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Optical Materials Express

Optical Materials Express

  • Editor: David J. Hagan
  • Vol. 1, Iss. 7 — Nov. 1, 2011
  • pp: 1292–1300
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Nonlinear, dispersive, and phase-matching properties of the new chalcopyrite CdSiP2 [Invited]

Vincent Kemlin, Benoit Boulanger, Valentin Petrov, Patricia Segonds, B. Ménaert, Peter G. Schunneman, and Kevin T. Zawilski  »View Author Affiliations


Optical Materials Express, Vol. 1, Issue 7, pp. 1292-1300 (2011)
http://dx.doi.org/10.1364/OME.1.001292


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Abstract

We compare the nonlinear and dispersive properties of the recently discovered mid-infrared nonlinear crystal CdSiP2 with other chalcopyrite materials to establish its potential for super-continuum generation through a second-order nonlinear process.

© 2011 OSA

1. Introduction

The nonlinear optical crystal CdSiP2 (CSP) belongs to the tetragonal point group 4¯2m, with lattice constants a = 5.68Å, c = 10.431 Å, and Z = 4 for the unit cell parameters [1

1. S. G. Abrahams and J. L. Bernstein, “Luminescent piezoelectric CdSiP2: Normal probability plot analysis, crystal structure, and generalized structure of the AIIBIVCV2 family,” J. Chem. Phys. 55(2), 796–803 (1971). [CrossRef]

]. It was grown in the past in small sizes that did not allow measurement of essential physical properties [2

2. G. A. Ambrazyavichyus, G. A. Babonas, and A. Yu. Shileika, “Birefringence of pseudodirect bandgap A2B4C52 semiconductors,” Sov. Phys. Collect. 17, 51–55 (1977) [transl. from Lit. Fiz. Sb. 17, 205–211 (1977)].

7

7. A. Ambrazevicius and G. Babonas, “Dependence of birefringence of pseudodirect gap A2B4C52 compounds on hydrostatic pressure and on temperature,” Sov. Phys. Collect. 18, 52–59 (1978) [transl. from Lit. Fiz. Sb. 18, 765–774 (1978)].

].

CSP is optically negative uniaxial chalcopyrite so that non-critical type-I (oo-e) phase-matching is possible in contrast to the positive ZnGeP2 (ZGP) which is the only commercially available II-IV-V2 type chalcopyrite. The birefringence, (ne-no), of CSP was found to be - 0.06 approaching a wavelength of 6 µm [2

2. G. A. Ambrazyavichyus, G. A. Babonas, and A. Yu. Shileika, “Birefringence of pseudodirect bandgap A2B4C52 semiconductors,” Sov. Phys. Collect. 17, 51–55 (1977) [transl. from Lit. Fiz. Sb. 17, 205–211 (1977)].

], - 0.051 near 2 µm [7

7. A. Ambrazevicius and G. Babonas, “Dependence of birefringence of pseudodirect gap A2B4C52 compounds on hydrostatic pressure and on temperature,” Sov. Phys. Collect. 18, 52–59 (1978) [transl. from Lit. Fiz. Sb. 18, 765–774 (1978)].

], - 0.05 at 1 µm [5

5. N. A. Goryunova, L. B. Zlatkin, and K. K. Ivanov, “Optical anisotropy of A2B4C52 crystals,” J. Phys. Chem. Solids 31(11), 2557–2561 (1970). [CrossRef]

], and - 0.045 at 840 nm [3

3. N. Itoh, T. Fujinaga, and T. Nakau, “Birefringence in CdSiP2,” Jpn. J. Appl. Phys. 17(5), 951–952 (1978). [CrossRef]

] in earlier work. An isotropic point, i.e. ne = no, was also observed close to the band-edge [5

5. N. A. Goryunova, L. B. Zlatkin, and K. K. Ivanov, “Optical anisotropy of A2B4C52 crystals,” J. Phys. Chem. Solids 31(11), 2557–2561 (1970). [CrossRef]

7

7. A. Ambrazevicius and G. Babonas, “Dependence of birefringence of pseudodirect gap A2B4C52 compounds on hydrostatic pressure and on temperature,” Sov. Phys. Collect. 18, 52–59 (1978) [transl. from Lit. Fiz. Sb. 18, 765–774 (1978)].

]: at room temperature this point occurs at 2.41 eV (514.5 nm) [6

6. G. Ambrazyavichyus, G. Babonas, and V. Karpus, “Optical activity of CdSiP2,” Sov. Phys. Semicond. 12, 1210–1211 (1978) [trasl. from Fiz. Tekh. Poluprovodn. 12, 2034–2036 (1978)].

,7

7. A. Ambrazevicius and G. Babonas, “Dependence of birefringence of pseudodirect gap A2B4C52 compounds on hydrostatic pressure and on temperature,” Sov. Phys. Collect. 18, 52–59 (1978) [transl. from Lit. Fiz. Sb. 18, 765–774 (1978)].

] and near this point, optical activity can be observed [6

6. G. Ambrazyavichyus, G. Babonas, and V. Karpus, “Optical activity of CdSiP2,” Sov. Phys. Semicond. 12, 1210–1211 (1978) [trasl. from Fiz. Tekh. Poluprovodn. 12, 2034–2036 (1978)].

].

Recently, high optical quality crystals of CSP with sizes reaching 70 × 25 × 8 mm3 were grown successfully from the melt by using high purity starting materials via the horizontal gradient freeze technique [8

8. P. G. Schunemann, K. T. Zawilski, T. M. Pollak, D. E. Zelmon, N. C. Fernelius, and F. Kenneth Hopkins, “New nonlinear optical crystal for mid-IR OPOs: CdSiP2,” Advanced Solid-State Photonics, Nara, Japan, Jan. 27–30, 2008, Conference Program and Technical Digest, Post-Deadline Paper MG6.

10

10. K. T. Zawilski, P. G. Schunemann, T. C. Pollak, D. E. Zelmon, N. C. Fernelius, and F. K. Hopkins, “Growth and characterization of large CdSiP2 single crystals,” J. Cryst. Growth 312(8), 1127–1132 (2010). [CrossRef]

]. Important physical characteristics, including transparency, birefringence, and thermo-mechanical properties have already been measured and can be found in the literature [10

10. K. T. Zawilski, P. G. Schunemann, T. C. Pollak, D. E. Zelmon, N. C. Fernelius, and F. K. Hopkins, “Growth and characterization of large CdSiP2 single crystals,” J. Cryst. Growth 312(8), 1127–1132 (2010). [CrossRef]

].

In the present work we analyze the nonlinear and dispersive properties of CSP predicting broadband continuum generation phase-matching at a pump wavelength of 2.43 µm. A comparison with other chalcopyrite materials in the context of super-continuum generation through a second-order nonlinear process is also established.

2. Nonlinearity of CSP

The value of the d36 nonlinear optical coefficient of CSP was estimated relative to ZGP by second-harmonic generation (SHG) near 4.6 µm [11

11. V. Petrov, F. Noack, I. Tunchev, P. Schunemann, and K. Zawilski, “The nonlinear coefficient d36 of CdSiP2,” Proc. SPIE 7197, 71970M (2009). [CrossRef]

]. The fundamental beam that we used was produced by a femtosecond KNbO3-based optical parametric amplifier (OPA) pumped near 800 nm at a repetition rate of 1 kHz. The OPA used a 6-mm-long KNbO3 crystal cut at θ = 41.9° for type I phase matching. As an OPA seed we used the frequency doubled idler output of a BBO type-II OPA near 1 μm. The idler pulses of the KNbO3 OPA were temporally broadened but simultaneously spectrally narrowed (typical FWHM of 90 nm). The uncoated CSP sample was 0.53 mm thick with an aperture of 7 × 7 mm2. It was cut at (θ = 43°, φ = 45°) for type-I SHG. An uncoated sample of ZGP, cut at (θ = 50.5°, φ = 0°) with identical size and thickness, was used as a reference.

For the chosen wavelength and crystal thickness, the spectral acceptance was much larger than the spectral extent of the pump pulses (~12 times for CSP and ~7 times for ZGP). The angular acceptance was also much larger (>11 times for CSP and >16 times for ZGP) than the angular extent of the incident beam focused by a 25 cm BaF2 lens. Finally, according to the beam diameter at the position of the crystals, the birefringence walk-off (tanρ = 0.009 for CSP and tanρ = 0.005 for ZGP) could be neglected. The incident pulse energy near 4.6 µm was limited to less than 2 µJ and the internal conversion efficiency was below 10%. This justifies the plane-wave approximation. The effective nonlinear coefficient was estimated by correcting the relative SHG efficiency only for the different Fresnel losses and index of refraction although both corrections did not exceed 5%.

An average of 20 measurements for each crystal was taken, in which the results in terms of SHG output did not deviate by more than ± 5%. The experimentally measured internal phase-matching angles were used then to derive the ratio for the d36 coefficients: we found d36(CSP) = 1.07d36(ZGP) with a relative error estimate of ± 5%. Assuming d36 = 75 pm/V for of ZGP at a fundamental wavelength of λF = 9.6 µm [12

12. P. D. Mason, D. J. Jackson, and E. K. Gorton, “CO2 laser frequency doubling in ZnGeP2,” Opt. Commun. 110(1-2), 163–166 (1994). [CrossRef]

], which gives 79 pm/V at λF = 4.56 µm when using Miller’s rule, it is found d36 = 84.5 pm/V for CSP at λF = 4.56 µm.

Fully independent, the result for d36(CSP) was confirmed in frequency doubling of 100 ns long pulses at the second harmonic (λF = 4.78 µm) of a TEA CO2 laser operating at 4 Hz repetition rate [14

14. L. P. Gonzalez, D. Upchurch, J. O. Barnes, P. G. Schunemann, K. Zawilski, and S. Guha, “Second harmonic generation in CdSiP2,” Proc. SPIE 7197, 71970N (2009). [CrossRef]

].

3. Sellmeier equations and phase-matching properties

Note that, based on older data of the temperature dependence of the birefringence [7

7. A. Ambrazevicius and G. Babonas, “Dependence of birefringence of pseudodirect gap A2B4C52 compounds on hydrostatic pressure and on temperature,” Sov. Phys. Collect. 18, 52–59 (1978) [transl. from Lit. Fiz. Sb. 18, 765–774 (1978)].

], thermo-optic coefficients had also been fitted for CSP [16

16. G. Ghosh, “Dispersion of temperature coefficients of birefringence in some chalcopyrite crystals,” Appl. Opt. 23(7), 976–978 (1984). [CrossRef] [PubMed]

]. The Sellmeier coefficients of Schunemann et al. [9

9. P. G. Schunemann, K. T. Zawilski, T. M. Pollak, V. Petrov, and D. E. Zelmon, “CdSiP2: a new nonlinear optical crystal for 1 and 1.5-micron-pumped, mid-IR generation,” Advanced Solid-State Photonics, Denver (CO), USA, Feb. 1–4, 2009, Conference Program and Technical Digest, Paper TuC6.

] were also extended with temperature dependence, with validity between 10°C and 70°C, which was derived fitting optical parametric oscillator (OPO) tuning data recorded for a pump wavelength of 1.99 µm emitted by a Tm:YALO laser [17

17. P. G. Schunemann, L. A. Pomeranz, K. T. Zawilski, J. Wei, L. P. Gonzalez, S. Guha, and T. M. Pollak, “Efficient mid-infrared optical parametric oscillator based on CdSiP2,” Advances in Optical Materials, San Jose (CA), USA, Oct. 14–15, 2009, Conference Program and Technical Digest, Paper AWA3.

].

The physical validity of these Sellmeier equations can be assessed from the corresponding infrared pole wavelengths λIR. These values were taken as initial parameters at λIRo,e = 20.4 µm for both the ordinary and the extraordinary indices by Lambrecht et al. in their calculations [15

15. W. R. L. Lambrecht and X. Jiang, “Noncritically phase-matched second-harmonic-generation chalcopyrites based on CdSiAs2 and CdSiP2,” Phys. Rev. B 70(4), 045204 (2004). [CrossRef]

]. The Sellmeier equations of Schunemann et al. [8

8. P. G. Schunemann, K. T. Zawilski, T. M. Pollak, D. E. Zelmon, N. C. Fernelius, and F. Kenneth Hopkins, “New nonlinear optical crystal for mid-IR OPOs: CdSiP2,” Advanced Solid-State Photonics, Nara, Japan, Jan. 27–30, 2008, Conference Program and Technical Digest, Post-Deadline Paper MG6.

,9

9. P. G. Schunemann, K. T. Zawilski, T. M. Pollak, V. Petrov, and D. E. Zelmon, “CdSiP2: a new nonlinear optical crystal for 1 and 1.5-micron-pumped, mid-IR generation,” Advanced Solid-State Photonics, Denver (CO), USA, Feb. 1–4, 2009, Conference Program and Technical Digest, Paper TuC6.

,17

17. P. G. Schunemann, L. A. Pomeranz, K. T. Zawilski, J. Wei, L. P. Gonzalez, S. Guha, and T. M. Pollak, “Efficient mid-infrared optical parametric oscillator based on CdSiP2,” Advances in Optical Materials, San Jose (CA), USA, Oct. 14–15, 2009, Conference Program and Technical Digest, Paper AWA3.

] cannot provide λIRo,e since the fits were based on expressions using infrared correction terms. In the case of Kemlin et al. [18

18. V. Kemlin, P. Brand, B. Boulanger, P. Segonds, P. G. Schunemann, K. T. Zawilski, B. Ménaert, and J. Debray, “Phase-matching properties and refined Sellmeier equations of the new nonlinear infrared crystal CdSiP2.,” Opt. Lett. 36(10), 1800–1802 (2011). [CrossRef] [PubMed]

], the values can be deduced from the ordinary and extraordinary refractive index equations that were experimentally obtained, which leads to λIRo = 45.5 µm and λIRe = 22.2 µm respectively. The procedure is the same for Kato et al. [19

19. K. Kato, N. Umemura, and V. Petrov, “Sellmeier and thermo-optic dispersion formulas for CdSiP2,” J. Appl. Phys. 109(11), 116104 (2011). [CrossRef]

], but the two infrared poles obtained are closer, i.e. λIRo = 24.8 µm and λIRe = 25.6 µm. Note that all these values are compatible with several optically active phonons measurements previously reported [21

21. G. C. Bhar, “Sphalerite vibration mode in chalcopyrites,” Phys. Rev. B 18(4), 1790–1793 (1978). [CrossRef]

,22

22. M. Bettini, W. Bauhofer, M. Cardona, and R. Nitsche, “Optical phonons in CdSiP2,” Phys. Status Solidi B 63(2), 641–648 (1974). [CrossRef]

].

Figures 1
Fig. 1 Type-I SHG (λωo, λωo, λe) and type-II SHG (λωo, λωe, λe) tuning curves at 21°C of CdSiP2. The fundamental wavelength λω is given as a function of the phase-matching angle θ. Circles stand for experimental data [18]. (o) and (e) stand for the ordinary and extraordinary polarizations, respectively.
and 2
Fig. 2 Type-I DFG (λpe, λso, λio) and type-III DFG (λpe, λse, λio) angular tuning curves at 21°C of CdSiP2 with a pump at λp = 1.064 μm. λi stands for the idler wavelength plotted as a function of the phase-matching angle θ. Circles are the experimental data from Kemlin et al. [18]. (o) and (e) stand for the ordinary and extraordinary polarizations, respectively.
compare the SHG and difference-frequency generation (DFG) phase-matching directions measured by Kemlin et al. [18

18. V. Kemlin, P. Brand, B. Boulanger, P. Segonds, P. G. Schunemann, K. T. Zawilski, B. Ménaert, and J. Debray, “Phase-matching properties and refined Sellmeier equations of the new nonlinear infrared crystal CdSiP2.,” Opt. Lett. 36(10), 1800–1802 (2011). [CrossRef] [PubMed]

] with those predicted by the other Sellmeier equations from Table 1.

The DFG phase-matching curves predicted by the equations of Lambrecht et al. [15

15. W. R. L. Lambrecht and X. Jiang, “Noncritically phase-matched second-harmonic-generation chalcopyrites based on CdSiAs2 and CdSiP2,” Phys. Rev. B 70(4), 045204 (2004). [CrossRef]

] are not shown in Fig. 2 because they noticeably deviate from the experimental points. Nevertheless, the discrepancy is not so large in the case of SHG, which is a good result for dispersion equations coming from a computational method. The best agreement is obtained with the equations of Kemlin et al. [18

18. V. Kemlin, P. Brand, B. Boulanger, P. Segonds, P. G. Schunemann, K. T. Zawilski, B. Ménaert, and J. Debray, “Phase-matching properties and refined Sellmeier equations of the new nonlinear infrared crystal CdSiP2.,” Opt. Lett. 36(10), 1800–1802 (2011). [CrossRef] [PubMed]

].

The temperature dependence of the Sellmeier equations is an important issue for applications. We then combined the room temperature equations of Kemlin et al. [18

18. V. Kemlin, P. Brand, B. Boulanger, P. Segonds, P. G. Schunemann, K. T. Zawilski, B. Ménaert, and J. Debray, “Phase-matching properties and refined Sellmeier equations of the new nonlinear infrared crystal CdSiP2.,” Opt. Lett. 36(10), 1800–1802 (2011). [CrossRef] [PubMed]

] with the thermo-optic coefficients derived by Kato et al. [19

19. K. Kato, N. Umemura, and V. Petrov, “Sellmeier and thermo-optic dispersion formulas for CdSiP2,” J. Appl. Phys. 109(11), 116104 (2011). [CrossRef]

], which provides the following expressions for the ordinary and extraordinary refractive indices of CSP:
no(λ,T)={(3.72202+5.91985λ2λ20.06408+3.92371λ2λ22071.59)1/2+105(T21)(1.1538λ31.1955λ2+0.7263λ+10.8238)                                                                                                                                    ne(λ,T)={(4.68981+4.77331λ2λ20.08006+0.91879λ2λ2496.71)1/2+105(T21)(1.3732λ30.6361λ2+0.8303λ+11.4051)
(1)
The temperature T is expressed in [°C] and the wavelength λ in [µm]. Equations (1) are the temperature-dependent Sellmeier equations of highest accuracy for CSP to the best of our knowledge.

4. Broadband infrared continuum generation

Continuum generation based on a second-order nonlinear process is attracting recently increasing attention for various applications and the potential to generate such continuum using ultrashort laser pulses has recently been evaluated for a number of oxide materials operating at shorter wavelengths [23

23. V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB3O6,” Laser Photon. Rev. 4(1), 53–98 (2010). [CrossRef]

]. An OPO where the idler and signal are in the same polarization state is of particular interest for the generation of a broadband continuum. However, in such OPOs, or for the case of ultrashort pump pulses in the so-called synchronously pumped OPOs, normally only the signal wave is resonated. Thus, to obtain smooth mid-infrared continuum, having in mind that seeding in this spectral range will require additional complexity in the case of OPA, most straightforward of the travelling-wave approaches seems to be the optical parametric generator (OPG), pumped by amplified picosecond or femtosecond pulses that possess sufficient intensity to initiate the parametric process from fluorescence noise [24

24. P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31(1), 71–73 (2006). [CrossRef] [PubMed]

].

In all the above cases, the nonlinear processes are equivalent to type-I DFG. The spectral acceptance for such DFG is very broad when the first derivative of the angular tuning curve with respect to the wavelength is infinite at degeneracy, i.e. at λs = λi = λp/2, which leads to a spectrally non-critical phase-matching at the corresponding angle and higher derivatives have to be considered [23

23. V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB3O6,” Laser Photon. Rev. 4(1), 53–98 (2010). [CrossRef]

]. But phase-matching at degeneracy is not necessarily given at any pump wavelength, as can be seen e.g. in Fig. 2 for the case of CSP which is a crystal possessing moderate birefringence at λp = 1.064 µm. It is then important to define the pump wavelength range over which an OPO or OPG can be phase-matched at degeneracy.

Furthermore, degenerate phase-matching can be allowed at a pump wavelength λpOpt for which the first derivative of the group velocity of the signal and idler waves is vanishing, leading to the broadest wavelength range that can be generated for a given crystal cut at the proper phase-matching angle θOpt [25

25. A. Birmontas, A. Piskarskas, and A. Stabinis, “Dispersion anomalies of tuning characteristics and spectrum of an optical parametric oscillator,” Sov. J. Quantum Electron. 13(9), 1243–1245 (1983) [transl. from Kvantovaya Elektron. (Moscow)10, 1881–1884 (1983)]. [CrossRef]

]. Experimentally this situation has been realized for the first time in the visible and near-infrared with a picosecond OPG based on KDP [26

26. B. Bareĭka, A. Birmontas, G. Dikchyus, A. Piskarskas, V. Sirutkaitis, and A. Stabinis, “Parametric generation of picosecond continuum in near-infrared and visible ranges on the basis of a quadratic nonlinearity,” Sov. J. Quantum Electron. 12(12), 1654–1656 (1982) [transl. from Kvantovaya Elektron. (Moscow)9, 2534–2536 (1982)]. [CrossRef]

].

According to Eqs. (1) at 21°C, the above condition is fulfilled in a CSP crystal cut at θOpt = 42.8° and pumped at λpOpt = 2.43 µm. This deviates from an earlier prediction of 2.55 µm [8

8. P. G. Schunemann, K. T. Zawilski, T. M. Pollak, D. E. Zelmon, N. C. Fernelius, and F. Kenneth Hopkins, “New nonlinear optical crystal for mid-IR OPOs: CdSiP2,” Advanced Solid-State Photonics, Nara, Japan, Jan. 27–30, 2008, Conference Program and Technical Digest, Post-Deadline Paper MG6.

,9

9. P. G. Schunemann, K. T. Zawilski, T. M. Pollak, V. Petrov, and D. E. Zelmon, “CdSiP2: a new nonlinear optical crystal for 1 and 1.5-micron-pumped, mid-IR generation,” Advanced Solid-State Photonics, Denver (CO), USA, Feb. 1–4, 2009, Conference Program and Technical Digest, Paper TuC6.

], but it confirms that such wavelengths can be provided from Cr2+:ZnSe or similar laser systems. We performed the same kind of calculation for the commercially available nonlinear chalcopyrite crystals AgGaS2, AgGaSe2 and ZGP using the corresponding Sellmeier equations [27

27. J.-J. Zondy and D. Touahri, “Updated thermo-optic coefficients of AgGaS2 from temperature-tuned noncritical 3ω ω → 2ω infrared parametric amplification,” J. Opt. Soc. Am. B 14(6), 1331–1338 (1997). [CrossRef]

29

29. G. C. Bhar and G. Ghosh, “Temperature-dependent Sellmeier coefficients and coherence lengths for some chalcopyrite crystals,” J. Opt. Soc. Am. 69(5), 730–733 (1979). [CrossRef]

], and we found for their respective optimum pump wavelengths λpOpt : 2.04 µm, 2.86 µm and 2.63 µm, slightly deviating from the values that can be found in the literature [30

30. S. I. Orlov, E. V. Pestryakov, and Y. N. Polivanov, “Optical parametric amplification with a bandwidth exceeding an octave,” Quantum Electron. 34(5), 477–481 (2004) [transl. from Kvantovaya Elektron. (Moscow)34, 477–481 (2004)]. [CrossRef]

]. The corresponding calculated angular tuning curves are plotted in Fig. 3
Fig. 3 OPO/OPG angular tuning curves at 21°C of several mid-infrared crystals pumped at the wavelength λpOpt corresponding to the broadest range of emission of the signal (λs) and idler (λi). Except for AgGaSe2, for which the infrared cut-off wavelength is above 14 µm, the tuning ranges of the different materials are determined by the idler mid-infrared absorption limit taken here at α = 2 cm−1. The dots correspond to degeneracy, which delimitates the idler range in the upper half-plane and the signal range in the lower half-plane. The indices (o) and (e) denote the ordinary and extraordinary polarizations, respectively.
, which shows the complementary of these materials for the generation of mid-infrared super-continuum.

The full wavelength range of the super-continuum emitted by a crystal cut at the phase-matching angle θOpt can be then estimated from the third derivative of the group velocity [23

23. V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB3O6,” Laser Photon. Rev. 4(1), 53–98 (2010). [CrossRef]

,25

25. A. Birmontas, A. Piskarskas, and A. Stabinis, “Dispersion anomalies of tuning characteristics and spectrum of an optical parametric oscillator,” Sov. J. Quantum Electron. 13(9), 1243–1245 (1983) [transl. from Kvantovaya Elektron. (Moscow)10, 1881–1884 (1983)]. [CrossRef]

]. While Fig. 3 provides a nice illustration basically valid for DFG, in the case of high parametric gain in an OPG this factor also enters the expression for the bandwidth and the parameter that can be quantitatively compared is the so-called parametric gain bandwidth. Expressed using the FWHM convention, this parametric gain bandwidth is written in the degenerate case [23

23. V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB3O6,” Laser Photon. Rev. 4(1), 53–98 (2010). [CrossRef]

]:
ΔνOpt=1π(ln2ΓL)1/8|24βi,s|1/4
(2)
where the gain factor is defined by Γ2=2π2deff2Ipnpns,i2λp2ε0c, and 1/βi,s = ∂4ωi,s/∂ki,s4 is the third derivative of the group velocity at λpOpt with ki,s denoting the wave vector of the signal or idler waves and ωi,s denoting the corresponding circular frequencies. Ip is the pump intensity, deff is the effective nonlinearity, L is the crystal length and np,s,i denote the refractive indices of the pump, signal and idler waves respectively.

The temperature acceptance of CSP is very large but lower than in ZGP. It is known that temperature tuning in ZGP is impractical, contrary to the case of CSP for which this still seems a feasible approach to tune the wavelength [17

17. P. G. Schunemann, L. A. Pomeranz, K. T. Zawilski, J. Wei, L. P. Gonzalez, S. Guha, and T. M. Pollak, “Efficient mid-infrared optical parametric oscillator based on CdSiP2,” Advances in Optical Materials, San Jose (CA), USA, Oct. 14–15, 2009, Conference Program and Technical Digest, Paper AWA3.

], also under non-critical phase-matching conditions [20

20. V. Petrov, G. Marchev, P. G. Schunemann, A. Tyazhev, K. T. Zawilski, and T. M. Pollak, “Subnanosecond, 1 kHz, temperature-tuned, noncritical mid-infrared optical parametric oscillator based on CdSiP2 crystal pumped at 1064 nm,” Opt. Lett. 35(8), 1230–1232 (2010). [CrossRef] [PubMed]

].

5. Conclusion

In conclusion, we compared existing dispersion relations for the CSP nonlinear crystal and extended the most reliable of them with temperature dependence. With the measured nonlinear coefficient, it was possible to estimate the parametric gain bandwidth for the special phase-matching configuration ensuring ultra-broad parametric amplification bandwidth in an OPG pumped by ultrashort pulses. CSP can be pumped by Cr2+:ZnSe ultrafast laser systems or tandem OPGs to generate super-continuum in the mid-infrared extending up to its upper transparency limit.

References and links

1.

S. G. Abrahams and J. L. Bernstein, “Luminescent piezoelectric CdSiP2: Normal probability plot analysis, crystal structure, and generalized structure of the AIIBIVCV2 family,” J. Chem. Phys. 55(2), 796–803 (1971). [CrossRef]

2.

G. A. Ambrazyavichyus, G. A. Babonas, and A. Yu. Shileika, “Birefringence of pseudodirect bandgap A2B4C52 semiconductors,” Sov. Phys. Collect. 17, 51–55 (1977) [transl. from Lit. Fiz. Sb. 17, 205–211 (1977)].

3.

N. Itoh, T. Fujinaga, and T. Nakau, “Birefringence in CdSiP2,” Jpn. J. Appl. Phys. 17(5), 951–952 (1978). [CrossRef]

4.

E. Buehler and J. H. Wernick, “Concerning growth of single crystals of the II-IV-V diamond-like compounds ZnSiP2, CdSiP2, ZnGeP2, and CdSnP2 and standard enthalpies of formation for ZnSiP2 and CdSiP2,” J. Cryst. Growth 8(4), 324–332 (1971). [CrossRef]

5.

N. A. Goryunova, L. B. Zlatkin, and K. K. Ivanov, “Optical anisotropy of A2B4C52 crystals,” J. Phys. Chem. Solids 31(11), 2557–2561 (1970). [CrossRef]

6.

G. Ambrazyavichyus, G. Babonas, and V. Karpus, “Optical activity of CdSiP2,” Sov. Phys. Semicond. 12, 1210–1211 (1978) [trasl. from Fiz. Tekh. Poluprovodn. 12, 2034–2036 (1978)].

7.

A. Ambrazevicius and G. Babonas, “Dependence of birefringence of pseudodirect gap A2B4C52 compounds on hydrostatic pressure and on temperature,” Sov. Phys. Collect. 18, 52–59 (1978) [transl. from Lit. Fiz. Sb. 18, 765–774 (1978)].

8.

P. G. Schunemann, K. T. Zawilski, T. M. Pollak, D. E. Zelmon, N. C. Fernelius, and F. Kenneth Hopkins, “New nonlinear optical crystal for mid-IR OPOs: CdSiP2,” Advanced Solid-State Photonics, Nara, Japan, Jan. 27–30, 2008, Conference Program and Technical Digest, Post-Deadline Paper MG6.

9.

P. G. Schunemann, K. T. Zawilski, T. M. Pollak, V. Petrov, and D. E. Zelmon, “CdSiP2: a new nonlinear optical crystal for 1 and 1.5-micron-pumped, mid-IR generation,” Advanced Solid-State Photonics, Denver (CO), USA, Feb. 1–4, 2009, Conference Program and Technical Digest, Paper TuC6.

10.

K. T. Zawilski, P. G. Schunemann, T. C. Pollak, D. E. Zelmon, N. C. Fernelius, and F. K. Hopkins, “Growth and characterization of large CdSiP2 single crystals,” J. Cryst. Growth 312(8), 1127–1132 (2010). [CrossRef]

11.

V. Petrov, F. Noack, I. Tunchev, P. Schunemann, and K. Zawilski, “The nonlinear coefficient d36 of CdSiP2,” Proc. SPIE 7197, 71970M (2009). [CrossRef]

12.

P. D. Mason, D. J. Jackson, and E. K. Gorton, “CO2 laser frequency doubling in ZnGeP2,” Opt. Commun. 110(1-2), 163–166 (1994). [CrossRef]

13.

V. Petrov, V. Badikov, and V. Panyutin, “Quaternary nonlinear optical crystals for the mid-infrared spectral range from 5 to 12 micron,” in Mid-Infrared Coherent Sources and Applications, M. Ebrahim-Zadeh and I. Sorokina, eds., NATO Science for Peace and Security Series - B: Physics and Biophysics (Springer, 2008), pp. 105–147.

14.

L. P. Gonzalez, D. Upchurch, J. O. Barnes, P. G. Schunemann, K. Zawilski, and S. Guha, “Second harmonic generation in CdSiP2,” Proc. SPIE 7197, 71970N (2009). [CrossRef]

15.

W. R. L. Lambrecht and X. Jiang, “Noncritically phase-matched second-harmonic-generation chalcopyrites based on CdSiAs2 and CdSiP2,” Phys. Rev. B 70(4), 045204 (2004). [CrossRef]

16.

G. Ghosh, “Dispersion of temperature coefficients of birefringence in some chalcopyrite crystals,” Appl. Opt. 23(7), 976–978 (1984). [CrossRef] [PubMed]

17.

P. G. Schunemann, L. A. Pomeranz, K. T. Zawilski, J. Wei, L. P. Gonzalez, S. Guha, and T. M. Pollak, “Efficient mid-infrared optical parametric oscillator based on CdSiP2,” Advances in Optical Materials, San Jose (CA), USA, Oct. 14–15, 2009, Conference Program and Technical Digest, Paper AWA3.

18.

V. Kemlin, P. Brand, B. Boulanger, P. Segonds, P. G. Schunemann, K. T. Zawilski, B. Ménaert, and J. Debray, “Phase-matching properties and refined Sellmeier equations of the new nonlinear infrared crystal CdSiP2.,” Opt. Lett. 36(10), 1800–1802 (2011). [CrossRef] [PubMed]

19.

K. Kato, N. Umemura, and V. Petrov, “Sellmeier and thermo-optic dispersion formulas for CdSiP2,” J. Appl. Phys. 109(11), 116104 (2011). [CrossRef]

20.

V. Petrov, G. Marchev, P. G. Schunemann, A. Tyazhev, K. T. Zawilski, and T. M. Pollak, “Subnanosecond, 1 kHz, temperature-tuned, noncritical mid-infrared optical parametric oscillator based on CdSiP2 crystal pumped at 1064 nm,” Opt. Lett. 35(8), 1230–1232 (2010). [CrossRef] [PubMed]

21.

G. C. Bhar, “Sphalerite vibration mode in chalcopyrites,” Phys. Rev. B 18(4), 1790–1793 (1978). [CrossRef]

22.

M. Bettini, W. Bauhofer, M. Cardona, and R. Nitsche, “Optical phonons in CdSiP2,” Phys. Status Solidi B 63(2), 641–648 (1974). [CrossRef]

23.

V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB3O6,” Laser Photon. Rev. 4(1), 53–98 (2010). [CrossRef]

24.

P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett. 31(1), 71–73 (2006). [CrossRef] [PubMed]

25.

A. Birmontas, A. Piskarskas, and A. Stabinis, “Dispersion anomalies of tuning characteristics and spectrum of an optical parametric oscillator,” Sov. J. Quantum Electron. 13(9), 1243–1245 (1983) [transl. from Kvantovaya Elektron. (Moscow)10, 1881–1884 (1983)]. [CrossRef]

26.

B. Bareĭka, A. Birmontas, G. Dikchyus, A. Piskarskas, V. Sirutkaitis, and A. Stabinis, “Parametric generation of picosecond continuum in near-infrared and visible ranges on the basis of a quadratic nonlinearity,” Sov. J. Quantum Electron. 12(12), 1654–1656 (1982) [transl. from Kvantovaya Elektron. (Moscow)9, 2534–2536 (1982)]. [CrossRef]

27.

J.-J. Zondy and D. Touahri, “Updated thermo-optic coefficients of AgGaS2 from temperature-tuned noncritical 3ω ω → 2ω infrared parametric amplification,” J. Opt. Soc. Am. B 14(6), 1331–1338 (1997). [CrossRef]

28.

D. A. Roberts, “Dispersion equations for nonlinear optical crystals: KDP, AgGaSe2, and AgGaS2.,” Appl. Opt. 35(24), 4677–4688 (1996). [CrossRef] [PubMed]

29.

G. C. Bhar and G. Ghosh, “Temperature-dependent Sellmeier coefficients and coherence lengths for some chalcopyrite crystals,” J. Opt. Soc. Am. 69(5), 730–733 (1979). [CrossRef]

30.

S. I. Orlov, E. V. Pestryakov, and Y. N. Polivanov, “Optical parametric amplification with a bandwidth exceeding an octave,” Quantum Electron. 34(5), 477–481 (2004) [transl. from Kvantovaya Elektron. (Moscow)34, 477–481 (2004)]. [CrossRef]

31.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94(10), 6447–6455 (2003). [CrossRef]

32.

E. Takaoka and K. Kato, “Thermo-optic dispersion formula for AgGaS2.,” Appl. Opt. 38(21), 4577–4580 (1999). [CrossRef] [PubMed]

33.

E. Tanaka and K. Kato, “Thermo-optic dispersion formula of AgGaSe2 and its practical applications,” Appl. Opt. 37(3), 561–564 (1998). [CrossRef] [PubMed]

34.

J.-J. Zondy, D. Touahri, and O. Acef, “Absolute value of the d36 nonlinear coefficient of AgGaS2: prospect for a low-threshold doubly resonant oscillator-based 3:1 frequency divider,” J. Opt. Soc. Am. 14(10), 2481–2497 (1997). [CrossRef]

35.

J.-J. Zondy, “Experimental investigation of single and twin AgGaSe2 crystals for CW 10.2 µm SHG,” Opt. Commun. 119(3-4), 320–326 (1995). [CrossRef]

36.

T. Skauli, K. L. Vodopyanov, T. J. Pinguet, A. Schober, O. Levi, L. A. Eyres, M. M. Fejer, J. S. Harris, B. Gerard, L. Becouarn, E. Lallier, and G. Arisholm, “Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation,” Opt. Lett. 27(8), 628–630 (2002). [CrossRef] [PubMed]

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.4975) Nonlinear optics : Parametric processes

ToC Category:
Nonlinear Optical Materials

History
Original Manuscript: September 19, 2011
Revised Manuscript: October 13, 2011
Manuscript Accepted: October 13, 2011
Published: October 17, 2011

Virtual Issues
Nonlinear Optics (2011) Optical Materials Express

Citation
Vincent Kemlin, Benoit Boulanger, Valentin Petrov, Patricia Segonds, B. Ménaert, Peter G. Schunneman, and Kevin T. Zawilski, "Nonlinear, dispersive, and phase-matching properties of the new chalcopyrite CdSiP2 [Invited]," Opt. Mater. Express 1, 1292-1300 (2011)
http://www.opticsinfobase.org/ome/abstract.cfm?URI=ome-1-7-1292


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References

  1. S. G. Abrahams and J. L. Bernstein, “Luminescent piezoelectric CdSiP2: Normal probability plot analysis, crystal structure, and generalized structure of the AIIBIVCV2 family,” J. Chem. Phys.55(2), 796–803 (1971). [CrossRef]
  2. G. A. Ambrazyavichyus, G. A. Babonas, and A. Yu. Shileika, “Birefringence of pseudodirect bandgap A2B4C52 semiconductors,” Sov. Phys. Collect.17, 51–55 (1977) [transl. from Lit. Fiz. Sb. 17, 205–211 (1977)].
  3. N. Itoh, T. Fujinaga, and T. Nakau, “Birefringence in CdSiP2,” Jpn. J. Appl. Phys.17(5), 951–952 (1978). [CrossRef]
  4. E. Buehler and J. H. Wernick, “Concerning growth of single crystals of the II-IV-V diamond-like compounds ZnSiP2, CdSiP2, ZnGeP2, and CdSnP2 and standard enthalpies of formation for ZnSiP2 and CdSiP2,” J. Cryst. Growth8(4), 324–332 (1971). [CrossRef]
  5. N. A. Goryunova, L. B. Zlatkin, and K. K. Ivanov, “Optical anisotropy of A2B4C52 crystals,” J. Phys. Chem. Solids31(11), 2557–2561 (1970). [CrossRef]
  6. G. Ambrazyavichyus, G. Babonas, and V. Karpus, “Optical activity of CdSiP2,” Sov. Phys. Semicond.12, 1210–1211 (1978) [trasl. from Fiz. Tekh. Poluprovodn. 12, 2034–2036 (1978)].
  7. A. Ambrazevicius and G. Babonas, “Dependence of birefringence of pseudodirect gap A2B4C52 compounds on hydrostatic pressure and on temperature,” Sov. Phys. Collect.18, 52–59 (1978) [transl. from Lit. Fiz. Sb. 18, 765–774 (1978)].
  8. P. G. Schunemann, K. T. Zawilski, T. M. Pollak, D. E. Zelmon, N. C. Fernelius, and F. Kenneth Hopkins, “New nonlinear optical crystal for mid-IR OPOs: CdSiP2,” Advanced Solid-State Photonics, Nara, Japan, Jan. 27–30, 2008, Conference Program and Technical Digest, Post-Deadline Paper MG6.
  9. P. G. Schunemann, K. T. Zawilski, T. M. Pollak, V. Petrov, and D. E. Zelmon, “CdSiP2: a new nonlinear optical crystal for 1 and 1.5-micron-pumped, mid-IR generation,” Advanced Solid-State Photonics, Denver (CO), USA, Feb. 1–4, 2009, Conference Program and Technical Digest, Paper TuC6.
  10. K. T. Zawilski, P. G. Schunemann, T. C. Pollak, D. E. Zelmon, N. C. Fernelius, and F. K. Hopkins, “Growth and characterization of large CdSiP2 single crystals,” J. Cryst. Growth312(8), 1127–1132 (2010). [CrossRef]
  11. V. Petrov, F. Noack, I. Tunchev, P. Schunemann, and K. Zawilski, “The nonlinear coefficient d36 of CdSiP2,” Proc. SPIE7197, 71970M (2009). [CrossRef]
  12. P. D. Mason, D. J. Jackson, and E. K. Gorton, “CO2 laser frequency doubling in ZnGeP2,” Opt. Commun.110(1-2), 163–166 (1994). [CrossRef]
  13. V. Petrov, V. Badikov, and V. Panyutin, “Quaternary nonlinear optical crystals for the mid-infrared spectral range from 5 to 12 micron,” in Mid-Infrared Coherent Sources and Applications, M. Ebrahim-Zadeh and I. Sorokina, eds., NATO Science for Peace and Security Series - B: Physics and Biophysics (Springer, 2008), pp. 105–147.
  14. L. P. Gonzalez, D. Upchurch, J. O. Barnes, P. G. Schunemann, K. Zawilski, and S. Guha, “Second harmonic generation in CdSiP2,” Proc. SPIE7197, 71970N (2009). [CrossRef]
  15. W. R. L. Lambrecht and X. Jiang, “Noncritically phase-matched second-harmonic-generation chalcopyrites based on CdSiAs2 and CdSiP2,” Phys. Rev. B70(4), 045204 (2004). [CrossRef]
  16. G. Ghosh, “Dispersion of temperature coefficients of birefringence in some chalcopyrite crystals,” Appl. Opt.23(7), 976–978 (1984). [CrossRef] [PubMed]
  17. P. G. Schunemann, L. A. Pomeranz, K. T. Zawilski, J. Wei, L. P. Gonzalez, S. Guha, and T. M. Pollak, “Efficient mid-infrared optical parametric oscillator based on CdSiP2,” Advances in Optical Materials, San Jose (CA), USA, Oct. 14–15, 2009, Conference Program and Technical Digest, Paper AWA3.
  18. V. Kemlin, P. Brand, B. Boulanger, P. Segonds, P. G. Schunemann, K. T. Zawilski, B. Ménaert, and J. Debray, “Phase-matching properties and refined Sellmeier equations of the new nonlinear infrared crystal CdSiP2.,” Opt. Lett.36(10), 1800–1802 (2011). [CrossRef] [PubMed]
  19. K. Kato, N. Umemura, and V. Petrov, “Sellmeier and thermo-optic dispersion formulas for CdSiP2,” J. Appl. Phys.109(11), 116104 (2011). [CrossRef]
  20. V. Petrov, G. Marchev, P. G. Schunemann, A. Tyazhev, K. T. Zawilski, and T. M. Pollak, “Subnanosecond, 1 kHz, temperature-tuned, noncritical mid-infrared optical parametric oscillator based on CdSiP2 crystal pumped at 1064 nm,” Opt. Lett.35(8), 1230–1232 (2010). [CrossRef] [PubMed]
  21. G. C. Bhar, “Sphalerite vibration mode in chalcopyrites,” Phys. Rev. B18(4), 1790–1793 (1978). [CrossRef]
  22. M. Bettini, W. Bauhofer, M. Cardona, and R. Nitsche, “Optical phonons in CdSiP2,” Phys. Status Solidi B63(2), 641–648 (1974). [CrossRef]
  23. V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB3O6,” Laser Photon. Rev.4(1), 53–98 (2010). [CrossRef]
  24. P. S. Kuo, K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, X. Yu, J. S. Harris, D. Bliss, and D. Weyburne, “Optical parametric generation of a mid-infrared continuum in orientation-patterned GaAs,” Opt. Lett.31(1), 71–73 (2006). [CrossRef] [PubMed]
  25. A. Birmontas, A. Piskarskas, and A. Stabinis, “Dispersion anomalies of tuning characteristics and spectrum of an optical parametric oscillator,” Sov. J. Quantum Electron.13(9), 1243–1245 (1983) [transl. from Kvantovaya Elektron. (Moscow)10, 1881–1884 (1983)]. [CrossRef]
  26. B. Bareĭka, A. Birmontas, G. Dikchyus, A. Piskarskas, V. Sirutkaitis, and A. Stabinis, “Parametric generation of picosecond continuum in near-infrared and visible ranges on the basis of a quadratic nonlinearity,” Sov. J. Quantum Electron.12(12), 1654–1656 (1982) [transl. from Kvantovaya Elektron. (Moscow)9, 2534–2536 (1982)]. [CrossRef]
  27. J.-J. Zondy and D. Touahri, “Updated thermo-optic coefficients of AgGaS2 from temperature-tuned noncritical 3ω ω → 2ω infrared parametric amplification,” J. Opt. Soc. Am. B14(6), 1331–1338 (1997). [CrossRef]
  28. D. A. Roberts, “Dispersion equations for nonlinear optical crystals: KDP, AgGaSe2, and AgGaS2.,” Appl. Opt.35(24), 4677–4688 (1996). [CrossRef] [PubMed]
  29. G. C. Bhar and G. Ghosh, “Temperature-dependent Sellmeier coefficients and coherence lengths for some chalcopyrite crystals,” J. Opt. Soc. Am.69(5), 730–733 (1979). [CrossRef]
  30. S. I. Orlov, E. V. Pestryakov, and Y. N. Polivanov, “Optical parametric amplification with a bandwidth exceeding an octave,” Quantum Electron.34(5), 477–481 (2004) [transl. from Kvantovaya Elektron. (Moscow)34, 477–481 (2004)]. [CrossRef]
  31. T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys.94(10), 6447–6455 (2003). [CrossRef]
  32. E. Takaoka and K. Kato, “Thermo-optic dispersion formula for AgGaS2.,” Appl. Opt.38(21), 4577–4580 (1999). [CrossRef] [PubMed]
  33. E. Tanaka and K. Kato, “Thermo-optic dispersion formula of AgGaSe2 and its practical applications,” Appl. Opt.37(3), 561–564 (1998). [CrossRef] [PubMed]
  34. J.-J. Zondy, D. Touahri, and O. Acef, “Absolute value of the d36 nonlinear coefficient of AgGaS2: prospect for a low-threshold doubly resonant oscillator-based 3:1 frequency divider,” J. Opt. Soc. Am.14(10), 2481–2497 (1997). [CrossRef]
  35. J.-J. Zondy, “Experimental investigation of single and twin AgGaSe2 crystals for CW 10.2 µm SHG,” Opt. Commun.119(3-4), 320–326 (1995). [CrossRef]
  36. T. Skauli, K. L. Vodopyanov, T. J. Pinguet, A. Schober, O. Levi, L. A. Eyres, M. M. Fejer, J. S. Harris, B. Gerard, L. Becouarn, E. Lallier, and G. Arisholm, “Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation,” Opt. Lett.27(8), 628–630 (2002). [CrossRef] [PubMed]

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