayed to higher um energies. Consequently, and as exected, the conversion to signal and idler energy from the um was also lacking resulting in lower sloe efficiencies and higher thresholds. The sloe efficiencies obtained from the SRO cavity is shown Figure 5 and sloe efficiencies from the asymmetric cavity is shown in Figure 6. Figure 5: OPO erformance for SRO cavity showing both idler and combined outut (Samle number is in arentheses and sloe efficiency is listed in lot). 14

31 6 Outut Energy (J) =76 m (6) Total =1.5% =8 m (9) Total =.6% =84 m (7) Total =5.3% =84 m (8) Total =8.5% =76 m (6) Idler =4.5% =8 m (9) Idler =1.% =84 m (7) Idler =1.4% =84 m (8) Idler =.5% Inut Energy (J) Figure 6: OPO erformance for asymmetric cavity showing both idler and combined outut (Samle number is in arentheses and sloe efficiency is listed in lot). High round tri cavity losses due to non-otimal crystal and mirror coatings limited outut and conversion efficiency, articularly for the idler. Figure 7 and Figure 8 show udated sloe efficiency lots where we've been able to increase OPO outut due to imroved mirrors coatings but still with the non-otimal crystal coatings. Figure 7 lots the sloe efficiencies from the SRO OPO cavity while the Figure 8 lots the sloe efficiencies from a doubly resonant OPO (DRO) configuration. Overall erformance in the SRO cavity is slightly worse, comared to the DRO cavity, but there were slight imrovements in the sloe efficiency of the idler. Imroved anti-reflective (AR) crystal coatings covering the entire range of OPO wavelengths should allow us to imrove further on our revious results. The figure shows how most of the energy of the OPO outut is contained in the signal. 15

32 15 15 = 76 m T = 15.7% = 8 m T = 5.5% = 84 m T = 3.5% Outut Energy (J) = 84 m T = 4.1% = 76 m i = 11.7% = 8 m i = 4.3% = 84 m i =.7% = 84 m i = 3.3% Inut Energy (J) Figure 7: OPO erformance for SRO cavity showing both idler and combined outut (Samle number is in arentheses and sloe efficiency is listed in lot). Outut Energy (J) = 76 m T = 31% = 8 m T = 8% = 84 m T = 7% = 84 m T = 7% = 76 m i = 1% = 8 m i = 3% = 84 m i = % = 84 m i = % Inut Energy (J) Figure 8: OPO erformance for DRO showing both idler and combined outut (Samle number is in arentheses and sloe efficiency is listed in lot). 1.8 Dissertation Overview A cascaded OPGaAs OPO has not been reviously reorted. To demonstrate such a device is the natural extension of the revious LWIR OPGaAs work where the energetic signal clearly dominated the OPO outut. Chater this dissertation describes the 16

33 fundamental nonlinear otical theory relevant to cascaded OPO oeration. Due to the significant increase in comlexity given the fields involved, cascaded systems are numerically modeled. Chater 3 introduces and discusses numerical modeling of nonlinear interactions via Fourier slit-ste method in both single-stage OPOs and cascaded OPOs. Chater 4 then discusses the numerical results and validates the model with widely acknowledged numerical modeling software SNLO [85] for the single-stage OPO case. The exerimental set-u is then introduced in Chater 5 and resents the exerimental results from the cascaded OPO are resented in Chater 6. Chater 7 finally discusses the results and suggests further exerimentation to imrove OPO erformance. Finally, Chater 8 rovides conclusions to this dissertation. 17

34 CHAPTER NONLINEAR OPTICS BACKGROUND There are numerous resources readily available on theory of nonlinear otics [86 9], and in articular on OPOs [93 98] and cascaded OPOs [66 74]. Therefore the theoretical ortion of this roosal will serve more as a brief introduction and overview to χ () rocesses and quasi-hase matching on a macroscoic level, and how they relate to the exerimental work underway. A more comlete descrition of nonlinear suscetibilities and rocesses would take a quantum aroach that is outside the scoe of the research, so classical aroach is taken instead. The nonlinear induced olarization is the rincial factor for achieving frequency conversion through arametric rocesses. In linear otics, in the resence of an electric field an induced olarization will be generated in the material. This induced olarization deends on the strength of the electric field resent and is described by P o E, (1) where χ is known as the suscetibility and εo is the ermittivity of free sace. With higher intensity fields, such as those created by a focused laser, the induced olarization will start exhibiting nonlinear resonses and will deviate from the linear model. Thus higher ordered olarization terms are needed to correct for the behavior of the induced olarization. The 18

35 olarization can be exanded into a ower series and exressed with both linear and higher order nonlinear terms given by P o E E E, () where χ (1), χ () and χ (3) are known as the first, second and third order nonlinear suscetibilities resectively. The first term is known as the linear olarization and is the same as given in Equation 1. We assume that the resonse of the material suscetibility is instantaneous and any delayed resonse in the material from the electric field is negligible. This assumtion holds true for arametric interactions in the nanosecond regime but the material resonse cannot be neglected with ulses in the femto- and icoseconds regimes. An OPO exloits second order nonlinear interactions so only χ () rocesses are considered and the induced olarization is reresented by P Therefore, if we exand the cross term with trigonometric identities we get 19 o E. (3).1 Parametric Process The resulting induced nonlinear olarization will drive the arametric rocess. Various nonlinear rocesses can be shown classically, using an inut field consisting of the suerosition of two monochromatic lane waves roagating in the z-direction, which is given by E E k z t E cosk z t cos, (4) where by convention, ω>ωs. Therefore, the lowest nonlinear olarization term, P (), is given by E cos k z t Es cos ksz st s o E Es cos ksz st s cos k z t s P. (5) s s s

36 s s s s s s s s s s s s s o t z k k E E t z k k E E E E t z k E t z k E P cos cos 1 cos 1 cos 1. (6) The equation above indicates that for a field consisting of two suerimosed monochromatic lane waves, the induced nonlinear olarization has a resonse at the second harmonic of ω and ωs, an otically rectified field, and resonses at the sum and difference frequencies of ω and ωs. Each term reresents a different rocess and all are resent within the olarization. The contributions are relatively weak comared to the linear olarization and each rocess does not affect the other. Tyically, a given rocess can be isolated through various hase matching techniques. With most χ () rocesses we assume that the hoton energies are not resonant with any real electronic states of the material. As new frequencies are generated, at the sum or difference frequency for examle, energy needs to be conserved. The energy of the generated hoton, at frequency ωi, for difference frequency generation, is given by s i. (7). Nonlinear Suscetibility The origin of the nonlinearity in the system resides in the resonse of the nonlinear material, i.e. χ () suscetibility. For dielectric media in the classical model, the electrons are bound to the host and held in equilibrium by a quadratic otential well. As the electron

37 is erturbed, it exeriences a linear restoring force, which takes the form of Hooke s law and behaves similarly to a mass on a sring in a harmonic oscillator. As the incident field strength increases, the behavior of the electron deviates from this harmonic behavior and the restoring force can be described as that of an anharmonic oscillator. Here, it is assumed that the electrons in the material behave indeendently of each other and local field corrections are ignored. Therefore, the induced olarization is then taken as a collection of electron oscillators. In materials, such as glasses and gases, that exhibit inversion symmetry, called centrosymmetric materials, the χ () nonlinearity vanishes and in threewave mixing rocesses are rohibited. Thus only non-centrosymmetric materials can be used in χ () rocesses. The χ () suscetibility links the inut fields to the nonlinear olarization. It is often necessary to account for more general coulings and χ () should be exressed as a tensor based on all inut frequency combinations and roagation directions. In ractice, however, only a single interaction is tyically of interest and χ () can be determined based on the given interaction s roagation direction and inut olarization. It is often customary to refer to χ () in terms of a d-tensor where the relationshi between d and χ () is 1 d. (8).3 Couled Amlitude Equations Each field in () rocesses must satisfy Maxwell s electromagnetic wave equations, given by H E o, (9) t 1

38 H J oe P, (1) t where µo is the ermeability of free sace, o is the ermittivity of free sace, the olarization vector has a linear and nonlinear comonent such that P =P L +P NL. This yields the nonlinear wave equation E PL PNL E o o o o, (11) t t t where is the Lalacian of the electric field. It is imortant to note the term Equation 11 is the driving term. Assuming lane wave roagation along the z-axis, the um, signal, and idler beams with frequencies, s, and i resectively, can be reresented in comlex form as t P NL in A A A s i A A A i s z i e i ze i ze k z t k z s k z i t s t i c. c., (1) c. c., (13) c. c.. (14) The comlex form of the inuts must satisfy the wave Equation 11 and by convention >s>i. This yields a set of couled equations for a single ass through a loss-less medium ik A z ei k z c d eff A A e s i i k k z s i, (15) ik s As ik z s s e deff A * i z c i A e k ki z, (16)

39 ik i Ai ik z i i\ e deff A * s z c i A e k ks z, (17) where deff is the effective nonlinear coefficient. The left side of each equation describes a given field s evolution as it roagates through the nonlinear crystal, while the right side describes the induced nonlinear olarization. One key assumtion in the derivation of Equations is that the terms in the ower series exansion of the olarization given in Equation are small corrections to the linear olarization. Thus, it is exected that the growth of the signal and idler fields, due to the second order olarization term, occurs gradually over many otical cycles. This assumtion is called the slowly varying enveloe aroximation (SVEA) and it allows the raidly varying comonents, e ikz, and the enveloe, A(z), to be treated searately. Taking this into account, Equations are exressed as A z d i n c eff A A e s i ikz, (18) d As s eff i A A * i z nsc d Ai i eff i A A * s z nic e e kz ikz, (19), () where the hase mismatch is exressed more conveniently as n n n s i k k ks ki, (1) s i where λj is the free sace wavelength, nj is the wavelength deendent refractive index and the subscrit j can be, s, or i. Along with the conservation of energy, hase matching or conservation of momentum, needs to be satisfied as well. 3

40 .4 Poynting Vector and Phase Matching The Poynting vector rovides the connection between electric field, magnetic field, and the direction of energy. By considering only free charges, Poynting s theorem is derived by examining the work done with the free current density. Given by closed surface dw S da dt mech t UdV P E dv, () t it describes the total ower flow out of a closed surface, where da is the surface normal on the surface bounding the volume, and dwmech is the work done on all charges in the volume. The first term on the right side of Equation is the rate at which work is done by the fields on free charges. The second term is the rate of change in the EM energy stored in the fields bounded by the surface. The last term is the rate at which work is done by the field on the medium via the olarization. This last term is central to describing how the energy is exchanged between the driving field and the material s olarization. From Equations 15 17, it is clear that the evolution of a given field is deendent on the other two interacting fields via the nonlinear olarization. In Equation 17, for examle, the raidly varying exonential term of the idler field is deendent on ki while the raidly varying exonential term of the nonlinear olarization is deendent on k ks. Therefore, if the hase of the driving olarization is equal to the hase of the field being driven then the rocess is said to be hase matched. If the hase between the field and the induced olarization is not the same there will be a continual hase sliage between the two as they roagate down the material and they will reeatedly go in and out of hase along the length of the crystal, as deicted in Figure 9. 4

41 1.8 E dp/dt Normalized Amlitude Distance in Crystal (Coherence Length) Figure 9: Phase sliage between electric field and nonlinear olarization. As the hase of the field and the olarization driving it become more in hase, then the driving olarization will coherently transfer energy into the driven field. This energy reverses direction back into the olarization as the hase sliage reaches a π hase shift. The hase sliage will continue until it reaches another π hase shift where the energy transfer rocess again reverses. The distance over which the generated fields exerience growth/decay is called the coherence length, defined by L c k k k s k i. (3) The field intensity will build u over one coherence length and decay over the next as the olarization and field go in and out of hase with each other, as illustrated in Figure 1. If the hase between the olarization and the driven field can be selected such that they are hase matched, then a continual energy flow into the drive field will occur and the coherence length goes to infinity. 5

42 Figure 1: Time averaged intensity as field and induced olarization roagate along crystal. Recalling that kj=njj/c, the hase mismatch can be exressed as n nss nii k, (4) c c c 1 k c n 1 k s c s i Therefore in isotroic materials, in normal disersion, where n>ns>ni, the hase mismatch will always be ositive and hase matching is not ossible (however, in rincile hase matching is ossible in anomalous disersion). One aroach to achieving hase matching is to use birefringent crystals with a correct combination of roagation direction through the crystal and beam olarization. Obviously this won t work for three-waves olarized in the same direction. This technique is known as birefringent hase matching (BPM). The refractive index in a birefringent material deends on both the olarization and the direction of light roagating through it. Since different indices can be accessed by different 6 s s i i n n, (5) n n n n s i i. (6)

43 olarizations, hase matching can be achieved, but it is limited by the birefringence of the material. Not all interactions will be suorted by the range of refractive indices available. As mentioned before, in the case of LiNbO3, BPM utilizes the coefficient d31 = 4.35 m/v but its highest nonlinearity is d33 = 7 m/v which cannot be accessed through BPM. Quasi-hase matching (QPM), however, allows interactions to occur over all crystal directions and olarizations. Even, isotroic materials, such as GaAs and other zincblende semiconductors, can achieve hase matched interactions via QPM, by engineering a crystal domain reversal with suitable eriodicity..5 Quasi-Phase Matching QPM is a technique to circumvent the eriodic growth and decay of the converted field that results when insufficient or absent birefringence in the crystal leaves a net hase mismatch. In QPM, the sign of the nonlinear suscetibility in the material is reversed at each coherence length, equivalent to a π hase shift. Thus the hase shift from the material inversion negates the π hase shift from the hase sliage between the olarization and the field. This results in the reversal of the hase of the nonlinear olarization such that, instead of the field decaying over the next coherence length, the field intensity continues to increase. Instead of the energy flowing back into the um at every coherence length, it continues to flow into the signal and idler oututs along the length of the crystal. Figure 11 shows the comarison between 1 st and 3 rd order QPM, and the case of no hase matching. Higher order QPM oerates over eriods that are an odd number of coherence lengths. Only odd multiles of coherence length can achieve QPM since even numbers result in multiles of a π hase shift. Higher order QPM obviously leads to a 7

44 slower intensity build u, yet can be beneficial if one coherence length is too small to fabricate (as was the case with achieving QPM through diffusion bonded GaAs or total internal reflection). Even though QPM allows for nonlinear conversion it results in a lower effective nonlinearity when comared with comletely birefringent hase matching. Secifically the nonlinear coefficient is reduced by a factor of /π. The eriodic reversal of material essentially acts as a grating and effectively contributes to the total momentum of the system. The additional momentum contributed by the alternating eriods is included as the last term in the hase matching condition show below k k ks ki m, (7) where m is an odd integer. Figure 11: Comarison between 1st and 3rd order QPM vs. no QPM. 8

45 The crystal s domain eriod,, can be calculated for by setting k=. For firstorder quasi-hase matching, the domain eriod is two times the coherence length. It is ossible to determine and design the aroriate QPM grating eriod for a given um frequency and a nonlinear material with well-defined disersion. The grating eriod for first order QPM interaction is given by n k n s ni s i 1, (8) where, s, and i are the wavelengths of the um, signal and idler resectively while n, ns, and ni are the refractive indices at their resective wavelengths. These indices can be found using Sellmeier equations for GaAs [99]..6 Manley Rowe The Manley Rowe equations can be derived from the couled amlitude equations and they are given by 1 di s dz s 1 di di i 1. (9) dz dz i The relation exlains that as a um hoton is annihilated, one signal and one idler hoton are generated. Due to conservation of energy, neither the signal nor idler can be generated without the other. Therefore, generating low-hoton-energy idlers in the 8 1 µm region from a µm um already limits the hoton conversion efficiency to 5% and 16% resectively since most of the outut energy is contained within the signal. Therefore, as reviously mentioned, in order to overcome this large quantum defect, one can recycle the higher energy signal hoton into more idler in a second frequency conversion stage. An 9

46 illustration of the energy conservation of the cascaded rocess is shown in Figure 1. A second signal wavelength is also generated as a byroduct of the cascaded rocess. Figure 1: Diagram of cascaded difference frequency generation where the signal from the first-stage is used as a um for a second interaction..7 Otical Parametric Amlification There are several system configurations which can achieve the desired frequency conversion. Difference frequency generation, as mentioned above will take two inut hotons and roduce a new hoton at the difference frequency. Not only does a new frequency get generated, but the signal inut gets amlified at the exense of the um. Therefore, DFG is also commonly referred to as otical arametric amlification (OPA). Illustrated in Figure 13, a strong um field and a signal field, tyically treated as a seed, are resent at the inut face of the crystal. The energy in the signal beam will be amlified at the exense of the energy in the um beam and an idler beam will be generated as well. Since ω and ωs are resent at the inut, the arametric gain does not deend on the relative hase between the two inuts since the idler will assume the hase that results in the highest gain. If all three are resent, then the relative hases are significant [1]. 3

47 Figure 13: Illustration of OPA where the signal is amlified and an idler is generated in a QPM material..8 Otical Parametric Generation In otical arametric generation (OPG), Figure 14, the seed source is removed and a strong um field is still resent at the inut, roducing quantum noise which can be amlified to macroscoic levels. OPG is a high-gain rocess since these quantum fluctuations which serve as the seed need to be amlified by many orders of magnitude. For this reason, OPG is tyically used in the femto- and icosecond regimes due to the high eak owers roduced. The um hotons are slit into signal and idler hotons, a rocess sometimes referred to as sontaneous arametric fluorescence or sontaneous arametric scattering (SPS). Only those frequencies and directions that satisfy conservation of energy and conservation of momentum (hase matching) are favored with amlification [11]. Figure 14: Illustration of otical arametric generation where the signal and idler are generated in a QPM material..9 Otical Parametric Oscillator If the OPG rocess is conducted within a resonator, then the device is called an otical arametric oscillator (OPO). An OPO, illustrated in Figure 15, is formed when the nonlinear crystal is laced inside an otical cavity. The resence of resonator feedback 31

48 allows for greater deletion of the um beam and higher conversion efficiencies comared to the non-resonant OPA or OPG rocesses for similar inut energies. An OPO is a light source that shares characteristics similar to a laser, in that the cavity s gain needs to overcome losses to reach threshold. Here the gain is nonlinear gain, though, and comes from instantaneous arametric generation in a nonlinear crystal rather than from stimulated emission, as in a laser. Cavity stability and determining resonant modes, however, follow similar calculations. One key difference between an OPO and a laser is that the OPO requires a coherent source, such as a Q-switched solid-state laser, whereas many lasers can be umed with an incoherent source, such as a flash lam. In laser cavities, the gain material needs to absorb the um to achieve oulation inversion, but if the nonlinear material in an OPO absorbs the um, arametric amlification will be more difficult. Absortion in nonlinear materials will lead to increased free carriers, localized heating, and modification of the temerature deendent refractive indices, which will alter the hase matching conditions. Ideally, then, the OPO crystal should be transarent to the um source. The tunability of the OPO is determined by hase matching and crystal transarency while the tunability of the laser is dictated by the energy level structure of the gain medium. Figure 15: Illustration of an otical arametric oscillator. 3

49 Tyically, OPOs are designed either as a singly resonant oscillator (SRO) resonating either the signal or idler wavelength; or as a doubly resonant oscillator (DRO), resonating both in the cavity. DRO cavities tyically roduce higher oututs due to both fields building u large intensities as they resonate within the cavity, but DROs also suffer more from stability roblems and mode hoing [98, 1] because both signal and idler must satisfy cavity conditions. Resonant beams tyically make 1 s 1 s of cavity round tris for nanosecond um ulses. To increase the number of round tris, mirrors tyically are laced as close as ossible to the nonlinear crystal. Tyically, OPO outut ulses are slightly shorter than the um ulse, as shown in Figure 16. The energy in a um ulse needs to generate enough gain to allow the signal and idler to reach threshold and sufficient build u time is required. Once threshold is met, signal and idler amlification skyrockets as the um is significantly deleted. Figure 16 illustrates normalized temoral rofiles of the um, signal, and idler ulses from an OPO. (Note: The signal in Figure 16 aears to be absent but the ulses are a result of a DRO OPO with the same mirror reflectivity for the signal and idler. Therefore, the same number of hotons of signal and idler were generated, and thus, have the same ulse shae. Therefore, as the ulse are normalized, the ulse shae for both the signal and idler overla.) 33

50 1.9.8 Pum Signal Idler Norm. Outut Time (ns) Figure 16: Normalized OPO temoral outut ulse..1 Cascaded Otical Parametric Oscillator One roblem with uming an OPO with a μm source to get an idler in the 8 1 μm regime is the large quantum defect from um to idler energies. Most of the converted energy is contained in the signal, but it is ossible, with another nonlinear rocess, to recycle that hoton into another idler hoton and a hoton at the difference frequency. This could be accomlished by following the OPO with an OPA stage in a MOPA configuration, where the OPA crystal is atterned such that the signal coming in from the OPO will hase match to generate the same idler wavelength. A variation on this method is to insert that crystal into the OPO cavity and oerate it as a cascaded dual crystal OPO, as shown in Figure 17. This allows the second crystal to access the high resonant intensity within the OPO. Again, the second crystal is atterned to generate the same idler as the first stage. Now, for a single um hoton, two idler hotons will be generated, resulting in a significant increase in efficiency. 34

51 Figure 17: Illustration of a linear cascaded otical arametric oscillator. While oerating two rocesses in a linear cavity is very simle schematically, including a second crystal within the cavity leads to very comlex nonlinear interactions. This rocess requires generating a signal in the first crystal, while deleting that signal in the second. There are many different tyes of intracavity nonlinear devices including OPO/OPO [13, 14], OPO/DFG [71], OPO/SFG [7], and OPO/SHG [73] along with devices for third harmonic generation [15]. Devices using multistage interactions can extend the tuning range of the original OPO to either higher or lower frequencies and unwanted nonlinear interactions are likely to occur unless undesired fields are couled out after each crystal ass. Tyically ring resonators are used in this scenario. For µm umed OPGaAs, however, the original um hoton will not hase match with the grating eriod required in the second crystal for it to be umed by the first signal hoton. Therefore, the um can roagate through the second crystal without inducing undesired effects, save from additional assive loss. Similarly, the difference frequency hoton in the second crystal will not hase match to roduce additional interactions in the first crystal. Therefore, like the um in the second crystal, the difference frequency signal can roagate through the first. The first crystal will utilize the couled amlitude Equations 18. Assuming a DFG rocess in the second crystal, simly changing the subscrit s1, s s, and i i in the couled 35

52 amlitude equations will govern the interaction in the second crystal (the subscrits s, from the couled amlitude equations, and s1 are the same frequency and s is the difference frequency beam between s1 and i, which we refer to as the second signal or signal ). Due to the comlex nature of the interactions, otimizing arameters such as mirror reflectivities, crystal length, cavity length, etc., tyically involves some degree of numerical modeling..11 Polarization and Nonlinear Coefficient in OPGaAs While atterned zincblende semiconductors do not require secific inut olarizations to hase match, certain olarizations yield slightly different nonlinear coefficients and scenarios can arise when deff goes to zero. The driving olarization for difference frequency generation (DFG) for a given um and signal beam is given by P () NL i i odijk i,, s E j E k s, (3) jk where d ijk is the second-rank nonlinear coefficient tensor and i, j, and k refer to the ermutations of the x, y, and z Cartesian comonents of the electric field vectors of two beams. GaAs is a 4 3m material whose nonlinear coefficient is given by d14 d d14, (31) d14 where d14=d5=d36 due to Kleinman symmetry. The driving olarization then becomes 36

53 37 s x y s y x s x z s z x s y z s z y s z z s y y s x x o z NL y NL x NL E E E E E E E E E E E E E E E E E E d d d P P P () () (), (3) s x y s y x s x z s z x s y z s z y o z NL y NL x NL E E E E E E E E E E E E d P P P 14 () () (). (33) Figure 18: Pum roagation with resect to OPGaAs crystal geometry (left); olarization directions of inut um and resulting signal field (right). Figure 18 illustrates the um direction with resect to the crystal geometry of an OPGaAs samle. The um is roagating along the [1 1] crystallograhic direction. The olarization of the inut um and of the generated signal and idler will lie in the transverse lane that is arallel to the [1] and [11] directions (such that [1] is vertically olarized and [11] is horizontally olarized). Unit vectors z ê and ê are given by z e z ˆ ˆ, (34)

54 eˆ 1 xˆ yˆ. (35) The driving olarization now becomes P () NLx o d 14 sin s, (36) P () NLy o d 14 sin s, (37) P d cos () NL z o 14 cos s, (38) P () NL P () NLx P () NLy P () NLz d sin o 14 cos cos s s, (39) where the effective nonlinear coefficient is given by d eff d (4) 14 sin s cos cos s and is a function of both the um and signal olarizations. Figure 19 illustrates the deendence of deff on um and signal olarization. In a DFG rocess, the olarization angle of both the um and the signal beam are secified. In an OPO however, only the inut angle of the um olarization is secified. OPGaAs is isotroic, and unlike birefringent crystals where only secific olarizations can be hase matched, the hase matching conditions in GaAs do not deend on olarization. Therefore for a given um olarization, as long as the hase matching conditions are obeyed, then a signal will be generated, and will be olarized along whatever direction exeriences the greatest gain. This "unconstrained" signal olarization is given by the blue curve. Additionally, in Figure 19, deff is lotted as the signal olarization is both erendicular and arallel to the um olarization. The um olarization is varied with resect to the [11] crystal direction. According to Equation 4 and Figure 19, the largest nonlinearity 38

55 should be observed when the um is olarized along the [111] direction. Additionally, for a DFG rocess when both the um and signal olarizations are chosen, if the um is olarized along [1] and the signal is olarized along [11] then deff=. Therefore, in the cascaded OPO where the secondary crystal is used as an intracavity amlifier, the olarizations must be taken into account to ensure this olarization scenario does not occur Unconstrained Perendicular Parallel 1 deff /d Angle between um olarization and [11] direction Figure 19: Theoretical effective nonlinear coefficient deff as a function of the angle between the um beam olarization vector and the OPGaAs [11] direction. 39

56 CHAPTER 3 NUMERICAL MODELING Solving the couled amlitude equations analytically, given in Equations 18, can get extremely chaotic and comlicated very quickly and therefore, these equations are tyically solved numerically. This becomes tremendously beneficial for redicting the comlex behavior of commonly imlemented devices such as OPA and OPO quickly. Currently available software, such as SNLO [83], offers a wide variety of nonlinear rocess models that include disersion curves and hase matching conditions for numerous nonlinear crystals along with devices like OPA, OPG, and OPO. One limitation of the available rograms is the inability to vary some arameters such as beam shae, and more imortantly the inability to include more than one crystal. Modeling exeriments such as an OPO-umed OPA is ossible if oerated as two distinct interactions where the outut of the first interaction can be coied and inserted as the inut for the second interaction. Modeling the two distinct interactions in one system, as in the cascaded OPO, however, is not ossible with SNLO and therefore a new model was develoed using MATLAB. The nonlinear induced olarization is the rincial factor in achieving frequency conversion through arametric rocesses. In linear otics, in the resence of an electric field an induced olarization will be generated within the material and this induced olarization deends on the strength of the electric field resent. With higher intensity 4

57 fields, such as those created by a focused laser, the induced olarization will start exhibiting nonlinear resonses and higher order olarization terms must be considered. The second order olarization term will act as the driving force for an otical rocess in which the energy in an incident hoton, named the um, will be slit between two newly generated hotons, named the signal and idler. By convention, the shorter wavelength, higher energy hoton is named the signal and the longer wavelength, lower energy hoton is the idler. As the signal and idler hotons are generated, each must satisfy Maxwell's electromagnetic wave equation, as well as conservation of momentum and conservation of energy. Assuming lane wave roagation along the z-axis, the following couled amlitude equations describe the interaction among the um, signal, and idler beams with frequencies, s, and i. A z i k 1 A A d i n c 1 d eff A A e As s s eff kz i As As i A A * i e z ks nsc Ai 1 id i eff ikz i Ai Ai i A A * s e z ki nic s i ikz, (41), (4). (43) Here is the Lalacian oerator, Aj is the comlex amlitude, j is the electric field loss, deff is the nonlinear coefficient tensor, nj is the wavelength-deendent refractive index, c is the seed of light, j is the frequency, kj is the wave vector and Δk is the net hase mismatch, given by n n s n i k k k s ki, s i (44) 41

58 4 where the subscrit j can be, s, or i indicating the um, signal or idler hoton resectively, and Λ is the crystal QPM eriod. Since the goal at hand is to model a bulk OPGaAs OPO, the terms reresenting waveguide effects and satial walk-off are ignored in the couled amlitude equations. Additionally, since the ulse times for these OPOs are on the order of tens of nanoseconds, time-deendent terms become negligible and can also be ignored. 3.1 Slit-Ste One method that is well-suited for solving these nonlinear systems is the slit-ste Fourier transform method. This model follows the framework set by Powers [89] and Smith et al. [87, 16, 17]. In the slit ste Fourier transform method, for a small enough ste size through the crystal, the linear and nonlinear comonents of the wave equation essentially become decouled and each can be solved indeendently with relatively small error. The couled amlitude equations can be rewritten as V e A k e A k A e k c d i V O O O z V kz i s i i kz i i s s kz i i eff i s * *, (45) where i s A A A V, (46) k i O, (47)

59 O O s i i s, (48) k s i i (49) k.. i Thus, Equation 45 simlifies to V z Lˆ Nˆ V, (5) where the Lˆ and Nˆ are the linear and nonlinear oerators and they are given by the two matrices in Equation 45 The solution to Equation 5 is thus straightforward and is given by V. L Nˆ z dz e ˆ dz Vz (51) We may aroximate this exression by exanding the exonential e e 1! Lˆ Nˆ dz 3 1 Lˆ Nˆ dz Lˆ Nˆ dz Lˆ Nˆ dz 3 ˆ ˆ Lˆ Nˆ dz ˆ ˆ L dz N dz LNdz NLdz 3 1 Ldz Ndz Odz If we also exand the following ˆ ˆ 1 3! ˆ ˆ, (5). (53) e Ldz ˆ e Ndz ˆ Ldz ˆ Lˆ dz 1 Ndz ˆ Nˆ dz!!, (54) e Ldz ˆ e Lˆ dz Nˆ dz Ndz ˆ ˆ ˆ ˆ ˆ 3 1 Ldz Ndz LNdz O dz, (55) it can be seen that the exonential oerator in Equation 51 is aroximately Lˆ Nˆ dz Ldz ˆ Nˆ dz e e e, (56) 43

60 where the difference is a factor of 1/ [ Lˆ, Nˆ ]. Therefore we can say Equation 56 is accurate to the order of dz (Lie Slitting). We can then write V. (57) Ldz ˆ Ndz ˆ z dz e e Vz This now allows, for a given ste size dz, the fields at V(z+dz) to be calculated from the field at V(z) by first oerating it with the nonlinear exonential oerator alone, followed by the linear oerator by itself. We can increase the order of accuracy to dz by the imlementation of Strang slitting given by e Lˆ dz e Ndz ˆ e Lˆ dz Lˆ 1 Lˆ ˆ ˆ ˆ 1 ˆ L 1 L 1 dz dz 1 Ndz N dz 1 dz dz!!! (58) Lˆ Lˆ dz dz Ndz ˆ e e e Lˆ dz Nˆ dz LNdz ˆ ˆ NLdz ˆ ˆ ˆ ˆ 3 1 Ldz Ndz O dz, (59) Here we can see that Lˆ Lˆ dz dz Ndz ˆ e e e is now equivalent to e Lˆ Nˆ dz to an accuracy of dz. Now, Lˆ Lˆ e dz dz Lˆ Nˆ dz Ndz ˆ e e e, (6) thus leaving V Lˆ Lˆ. (61) dz dz Ndz ˆ z dz e e e V z This means that we first linearly roagate the fields by a half ste, which is then used as the inut for the nonlinear ste, which is solved over the full ste. Finally, we roagate linearly by another half ste. This rocess is then carried out over the entirety of the nonlinear crystal. 44

61 3. Linear Ste: Beam Proagation The slit-ste method first starts with the linear roagation ste while ignoring the nonlinear terms. By droing the nonlinear terms in Equation 41 43, we are essentially left with three uncouled differential equations and we can solve the roagation of each term indeendently. The linear comonent for the field A, for examle, is given by A z 1 i A k. (6) The solution can be obtained by transforming the linear comonent into the Fourier domain, given by A ~ A i fxx f y y f, f, ze x y df x df y, (63) where fx and fy are satial frequencies in the transverse direction and the algorithm for a linear roagation ste with loss is given by A x, y, z dz F 1 e i fx f y dz k F A x, y, z, (64) where F and F -1 denote the Fourier transform and inverse Fourier transform resectively. The signal and idler fields are both roagated in a similar fashion. Similar beam roagation techniques have utilized imlicit finite difference method [18] instead of Fourier slit-ste method. 3.3 Nonlinear Ste: Couled Amlitude Equations Finally, the nonlinear terms A z i d n eff A A e s i ikz, (65) 45

62 As i deff A A * i z nss e ikz, (66) Ai i deff A A * s z nii e ikz, (67) can be solved using a Runge-Kutta algorithm. Most mathematical ackages, like MATLAB or Mathmatica, include ODE solvers, but, Runge-Kutta algorithms can also be exlicitly imlemented by using the following method. The classical fourth-order scheme is given by where A 1 6 z 1 Az k1 k k3 k4, (68) k1 hf A z, (69) k1 k hf Az, (7) k k3 hf Az, (71) k 4 hf A z k 3. (7) Here Az is the initial value of the equation, which is defined by the comlex amlitudes of each beam; Az+1 is the solution of each comlex amlitude as each beam roagates in the crystal with a ste size of h; and f is the function, which is given by the couled nonlinear terms in Equations The Runge-Kutta algorithm is alied at each ste within the crystal to solve the nonlinear couled amlitude equations, and calculates each beam's evolution along the length of the crystal. To revent any given ste from creating a very large inaccuracy in the solution, adative Runge-Kutta algorithms can be utilized such as 46

63 a Runge-Kutta-Fehlberg method or a Cash-Kar Runge-Kutta algorithm, which is used in SNLO. In adative algorithsm, if the solution for a single ste does not fall within a secified tolerance, the ste size is reduced and reeated. In the model used here, imlementing adative ste algorithms significantly increased run time while roducing results comarable to that of the traditional fourth order Runge-Kutta solver, so the traditional fourth order Runge-Kutta was emloyed on all subsequent calculations. 3.4 Model Parameters In addition to the slit ste method above, the fields need to obey boundary conditions of the resonator. For a given wavelength, the outut emitted from the outut couler is just the transmission of the internal cavity fields through the outut mirror M, given by Equation 74. The field emitted from the inut couler is the summation of the transmission of the internal cavity field at the inut mirror and the reflection from the inut field at the same mirror, given by Equation 77. The minus sign in Equation 77 comes from the π hase sift uon reflection. Finally, the circulating field within the cavity consists of the sum of the inut field transmitted through the inut couler, and the field that is retained within the cavity from the revious round tri, given by Equation

64 Figure : Boundary conditions of the OPO. '', t E L, t 1 R E t E,, (73) circ n circ n 1 M1 L t 1 R E L t E,, (74) out, M, n M ' circ circ L t R E L t, n M circ n The numerical model includes diffraction through the Lalacian oerator but it does not incororate walk-off since GaAs isn t a birefringent material. Walk-off can, however, be imlemented very easily to accommodate other crystals in which it is an issue. Grou velocity disersion and temoral walk-off have also been neglected since the ulse durations in our exeriment are sufficiently large. Each of the interacting fields is treated as monochromatic. Internal crystal losses and losses due to mirror and crystal surface reflectivity are included as well. The inut beam is Gaussian, but other inut beam rofiles can be used if desired. There will be no unwanted conversion rocesses in either crystal and therefore, for each crystal, only three fields are considered in the mixing equations; the 48 n E,, (75) '' circ ' L, t R E L t E,, (76) out M n M 1 circ n ', t 1 R E L, t R E t E,. (77) n M circ n 1 M1, 1 1 in n in n

65 49 fourth field simly roagates through the crystal. For each crystal, the familiar threewave arametric couled amlitude equations are given by z k i m i m s eff m m m m m m m m e A A d c n i A A k i z A,,,,,,,,, 1, (78) z k i m i m eff m s m s m s m s m s m s m s m e A A d c n i A A k i z A *,,,,,,,,, 1, (79) z k i m s m eff m i m i m i i m i m i m i m e A A d c n i A A k i z A *,,,,,,,, 1, (8) where m denotes either the first or second crystal, with eriod Λ1 or Λ. The subscrits,m, s,m, and i,m indicate the resective um, signal, and idler for crystal with eriod Λ1 or Λ. The hase mismatch in given by Δkm and is defined by Δk=k,m ks,m ki,m kg.m, where kg.m is the wave vector due to the grating of either Λ1 or Λ. The transverse Lalacian oerator is and α is the internal loss of the crystal. The temerature-deendent refractive indices, n,m, ns,m, and ni,m are calculated using the Sellmeier equation for GaAs, and the effective nonlinear coefficient is deff=/π d14 where d14=94 m/v. Injection-seeding the OPO with some small amount of energy, also Gaussian in shae and with the energy of one hoton er mode, can be used to reresent the otical generation from quantum noise, to initiate the otical amlification rocess [19]. The resonant mode of the seeded field, tyically the signal, is solved for a given cavity configuration and is initialized to have the same hase curvature and beam radius for this calculated resonant mode. These nonlinear interactions are strongly intensity driven and therefore the temoral change of intensity within a given ulse cannot be ignored. The inut ulse is broken u into time slices searated by the roundtri cavity time of the idler wavelength. (The idler was chosen because it has the shortest round tri cavity time.

66 Comarable results were achieved when the inut ulse was broken u into time slices searated by the roundtri cavity of the um). Since temoral walk-off has been ignored in this model, all four fields are assumed to roagate together with the same grou velocity. Outut energies are calculated by satially and temorally integrating the fields that are emitted from the OPO. 3.5 Inut Seed Energy Initially, the cascaded OPGaAs OPO model was seeded with inut signal energy of 1 - J, and roduced results suggesting that couling out the idler would result in outut idler energies just as high as artially resonating the idler, as resented in [11]. The seed inut energy of 1 - J was selected because it is on the same order as the energy of a single signal hoton. Later, it was noticed that signal and idler oututs for the single-stage OPO would vary deending on the seed energy. In a sense, higher seed energies should yield higher oututs, but when the seed energy is suosed to reresent quantum fluctuations, signal and idler generation should be more deendent on inut um energy and cavity configurations. As the seed energy was varied between 1 - J 1-4 J, OPO oututs would vary even though seed energies were effectively zero. The seed energy was eventually lowered to 1-8 J and there was relatively no difference between seeding the single-stage OPO with 1-8 J and 1-15 J. The single-stage OPO results were then verified using different seed energies in SNLO. SNLO also incororates quantum noise so it is ossible to have a seed inut of J and generate signal and idler oututs. (If J is used for the seed energy in the custom numerical routine, then the couled amlitude equations will never generated any signal since quantum noise is not imlemented in the model.) In 5

67 SNLO, seed energy of both 1-8 J and J yielded similar OPO outut results. Both seed energies were also used with low and high energy inut um and again, both yielded similar OPO oututs. This suggests that 1-8 J an aroriate seed energy to reresent quantum noise, and this value was therefore used for all subsequent simulations. With a reasonable inut seed energy defined, the modeling results then suggested that the greatest idler generation would occur when the idler was artially resonant in the cascaded OPO. 51

68 CHAPTER 4 MODELING RESULTS The modeled um laser is a Tm,Ho:YLF laser oerating at λ=.54 µm with a 45 ns um ulse. Both OPGaAs crystals were assumed to be 15 mm in length with a free sace crystal-to-crystal searation of 1 mm. In the linear cavity shown in Figure 1, both mirrors, M1 and M, had 5 cm ROC with a free sace searation of mm between the mirror and the crystal. These arameters are chosen to reflect the um laser and crystal lengths tyically found in the exerimental set-u. The reduction of free sace roagation will increase the number of roundtri within the cavity and free sace between the crystals was ket fairly minimal. The revious LWIR OPGaAs exerimentation utilized 5 cm ROC mirrors with ~15 mm long crystals and these values were carried over for the model. To identify the otimal mirror reflectivities for eak idler outut, M reflectivities at the idler, signal 1, and signal wavelengths were varied while the um was consistently double assed, and the inut um energy was set at a constant 3 µj. Once the mirror reflectivities were otimized, a comarison between the single-stage OPO and cascaded OPO was made. The mirror otimization was simulated using rimarily the Λ1=76 µm and, Λ=15 µm grating air, which corresonds to OPO wavelengths of λs1=.7 µm, λs=3.8 µm, and λi=8.8 µm. Assuming these otimized arameters hold true for the other crystal airs, the comarison was extended to them as well, with the Λ1=8 µm and Λ=118 5

69 combination roducing fields at wavelengths λs1=.55 µm, λs=3.3 µm, and λi=1.7 µm; and the Λ1=84 µm and Λ=116 µm combination roducing fields at wavelengths λs1=.5, λs=3., and λi=11.5 µm, as summarized in Table. Figure 1: Linear cascaded OPGaAs OPO. Table : Summary of grating eriods and associated wavelengths involved in the cascaded rocess. First Stage Second Stage λ(µm) Λ1(µm) λs1(µm) λi(µm) λ =λs1(µm) Λ(µm) λs(µm) λi(µm) Comarison to SNLO Before modeling the cascaded OPO, the first ste was to confirm that the model was oerating correctly for a single-stage OPO. The single-stage OPO was comared with the single-stage nanosecond OPO feature within SNLO. Figure below shows the temoral ulse, from the outut couler, for the SNLO and our numerical results for a linear SRO configuration that double-asses the um and resonates the signal with a 9% R outcouler. Crystal loss is.1/cm crystal loss and crystal surface reflectivity is 1%, and the inut um ulse energy is µj. (M1 is 1% R at λ and 99% R at λs and λi; M 53

70 is 99 % R at λ, 9% R λs1, and 1% R at λi). The temoral rofiles are extremely close in structure and when the ulses are temorally integrated, the ulse energies from both models are extremely close all well, as is summarized in Table 3. Figure : Illustration of temoral lots of OPO outut from SNLO (left) and MATLAB (right). Table 3: Outut energy comarison between SNLO and MATLAB. Left Outut (µj) Right Outut (µj) Wavelength Inut SNLO MATLAB SNLO MATLAB (µj) Pum Signal 1e Idler Total SNLO = MATLAB = Additionally, if we look at a DRO cavity that has a 5% R at the um and 8% R at the signal and idler with an inut energy of 4 µj, for examle, we see ractically the same result, confirming that the two models are in good agreement. (M1 is 1% R at λ and 99% R at λs and λi; M is 5% R at λ, and 8% R at λs1 and λi). Figure 3 shows the two temoral figures from the OPO outut generated by the numerical model and SNLO. Table 4 summarizes and comares the integrated energies from the OPO. There is clearly good 54

71 agreement between the numerical model and SNLO for both OPO designs. Overall we have found the two models consistently to be in good agreement across a variety of other cavity arrangements involving different crystal lengths, inut energies, mirror radii and reflectivity, etc. Any differences in the two algorithms can be attributed to using different nonlinear solvers and the imlementation of quantum noise. Additionally, qualitative tendencies, such as signal and idler outut based on different OPO cavity schematics, have been observed exerimentally such as greater idler roduction in SRO cavities where the signal is highly resonant but greater overall outut from DRO cavities. Figure 3: Comarison of temoral lots of OPO outut from SNLO (left) and MATLAB (right). Table 4: Outut energy comarison between SNLO and MATLAB. Left Outut (µj) Right Outut (µj) Wavelength Inut SNLO MATLAB SNLO MATLAB (µj) Pum Signal 1e Idler Total 4 SNLO = MATLAB =

72 4. Cascaded OPO Intracavity Intensities Once the numerical model was validated with SNLO for the case of a single-stage OPO, the second crystal was added to the OPO. Figure 4 shows the intracavity intensity for a single round tri through the cascaded OPO for all of the interacting wavelengths. As exected, the um in deleted in the first crystal and the signal and idler are amlified (from 'a' to 'b'). Then in the second crystal (from 'b' to 'c'), the signal starts to be deleted while the second signal and the idler are amlified. After mirror losses are taken into account at location c, we see the same rocess again where the first signal is deleted in the second crystal (from 'c' to 'd') and the um is deleted in the first crystal (from 'd' to 'a'). Figure 4: Internal intensities of cascaded OPO 4.3 Cascaded OPO Mirror Reflectivities Since the cascaded OPO aears to behave as exected, the next ste is to model which cavity arameters will result in the greatest roduction of idler. While there are numerous ossible arameters to change, mirror reflectivities will be considered first while 56

73 keeing crystal length, crystal loss, crystal reflectivity, inut energy, etc., constant. In the simulations below, the length for both crystals is L=15 mm, the inut energy is 3 µj, and the temerature is T=35 K. The OPGaAs grating air is Λ1=76 µm and Λ=15 µm for generating λi=8.8 µm to initially set the conditions for greatest idler generation. It is assumed that the same deendence on mirror reflectivities will translate to the two other OPGaAs grating airs used to generate λi=1.7 µm and λi=11.5 µm. Simulations were comleted using a bulk crystal loss of α=.1/cm and crystal reflectivity of 1% at each wavelength, which is labeled as "1% loss" in the figures below; and a lossless case where bulk crystal loss is α=./cm and crystal reflectivity is %, which is designated "% loss" in the figures below. (Note: 1% loss is just the naming convention for the combination of 1% crystal face reflectivity and.1 cm -1 bulk crystal loss. The total transmission loss for a 15 mm crystal with two interfaces is then 3.5% er crystal) Modifying mirror reflectivities for each beam will clearly change the intracavity intensities of each beam and will alter the nonlinear interactions. The cavity is a simle Fabry-Perot resonator and since each mirror has a reflection coefficient for each beam, that means there are eight variable reflection coefficients that can be modified to otimize idler outut. If each mirror reflectivity at each beam and each wavelength was varied from 1% R by 5% intervals, there will be 1 8 = 37.8 billion different OPO cavity simulations. To reduce this, we assume the inut mirror, M1, is AR and the outut mirror, M, is highlyreflective (HR) for the um. Double-assing the um in this fashion tyically results in greater transfer of um energy into the converted fields. M1 is also assumed to stay HR at the idler wavelength and idler outut will be collected only from M, whose reflection coefficient will remain a variable for the idler and will be determined later. This reduces 57

74 the number of variables in the mirror reflectivities, leaving five; reflection coefficients of both signals at M1 and both signals and the idler at M, which results in ~4 million individual OPO cavity simulations. By allowing only two mirror reflectivities to vary at any given time, while choosing some combination of mirror reflectivities for the other beams, the results can be lotted and the deendence for a given scenario can be observed. These small subsets should rovide valuable insight into the dynamics of the cascaded OPO cavity and allow us to understand the cavity requirements for the greatest idler generation while not having to simulate meticulously every single ossible combination of mirror reflectivities, which would lace stee demands on run time and memory. For a standard singly resonant OPO, the signal beam is tyically resonant within the OPO cavity and therefore, to enhance idler outut, resonating both signals and oerating as a dual SRO was initially roosed. This assumtion gives a reference on where to start searching for otimized idler. Figure 5 and Figure 6 show idler energy conversion as a function of mirror reflectivities for the lossless and 1% loss scenarios resectively. The mirror reflectivities at M for λi and λs are varied from 1% R by 5% R and the OPO mirror reflectivities for this cavity at all wavelengths are described in Table 5. Each oint in the figures reresents idler outut energy from M in an individual cascaded OPO simulation. As Figure 5 and Figure 6 show, the starting assumtion of resonating both signals is actually not a good idea. Clearly, we can see a strong evidence to coule out λs and actually run the cascaded OPO as a doubly resonant device, at least where the first-stage is concerned, where λs1 and λi are resonant within the cavity. The simulations indicate that when λs is retained in the cavity, its strong intracavity field starts a secondary back conversion rocess 58

75 with the λi into λs1 thus exterminating any idler hotons reviously generated. Therefore, in order to revent back conversion, λs must be couled out. This backconversion into λs1 should be reduced further if M1 is made AR for λs, but it may be necessary to investigate the degree to which it should be couled out. For examle, if M1 is ket HR at λs, λs will still be couled out of the cavity if M remains AR. As λs1 is reflected back into the cavity from M, however, it will generate more λs in the second-stage crystal as it roagates back into the cavity. Then, λs will reflect off M1 and be amlified as it roagates back through the second-stage crystal on its return before finally being couled out of M. The internal intensity of λs may be negligible since it is couled out on each round tri, or it might rove to be large enough to cause adverse effects on the idler. The same cavity modeled in Figure 6 will be revisited but with M1 made AR at λs to ensure that λs is couled out at each mirror. Table 5: Modeled mirror reflectivities, varying reflectivity of λs and λi at M. Wavelength M1 Reflectivity M Reflectivity Pum AR HR Signal 1 HR HR Signal HR 1% Idler HR 1% 59

76 6 5 Idler Energy (J) Signal Mirror Reflectivity 4 Figure 5: Idler energy deendence on M reflectivity at λs and λi % loss. 4 6 Idler Mirror Reflectivity 8 1 Outcouler - M 3 5 Idler Energy (J) Signal Mirror Reflectivity 4 Figure 6: Idler energy deendence on M reflectivity at λs and λi 1% loss. 4 6 Idler Mirror Reflectivity 8 1 Figure 7 and Figure 8 show idler energy conversion as a function of mirror for the lossless and 1% loss scenarios resectively. The mirror reflectivities at M for λi and λs varied from 1% R by 5% R while the reflectivity at M1 for λs is now AR. The OPO mirror reflectivities for all wavelengths are described in Table 6. The second signal 6

77 is couled out on each half round tri and illustrates that there isn't much variation in idler roduction from varying the reflectivity at M for λs since it will be couled out of M1. This also illustrates, at least at the inut energy used, that the internal intensity of λs is indeed negligible, whether it is couled out at both mirrors or just one. Again, there is a deendence on the idler reflectivity at M which suggests that the idler shouldn't be highly resonated rather reflect at a level of ~5 6%. Table 6: Modeled mirror reflectivities, varying reflectivity of λs and λi at M. Wavelength M1 Reflectivity M Reflectivity Pum AR HR Signal 1 HR HR Signal AR 1% Idler HR 1% 6 5 Idler Energy (J) Signal Mirror Reflectivity 4 Figure 7: Idler energy deendence on M reflectivity at λs and λi % loss. 4 6 Idler Mirror Reflectivity

78 Idler Energy (J) Signal Mirror Reflectivity 4 Figure 8: Idler energy deendence on M reflectivity at λs and λi 1% loss. 4 6 Idler Mirror Reflectivity 8 1 Since Figure 5 Figure 8 suggested that λs should not be resonated, contrary to our initial rediction, it is worth investigating the reflectivity of λs1. To drive the secondary interaction, a higher the signal intensity will generate the more idler and therefore, we susect that λs1 will need to be highly resonant. As soon as the signal is generated in the first crystal, it immediately starts to delete in the second. Therefore in order to kee the intracavity intensity high, the signal should be highly resonant and any leakage from the OPO mirrors will further reduce the signal intensity from driving the secondary interaction. Figure 9 and Figure 3 show idler energy conversion as a function of mirror reflectivities at M for λi and λs while λs is now comletely couled out of both mirrors. The OPO reflectivities of λi and λs1 are varied from 1% R by 5% R and the OPO mirror reflectivities for all wavelengths are described in Table 7. As exected, there's strong deendence on comletely resonating λs1 and the high Q-cavity for λs1 yields the highest idler energy oututs. Again, the lot indicates an idler reflectivity of ~5 6% R at M. 6

79 Table 7: Modeled mirror reflectivities, varying reflectivity of λs1 and λi at M. Wavelength M1 Reflectivity M Reflectivity Pum AR HR Signal 1 HR 1% Signal AR AR Idler HR 1% 6 5 Idler Energy (J) Signal 1 Mirror Reflectivity 4 Figure 9: Idler energy deendence on M reflectivity at λs1 and λi % loss. 4 6 Idler Mirror Reflectivity 8 1 Outcouler - M 3 5 Idler Energy (J) Signal 1 Mirror Reflectivity 4 Figure 3: Idler energy deendence on M reflectivity at λs1 and λi 1% loss. 4 6 Idler Mirror Reflectivity

80 So far, it aears that the idler generation will be the greatest when λs1 is highly resonant, λi is artially resonant and λs is couled out. To check this claim further, a few more combinations of varying mirror reflectivities are modeled. Figure 31 and Figure 3 show the idler generation as the reflectivity for λs at M1 and M was varied from 1% R by 5% R, essentially reexamining the deendence of couling out λs in Figure 8 but ensuring the otimized reflectivity for λs1. The idler is couled out of M and the OPO mirror reflectivities for all wavelengths are described in Table 8. There is a clear indication not to resonate λs, highly as exected from the results shown in Figure 6 and Figure 8. There does not, however, seem to be a significant deendence of idler generation on the reflectivities at λs on idler generation when the firststage is oerated as an SRO cavity, as long as λs is strongly couled out somewhere. This, in turn, should be exected. Since the idler is continuously couled out, this removes the conditions to back convert into λs1, even if a modest amount of λs is retained within the cavity. Figure 33 and Figure 34 show the idler generation as the reflectivity for λs at M1 and M was varied from 1% R by 5% R, but now with the idler artially resonant at 6% R. The OPO mirror reflectivities for all wavelengths are described in Table 9. Here the idler generation shows a greater sensitivity to the couling out of λs than that shown in Figure 3. This is exected, since the idler is now retained within the cavity. To revent backconversion into λs1, λs needs to be couled out. Without the necessary conditions for backconversion, then forward conversion can revail. Figure 33 and Figure 34 illustrate greater idler generation (6% R at M) comared with idler oututs in Figure 31 and Figure 3 (% R at M), which is consistent with idler oututs illustrated in the revious lots. 64

81 Table 8: Modeled mirror reflectivities, varying reflectivity of λs at M1 and λs at M. Wavelength M1 Reflectivity M Reflectivity Pum AR HR Signal 1 HR HR Signal 1% 1% Idler HR AR 35 3 Idler Energy (J) Signal M Reflectivity 4 Figure 31: Idler energy deendence on M1 and M reflectivity at λs % loss (% R of λi at M). 4 6 Signal M1 Reflectivity 8 1 Outcouler - M Idler Energy (J) Signal M Reflectivity 4 Figure 3: Idler energy deendence on M1 and M reflectivity at λs 1% loss (% R of λi at M). 4 6 Signal M1 Reflectivity

82 Table 9: Modeled mirror reflectivities, varying reflectivity of λs at M1 and λs at M. Wavelength M1 Reflectivity M Reflectivity Pum AR HR Signal 1 HR HR Signal 1% 1% Idler HR 6% Idler Energy (J) Signal M Reflectivity 4 Figure 33: Idler energy deendence on M1 and M reflectivity at λs % loss (6% R of λi at M). 4 6 Signal M1 Reflectivity 8 1 Outcouler - M 35 3 Idler Energy (J) Signal M Reflectivity 4 Figure 34: Idler energy deendence on M1 and M reflectivity at λs 1% loss (6% R of λi at M). 4 6 Signal M1 Reflectivity

83 Figure 35 and Figure 36 illustrate tyical satially integrated temoral ulse rofiles of the cascaded OPO. As exected, the fields at wavelengths λi and λs are transmitted through M (right) while the transmission through M1 (left) rimarily consists of residual double assed λ. The highly resonant λs1 wavelength signal is not couled out, which is why it is largely absent from Figure 36. Temorally integrating the outut ulses from both mirrors yields the total cascaded OPO outut energies for each wavelength. 6 Outut Power (kw) s1 s i Time (ns) Figure 35: Temoral structure of the fields at wavelengths λ, λs1, λs, and λi; the cavity outut is lotted from M1. 67

84 .5 s1 s i Outut Power (kw) Time (ns) Figure 36: Temoral structure of the fields at wavelengths λ, λs1, λs, and λi; the cavity outut is lotted from M. 4.4 Energy Scaling Cascaded OPO Figure 37 comares the erformance of a singly resonant, single-stage OPO with that of a cascaded OPO where only λs1 is resonant, showing that the cascaded OPO roduces more idler at higher um energies. At lower inut energies, the OPO tends to oerate with slightly higher idler outut, resumably due to the lower threshold resulting from a shorter cavity and lower intracavity losses. The conversion efficiency of the cascaded OPO idler at λi=8.8 µm, 1.7 µm, and 11.5 µm is 1%, 17%, and 15% resectively, yielding hoton conversion efficiencies of 89.8%, 89.% and 84.7%, thus aroaching the limit of the quantum defect. Figure 38 comares the hoton conversion efficiencies of the SRO cascaded OPO (SR-COPO) and the SRO single-stage OPO (SRO). The conversion efficiency of the single-stage OPO essentially saturates and reaches a oint where the same ercentage of the um ulse is deleted, while in the cascaded OPO, the 68

85 efficiency of the idler is continuously increasing as the inut energy increases. Both figures suggest that the cascaded OPO is beneficial only at higher inut energies. Figure 39 comares the erformance of a doubly resonant OPO with that of a cascaded OPO where λs1 is still highly resonant but the idler sees HR at M1 and 6% R at M. There is about a factor of two imrovement in the cascaded OPO idler erformance relative to that of the OPO. The conversion efficiency of the idler at λi=8.8 µm, 1.7 µm, and 11.5 µm is 5.%,.3%, and 18.5% yielding hoton conversion efficiencies of 18%, 14%, and 13%, thus overcoming the quantum defect. Figure 4 comares the doubly resonant cascaded OPO (DR-COPO) and the single-stage OPO (DRO) in terms of hoton conversion efficiency. Again, the conversion efficiency of the single-stage OPO saturates while the efficiency of the idler in the cascaded OPO is continuously increasing as the inut energy increases. Figure 41 lots the idler hoton conversion efficiencies of the two cascaded OPOs. 5 COPO i =8.8 m COPO i =1.7 m COPO i =11.5 m OPO i =8.8 m OPO i =1.7 m OPO i =11.5 m Outut Energy (J) Inut Energy (J) Figure 37: Numerical comarison in idler erformance between OPGaAs SR-COPO and SRO. 69

86 1.8 COPO i =8.8 m COPO i =1.7 m COPO i =11.5 m OPO i =8.8 m OPO i =1.7 m OPO i =11.5 m Conversion Efficiency Inut Energy (J) Figure 38: Numerical comarison in idler conversion efficiency OPGaAs SR-COPO and SRO. 3 5 COPO i =8.8 m COPO i =1.7 m COPO i =11.5 m OPO i =8.8 m OPO i =1.7 m OPO i =11.5 m Outut Energy (J) Inut Energy (J) Figure 39: Numerical comarison in idler erformance between OPGaAs DR-COPO and DRO. 7

87 1.8 COPO i =8.8 m COPO i =1.7 m COPO i =11.5 m OPO i =8.8 m OPO i =1.7 m OPO i =11.5 m Conversion Efficiency Inut Energy (J) Figure 4: Numerical comarison in idler conversion efficiency of OPGaAs DR-COPO and DRO DRO i =8.8 m DRO i =1.7 m DRO i =11.5 m SRO i =8.8 m SRO i =1.7 m SRO i =11.5 m Conversion Efficiency Inut Energy (J) Figure 41: Conversion efficiency lot of DR- and SR-COPO. 4.5 Limitations and Concerns The biggest factor that could lead the model to deviate from the hysical erformance of the cascaded OPO is that the model considers only monochromatic beams. While the linewidth of tyical um lasers is narrow enough to be aroximated as a 71

88 monochromatic source, the generated signal and idler, if generated from quantum fluctuations, will have some linewidth large enough that aroximating it as monochromatic is no longer valid. The broader linewidth signal from the first stage, which is used to um the second stage, may result in a lower conversion efficiency relative to what the monochromatic model suggests, due to varying degrees of hase matching from the various sectral comonents in the signal beam. However, seeding and imlementing line narrowing devices can reduce the linewidth of the first-stage signal, which should then lead to higher conversion efficiency in the second stage. If the fabrication of the grating attern in the second crystal is slightly off, the generated idler may not have exactly the same wavelength as the idler from the first crystal, which would lead to further deviation from the model. The model assumes the second crystal is erfectly hase matched to generate the same idler as the first, and that all of the idler hotons roduced in the OPO are sectrally identical. Sectrally distinct idlers will result in two discrete three-wave mixing interactions occurring within the same cavity and should result in an inefficient device. This can be remedied by temerature tuning one or both of the crystals until the generated idlers are equivalent for both stages. The linear cavities, as used in these numerical simulations, have relatively short distances between crystals and heating one crystal will most likely cause some residual heating of the other crystal simly due to their close roximity. This will cause a temerature gradient in the first crystal and has the chance to cause some adverse hase matching effects. Imlementing a ring cavity with the two crystals in searate legs could alleviate this roblem but at the cost of a longer cavity, with increased round tri cavity time and reduced intracavity resonant intensity. Numerical simulations have been run only for the linear 7

89 cascaded OPO so far. Tuning the um wavelength is another otion for adjusting the relative idler wavelengths, but this will change the hase matching conditions for both crystals and will need to be modeled accordingly. Finally, it should be noted that inclusion of a second crystal within the cavity doubles the interface losses. While these surfaces are tyically coated with anti-reflection coatings, these coatings are not erfect and each surface still contributes a small amount of loss due to reflection. Unexected material losses will also contribute to decreased conversion efficiency. Eitaxially grown OPGaAs has reviously demonstrated bulk absortion losses as low as.5 cm -1 [111], but for a given growth run, if defects are resent in the material, this will add to the overall loss of the device and the conversion efficiency will be decreased. The model also assumes the entire beam is contained within the OPGaAs crystal. This is tyically achieved with millimeter thickness, but for smaller aertures, say 5 6 µm, cliing may occur for the larger, longwave idler beam, adding another loss to reduce conversion efficiencies. 73

90 CHAPTER 5 EXPERIMENTAL SET-UP 5.1 Pum Laser For these exeriments, the OPO was umed with a.5 μm cryogenically cooled, diode-umed, Tm,Ho:YLF laser. The water-cooled um diode was a 15 W array of continuous wave aluminum gallium arsenide (AlGaAs) emitters roducing outut at 79 nm, and transmitted through a 1 m otical fiber. The laser diode outut was then couled through two AR coated 6 cm focal length lenses into a liquid nitrogen cooled 5x5x5 mm 3 YLF crystal doed with 6% Tm and 1% Ho. The side facing the diode laser was ARcoated for 79 nm to transmit the diode um and high-reflection (HR) coated for.5 μm essentially acting as a flat inut mirror for the lano-convex um laser cavity. The outcouler mirror had a radius of curvature (ROC) of 1 m with a 7% reflectivity at μm. The laser was ulsed using a water-cooled acousto-otic Q-switch caable of reetition rates from 1 Hz to 1 khz, and was oerated at 5 Hz for these exeriments, roducing a ulse width of aroximately 45 ns with an inut current to the um diode array of 18 Ams. At this um ower level, the Tm,Ho:YLF laser roduced about W of average ower, far in excess of the damage threshold of the OPGaAs samles at the corresonding ulse energy and tyical um sot size. In order to attenuate the ower incident uon the samle, a half-wave late was laced before the inut olarizer of a 74

91 faraday isolator, which allowed for recise control of the laser ower without affecting other beam arameters. The faraday isolator served to revent back reflections into the um laser, which can lead to um laser instability. Sectra of the OPO signal and idler were collected using a Horiba Triax 3 1/3 m sectrometer with a 1 g/mm grating blazed for 9 μm, a Stanford Research Systems lockin amlifier, and a cryogenically cooled HgCdTe detector. The HgCdTe detector and 1 g/mm grating were both most efficient at the idler but were still caable of detecting the signal and um. Slit widths were maintained at µm, which rovided a reasonable balance of resolution and throughut. The um laser s free-running wavelength has been measured at 5 nm on both the Horiba Triax and ThorLabs otical sectrum analyzer. Figure 4 shows the sectra of the um laser measured by the ThorLabs otical sectrum analyzer with and without an etalon. 1. No etalon Etalon.8 Normalized Intensity Wavelength (nm) Figure 4: Pum Sectra. 75

92 5. OPGaAs Crystals The grating eriod for the second-stage crystal was calculated using the signals measured in the revious LWIR OPGaAs OPO exeriments [7] as the um in Equation 1. Figure 43 lots the three different tuning curves for the three different secondary um (i.e. first signal) wavelengths for the second-stage crystal. The signals were measured to be λs=.55 μm,.54 μm, and.68 μm, which corresonds to a grating eriod in the second crystal of Λ=116 μm, 118 μm, and 15 μm resectively to generate the same idler wavelength from the first crystal. For each curve in Figure 43, the circles indicate the outut wavelengths from the second OPGaAs crystal s1 = =.7µm s1 = =.54µm s1 = =.55µm Wavelength (µm) Grating Period (µm) Figure 43: Cascaded turning curves. There are seven first-stage OPGaAs crystals and ten second-stage crystals that can be used for the cascaded OPO, but due to crystal damage, oor crystal olishing, and crystals out on loan, fewer crystals are available for use. Table 1 lists the samles that were used and in the cascaded OPO exeriments. 76

93 Table 1: Samle list of cascaded OPO samles. Samle # Crystal dimensions (mm) Grating Period (µm) x 6.5 x x 7.95 x x 7.88 x x 7.94 x x The modeling was conducted utilizing the three different grating eriods used in the original LWIR OPGaAs work, with the corresonding secondary crystal eriods. Of those original five samles with longwave gratings only one is currently available, samle 5, Λ1=76. µm. Another OPGaAs crystal with a slightly different eriod, Λ1=76.6 µm, was also used. Additionally, there are only three secondary samles all with eriod Λ=15. µm. (The new samle with eriod 76.6 µm may not hase match to Λ=15. µm since they will generate slightly different idler wavelengths but the idlers should be able to be tuned together). Therefore, only crystals hase matched to generate 8.8 µm idler have been included and the crystals used to generate idler wavelengths of 1.7 µm and 11.5 µm have been set aside for further research. The crystals, all ~13 17 mm in length were laced in a ~3 mm cavity with 5 cm ROC mirrors. The resonant mode in the cavity should be fairly collimated and a fairly non-diverging beam. The um beam was matched to the resonant mode of the cavity and the 1/e beam radius incident on the crystal was ~ µm. The cascaded OPGaAs OPO is shown in Figure

94 Figure 44: Cascaded OPGaAs OPO. 5.3 Mirror Coating Reflectivities The mirror reflectivities for the cascaded OPO were designed to be HR at M1 and AR at M for the idler after the initial round of modeling suggested greatest idler outut when only signal 1 was resonant. To summarize: M1 was designed to be AR at.54 µm and µm and HR at.5.7 µm and 8 1 µm; while M was HR at.54 µm and.5.7 µm, and AR at µm and 8 1 µm. Four band dielectric coatings, articularly those that san from µm to 1 µm, are fairly difficult to fabricate and meeting the secification can be difficult. The transmission lots for the mirrors M1 and M are shown below in Figure 45 and Figure 46. The transmissions in the regions of interest generally meet the secifications given, but there are a few areas of deviation. First, for M1, there is a 5% R at the um wavelength. The exeriment is not currently um limited, but reflecting half of the um energy away at the inut of the OPO is roblematic. Damaging the OPO mirror now becomes a concern when the um energy needs to be increased just to coule in enough energy for the OPO to reach threshold. The reflectivities for signal 1 at both mirrors are HR, and the only deviation in the idler secification is that M has a 1% R but, as the 78

95 modeling suggests, this should still work. The reflectivities at M1 and M for signal are % R and 1% R, and will effectively coule out signal on each ass. Therefore, the main roblem is the relatively high reflectivity of the um at M1. For this reason, it was relaced by the mirrors for the original LWIR OPGaAs work. This mirror wasn't originally designed for a coating at µm however it only has a ~4% R, as lotted in Figure 46, which should be low enough for the device to reach threshold. Now, the reflectivity at M1 for the um is 13% which is slightly higher than desired but it easier to deal with than 5% R. Inut um energies, as shown in all sloe efficiency measurements found in the next chater, were measured before M1 and the 13% loss in um energy was accounted for. 1 8 Transmission Pum Signal 1 Signal Idler Transmission (%) Wavelength (m) Figure 45: Cascaded OPGaAs OPO M1 mirror transmission. 79

96 1 8 Transmission Pum Signal 1 Signal Idler Transmission (%) Wavelength (m) Figure 46: Cascaded OPGaAs OPO M mirror transmission. 1 8 Transmission Pum Signal 1 Signal Idler Transmission (%) Wavelength (m) Figure 47: Longwave OPGaAs OPO M1 mirror transmission. 5.4 Polarization The Tm,Ho:YLF laser is linearly olarized and its orientation is determined by the osition of the olarizer on the faraday isolator. For these exeriments, the um was olarized horizontally going into the OPO. From revious exerience, when the um 8

97 olarization is horizontal, the signal is horizontal and the idler is vertical. As the (horizontally olarized) signal ums the second crystal, second signal will also be horizontal, and the idler again vertical. These combinations of olarization should result in the exected nonlinear coefficient of deff = 94 m/v. 81

98 CHAPTER 6 EXPERIMENTAL RESULTS 6.1 OPO The outut from the two first-stage crystals were initially measured individually without the second crystal in the OPO. The OPO functions as an SRO for the single-stage device, as exected based on the mirror reflectivities described in the revious chater. Figure 48 lots the sloe efficiency for samle 46, Λ1=76.6 µm, and Figure 49 lots the sloe efficiency for samle 5, Λ1=76. µm. The sloe efficiency comarison between the idlers of the two crystals is shown in Figure 5. The idler sloe efficiencies of both samles are roughly 5% before outut starts to flatten off around ~4 µj, with samle 46 slightly outerforming samle 5. Thresholds were reached at ~1 µj and ~18 µj for samle 46 and samle 5 resectively. Previous exerience with OPOs suggests that the onset of backconversion occurs when the OPO outut beings flattening off. This was determined by insecting the temoral rofiles of the outut and residual um ulses. The inut um ulse would be significantly deleted at threshold then exhibit an increase in energy later in the ulse. This is a clear sign of backconversion. The outut ulses however were not examined in this OPO. The sloe efficiencies and outut energy recorded from the SRO cavity, shown in Figure 48, are comarable to the SRO cavity from the revious LWIR OPGaAs SRO 8

99 cavity, shown in Figure 8, suggesting backconversion is once again leading to the observed rollover in outut. 3 Idler, Signal, Total, Outut Energy (J) Inut Energy (J) Figure 48: Sloe efficiency of samles 46. Idler=5.7% Signal, =.% Total, =5.9% 15 Outut Energy (J) Inut Energy (J) Figure 49: Sloe efficiency lots of first-stage crystals in OPO. 83

100 5 Samle 5 - =76. m Samle 46 - =76.6 m Outut Energy (J) Inut Energy (J) Figure 5: Idler sloe efficiency comarison. 6. Cascaded OPO The sloe efficiencies for the cascaded OPGaAs OPO are shown below. Figure 51 illustrates the oututs when samle 46 is utilized as the first-stage crystal along with each of the three second-stage crystals. The idler sloe efficiencies range from ~1.5 % while the second signal sloe efficiencies range from ~.7% 1.%. Figure 5 illustrates the oututs when samle 5 is utilized as first-stage crystal along with each of the three secondstage crystals. The idler sloe efficiencies range from ~ % while the second signal sloe efficiencies range from ~.5%.6%. Again, higher outut is observed for Λ1=76.6 µm, though both are still relatively oor comared to the revious SRO cavity that utilized only a first-stage crystal. Total sloe efficiencies for both crystals is ~3% and is less than when only a first-stage crystal is resent in the cavity. The oututs aear to have a urely linear relationshi to the inut energy and backconversion is not resent. This is to be exected given the relatively oor erformance of the OPO. The signal was not detectable on the ower meter or camera and this is due to its being highly resonant within the cavity 84

101 while also getting deleted in the second crystal. Images of the idler and the second signal were taken ~ cm away from the OPO outcouler with an ElectroPhysics PV3 camera and are shown in Figure 53. There are a handful of reasons why the cascaded OPO may be oerating less effectively than anticiated including incorrect hase matching, material defects and linewidth of signal Idler, Samle 55 Signal,Samle 55 Idler, Samle 56 Signal, Samle 56 Idler, Samle 57 Signal, Samle 57 Outut Energy (J) Inut Energy (J) Figure 51: Sloe efficiencies cascaded OPGAs OPO with samle 46 along with the three different secondary crystals. 85

102 5 4 Idler, Samle % Signal, Samle 55.6% Idler, Samle 56 1.% Signal, Samle 56.6% Idler, Samle % Signal, Samle 57.5% Outut Energy (J) Inut Energy (J) Figure 5: Sloe efficiencies cascaded OPGAs OPO with samle 5 along with the three different secondary crystals. Figure 53: Image of idler (left) and signal (right). 6.3 Sectra If the crystals are not roerly hase matched, then this may be one factor that will lead to oor erformance. If the grating eriods of the first- and second-stage crystals are not hase matched to generate the same idler, then two cometing nonlinear rocesses will occur within the cavity and neither rocess will run efficiently. As mentioned before, idlers from Λ1=76.6 µm should not be hase matched to Λ=15 µm. The sectral contributions 86

103 from signal 1, signal and idler for the cascaded OPO with Λ1=76.6 µm are shown in Figure 54 Figure 56 resectively. As exected, with a grating eriod that is slightly off, two idlers emerge in Figure 56. The searation of the idlers is ~7 nm. The sectral contributions from signal 1, signal and idler measurements for the cascaded OPO with Λ1=76. µm are shown in Figure 57 Figure 59 resectively. Again the idlers are searated but this time by ~5 nm, which is unexected since Λ=15 µm was designed to hase match with the reviously measured signal to generate the same idler wavelength. This could, however, hel to exlain the oor erformance in the COPOs, as two different three-wave mixing rocesses roducing two distinct idlers are resent. Greater conversion should occur if the two idlers are sectrally identical. Pum tuning or temerature tuning can modify the hase matching conditions of the crystals to shift the two idler wavelengths together. 1. Signal 1.8 Norm. Intensity Wavelength (nm) Figure 54: Signal 1 from cascaded OPO with Λ1=76.6 µm. 87

104 1. Signal.8 Norm. Intensity Wavelength (nm) Figure 55: Signal from cascaded OPO with Λ1=76.6 µm. 1. Idler.8 Norm. Intensity Wavelength (nm) Figure 56: Idler from cascaded OPO with Λ1=76.6 µm. 88

105 1. Signal 1.8 Norm. Intensity Wavelength (nm) Figure 57: Signal 1 from cascaded OPO with Λ1=76. µm. 1. Signal.8 Norm. Intensity Wavelength (nm) Figure 58: Signal from cascaded OPO with Λ1=76. µm. 89

106 1. Idler.8 Norm. Intensity Wavelength (nm) Figure 59: Idler from cascaded OPO with Λ1=76. µm. 9

107 CHAPTER 7 DISCUSSIONS AND NEAR-FUTURE EXPERIMENTATION While the oututs of the cascaded OPGaAs OPO are not otimized and true amlification of the idler was not observed, this demonstration still serves, to the best of our knowledge, as the first cascaded OPGaAs OPO and first longwave cascaded OPO. Techniques like the cascaded OPO are still of interest to surass the large quantum defect from converting a µm hoton into an 8 1 µm hoton. The issues described above must be addressed, however, in order consider the cascaded OPO as a viable otion. Thus far the obtained results have been significantly limited by the lack crystals and crystal damage. 7. Crystal Damage Initially, 5 cm ROC mirrors were used for a direct comarison to the revious LWIR OPGaAs and all erformance data reorted in Chater 6 utilized 5 cm ROC mirrors. However, since nonlinear interactions are intensity driven, smaller sot sizes should lead to increased conversion for the same inut um energy. Therefore 1 cm ROC mirrors were used in the cavity to generate resonant modes that are focused tighter with higher intensities. Additionally, if future mirror coatings are designed to artially resonate the idler, then cliing may become an issue with 5 cm ROC mirrors. The resonant mode of the idler with 5 cm ROC mirror and a ~3 cm long cavity has a ~4 91

108 µm 1/e radius. While the um and resonant signal beams roagate through the 5 µm thick atterned region of the crystal without cliing, the larger resonant mode of the idler leads to the wings of the beam cliing on the edges of the crystal face. An ElectroPhysics camera was used to align the cascaded OPO, and the oututs from cascaded OPO using 1 cm would simly flicker on the camera. This tyically suggests that the OPO is close to being aligned or it s near threshold. Significant outut was never observed with 1 cm ROC mirrors, however, and only resulted in damaging the OPGaAs crystals. The OPGaAs crystals exhibited damage at relatively low inut energies while using both sets of mirrors. Literature values suggest that bulk GaAs has a damage threshold of ~ 5 J/cm [11], but damage has been observed at inut fluences of ~1 J/cm [113]. Normally the limiting factor in damage has traditionally been the anti-reflective dielectric coatings. (The nonlinear crystals could be cut to Brewster s angle to exloit the higher damage threshold of the bulk material, but roblems arise as the Brewster s angle for all wavelengths is not the same, articularly for the longwave idler. Also it is not ossible for all three interacting waves to have the correct olarization for maximum transmission at Brewster s angle.) For a 5 cm ROC mirror, the um sot size incident on the crystal is ~ µm (1/e radius) and the crystal started exhibiting damage at incident owers as low as ~15 mw, which corresonds to a fluence of ~.4 J/cm. For 1 cm ROC mirrors the um sot size incident on the crystal is ~15 µm and the crystal started exhibiting damage with owers as low as ~1 mw, which corresonds to a fluence of ~.8 J/cm. This relatively low damage threshold makes aligning the OPO difficult when the crystals exhibit damage at energy levels close to threshold. The device would tyically turn on, but then the outut would start to dwindle away and the cavity could not be 9

109 realigned by adjusting the OPO mirrors. The samle would then be translated to an undamaged region of the crystal face and the same result occurred. Figure 6 shows laser damage on the front face of the OPGaAs crystal. Figure 6: Damage on LWIR OPGaAs samle. There are a coule ossible reasons for damaging the crystal at such a low ower. First, the sot size of the um laser could be smaller than exected and thus, the higher intensity of the beam could have surassed the damage threshold for the dielectric coating. Inut um sot sizes were confirmed, however, using a DataRay microbolometer and manual knife edge scans and were not focused tighter than exected. Second, the quality of coatings could be oor and have a much lower damage threshold than revious OPGaAs AR coatings. The four band coating we secified to the coating vendors is a fairly difficult coating to fabricate and an unusual custom order. Getting most of the reflectivity requirements correct may have come at the cost of ower handling. Third, the surface quality of the crystal after olishing may have been substandard, with remaining surface and subsurface defects. A damage study of ZGP has shown that residual subsurface damage from the cutting rocess affects the damage threshold of the coated samles. 93

110 Damage threshold was increased significantly when ~4 µm of material was olished off the surface rior to coating [114]. There are several follow-on exeriments and adjustments, which will serve as useful endeavors to increase the efficiency of the cascaded OPO, such as um tuning and temerature techniques mentioned above, to increase the erformance of the cascaded OPO from ~3%. 7.1 Crystal Transmission Higher losses, due to crystal coating reflectivity, scattering or bulk absortion, will raise OPO threshold and reduce the conversion efficiency of a device. Transmission of the um beam through each cascaded crystal is given in Table 11. The um transmission was measured though multile sots in each crystal with the corresonding inut energy listed in the table. The average transmission through the crystals is ~9%. Losing on average ~8% er crystal ass will add a significant amount of losses to the system and decrease conversion efficiency. Since the exeriment is not um limited, the inut energy can simly be increased, though the onset of crystal damage will now become a concern. Losses at the resonant signal 1 and at the idler are be a larger concern. Total samle loss can be tested at signal 1 using a Cr:ZnSe laser, if it ermits tuning to signal 1 wavelengths. Table 11: Pum transmission through samles with eriod s Λ1 and Λ. Samle # Inut Energy (µj) Outut Energy % Transmission (µj)

111 Temerature and Pum Tuning The oututs of nonlinear interactions can tyically be tuned with various techniques such as temerature tuning and um tuning. Heating and cooling crystals alters the temerature deendent indices of refraction and will modify the hase matching conditions for a given um and grating eriod. Thus, it should be ossible to tune the temerature of the crystals such that they both generate the same idler wavelength. Additionally, for a given nonlinear grating eriod, changing the um wavelength will change the outut wavelengths in order to meet the hase matching conditions. It might be ossible to tune the um in such a way that the idler oututs from both OPO stages coincide. Pum tuning may require a little more finesse to achieve erfect hase matching. Since there are two crystals, changing the um wavelength will change the signal 1 wavelength and thus the oututs from the second-stage crystal will be tuned as well. Phase matching to achieve the same idlers may be difficult. A small amount of tuning in the um wavelength should be ossible with an etalon in the um laser cavity, and a modest change of ~1 nm tyically leads to a much larger change in the longwave outut. Figure 6 illustrates the theoretical 95

112 tuning of the COPO as a function of um wavelength tuning. This is an obvious recommendation for future work = 76 m, = 15 m 9 Wavelength (m) Pum Wavelength (m) Figure 61: Theoretical outut of the two OPGaAs crystals as a function of um wavelength using Λ1=76. µm = 76.6 m, = 15 m 9 Wavelength (m) Pum Wavelength (m) Figure 6: Theoretical outut of the two OPGaAs crystals as a function of um wavelength using Λ1=76.6 µm. Utilizing Λ1=76.6 µm, Figure 63 Figure 65 illustrates the temerature tuning of the cascaded OPO. Figure 63 illustrates the temerature deendence of the cascaded OPO 96

113 as the first-stage crystal is heated indeendently while the temerature of the second-stage crystal remains constant at 3 K. Previous OPO oututs have agreed well with disersion relations when there was slight heating to the crystal (~ 3 35 K), thus 3 K was chosen. An oerating temerature slightly above room temerature is not unreasonable, since tyically, nothing is imlemented to control the temerature of the crystal and localized heating in the crystal is exected. (Note: the figure shows a temerature deendence of the behavior of the second-stage crystal. This originates in the hase matching conditions altered by the first-stage crystal as the signal wavelength, which serves to um second-stage crystal, is changed). Figure 64 illustrates the temerature deendence of the cascaded OPO as the second-stage crystal is heated indeendently while the temerature of first-stage crystal remains constant at 3 K. Figure 65 illustrates the temerature deendence of the cascaded OPO as both crystals are heated simultaneously with identical temeratures. (It is also ossible to heat both crystals simultaneously but at different temeratures. While this aroach offers significantly more scenarios for temerature tuning, it is not imlemented here). From the figures below, for a um wavelength of.5 µm and Λ1=76.6 µm, it aears that slightly cooling either to 95 K or both crystals to 97 K will result in the same idler in both stages. Figure 66 Figure 68 illustrated similar lots as Figure 63 Figure 65 but utilizing Λ1=76. µm instead. These figures indicate that heating either crystal to 31 K or both crystals to 35 K should hase match both crystals to generate the same idler. 97

114 = 76.6 m, = 15 m 1 9 Wavelength (m) Temerature (K) Figure 63: Theoretical oututs of the two OPGaAs crystals as only Λ1=76.6 µm is heated while Λ=15 µm temerature remains (Note: as the figure shows a temerature deendence on Λ, the temerature deendence originates in the hase matching conditions altered by the first crystal) = 76.6 m = 15 m 1 9 Wavelength (m) Temerature (K) Figure 64: Theoretical oututs of the two OPGaAs crystals as only Λ=15 µm is heated while Λ1=76.6 µm temerature remains. 98

115 = 76.6 m = 15 m 1 9 Wavelength (m) Temerature (K) Figure 65: Theoretical oututs of the two OPGaAs crystals as Λ1=76.6 µm and Λ=15 µm are heated simultaneously = 76 m = 15 m 1 9 Wavelength (m) Temerature (K) Figure 66: Theoretical oututs of the two OPGaAs crystals as only Λ1=76. µm is heated while Λ=15 µm temerature remains. 99

116 = 76 m = 15 m 1 9 Wavelength (m) Temerature (K) Figure 67: Theoretical oututs of the two OPGaAs crystals as only Λ=15 µm is heated while Λ1=76. µm temerature remains = 76 m = 15 m 1 9 Wavelength (m) Temerature (K) Figure 68: Theoretical oututs of the two OPGaAs crystals as Λ1=76. µm and Λ=15 µm are heated simultaneously. 7.4 OPO Linewidth and Line Narrowing Another factor that could lead to some deviations in the erformance of the cascaded OPO is the linewidth of signal 1. While the linewidth of the um is narrow enough to be aroximated as a monochromatic source, the generated signal and idler 1

117 fields will have some bandwidth large enough that aroximating them as monochromatic is no longer valid. The linewidths of the signal and idler from the LWIR OPO, however, are narrower than what has been observed in the MWIR OPGaAs OPOs and this is exected since the LWIR oututs are further from degeneracy. Still, the bandwidth of signal 1 used to um the second crystal may be broad enough to result in decreased conversion efficiency. Tyically, more narrowband oututs can be achieved from either seeding the rocess with a narrow linewidth source or imlementing line-narrowing devices, such as an etalon or grating in the OPO. Sloe efficiencies shown in Figure 48 Figure 5 were obtained with the free running um whose FWHM bandwidth is ~1. nm. There are numerous eaks in the um sectrum however it is within the accetance bandwidth of the intended interaction in OPGaAs. If each eak is contributing to its own nonlinear rocess then the resulting signal beam should be fairly broad. As the um linewidth is reduced to ~. nm with an etalon the linewidth of the signal should also be slightly reduced as well, though not as much as by introducing an etalon or grating to the OPO cavity itself. This may incrementally imrove the cascaded OPO efficiency but the main goal of imlementing the etalon is to achieve some degree of um tuning, as mentioned above. As the etalon was inserted into the um cavity, the OPGaAs crystals aear to damage even quicker than without the etalon and the OPO never reached threshold. Further investigation is needed here as well. 11

118 7.5 Additional OPGaAs Crystals New OPGaAs crystals have recently been grown and fabricated, and are awaiting olishing and coating. A new AR coating run may rove more robust. In addition to single domain crystals, monolithic cascaded samles with both eriods on a single crystal could be fabricated, as the crystal in Figure 69 illustrates. Reducing the number of interfaces within the cavity will reduce loss within the cavity and only hel matters. We also now have a Brewster cut cascaded monolithic crystal samle on loan from at BAE Systems. The crystal is designed with Λ1=76.5 µm and Λ=135 µm to generate an idler wavelength at 8.1 µm from a.9 µm Ho:YAG laser. The Q-switched Ho:YAG laser we currently have to um this samle consists of a 5 mm long rod doed with 1% Ho, and is umed by a 198 nm IPG Tm:fiber. It can readily roduce 5 W average ower with a ulse width of 6 ns. λ Λ 1 Λ λ s1 λ i M 1 M Figure 69: Brewster cut cascaded monolithic OPGaAs crystal OPO. 7.6 OPO Pumed OPA Another method to amlify the idler is to remove the second crystal from the cascaded OPO cavity and imlement the amlification as a tyical OPA stage with a tyical 1

119 signal-stage OPO um source. Again, the signal hoton can be used as the um hoton for the next crystal and the crystal should be hase matched to generate the same idler. Therefore, more signal hotons need to exit the OPO in order to um the OPA and DRO cavities will generally generate more signal outut than the SRO. Using the signal as the um in this scenario, however, may only result in relatively minimal amlification in the idler since the number of hotons for the signal and idler outut will be on the same order. It is also ossible to oerate the OPA stage with another first-stage crystal and amlify the idler with the original um. Since the first OPO isn't um limited, just crystal damage limited, there is lenty of leftover um that could be slit off and recombined before the amlifier stage. Comaring the idler amlification of this rocess to the gain exerienced by the cascaded OPO is not a fair comarison since more um hotons will be used in the rocess. It does, however, have ossibility of generating more idler, which one of the main goals of the exeriment. Neither of these amlifier stages has been modeled but this can easily be imlemented in either the numerical model or SNLO. Figure 7: Signal outut from a single-stage OPO uming an external OPA to amlify the idler. 13