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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 20, Iss. 8 — Aug. 1, 2003
  • pp: 1675–1694

Second-harmonic generation with monolithic walk-off-compensating periodic structures. I. Theory

Jean-Jacques Zondy, Christophe Bonnin, and Dominique Lupinski  »View Author Affiliations

JOSA B, Vol. 20, Issue 8, pp. 1675-1694 (2003)

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Second-harmonic generation in a periodic structure made from N pairs of optically contacted, birefringence phase-matched, walk-off-compensating bulk plates is theoretically investigated. In the undepleted-pump approximation, analytical (heuristic) expressions for conversion efficiency versus N are derived for both type I and type II phase matching. An explicit split-step beam propagation scheme that solves exactly the coupled paraxial-wave equations is used to check the validity of the heuristic results. For type II, stronger conversion enhancement than for bulk crystal is predicted in the low-depletion regime, whereas for type I such structures avoid harmonic beam ellipticity. The periodic structures are found to behave as nonlinear harmonic birefringent filters because of the presence of periodic wave-vector mismatch grating ±Δk that results from walk-off compensation. The effect of periodicity imperfections, such as residual plate orientation mismatches, was found to be responsible for broadening of the tuning bandwidth in walk-off-compensating devices.

© 2003 Optical Society of America

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4360) Nonlinear optics : Nonlinear optics, devices
(260.1180) Physical optics : Crystal optics
(260.1440) Physical optics : Birefringence
(350.5500) Other areas of optics : Propagation

Jean-Jacques Zondy, Christophe Bonnin, and Dominique Lupinski, "Second-harmonic generation with monolithic walk-off-compensating periodic structures. I. Theory," J. Opt. Soc. Am. B 20, 1675-1694 (2003)

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), Chap. 15.
  2. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chaps. 4 and 12.
  3. J.-J. Zondy, “Comparative theory of walkoff-limited type-II versus type-I second-harmonic generation with Gaussian beams,” Opt. Commun. 81, 427–440 (1991). In Eq. (3.1a) of this reference exp(−x2) should read as exp(−x2/2).
  4. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
  5. B. Boulanger, J. P. Fève, G. Marnier, B. Ménaert, X. Cabirol, P. Villeval, and C. Bonnin, “Relative sign and absolute magnitude of d(2) nonlinear coefficients of KTP from phase-matched second-harmonic generation,” J. Opt. Soc. Am. B 11, 750–757 (1994).
  6. B. Boulanger, J. P. Fève, G. Marnier, C. Bonnin, P. Villeval, and J. J. Zondy, “Absolute measurement of quadratic nonlinearities from phase-matched second-harmonic generation in a single KTP crystal cut as a sphere,” J. Opt. Soc. Am. B 14, 1380–1386 (1997).
  7. J.-J. Zondy, M. Abed, and A. Clairon, “Type-II frequency doubling at λ=1.30 μm and λ=2.53 μm in flux-grown potassium titanyl phosphate,” J. Opt. Soc. Am. B 11, 2004–2015 (1994).
  8. V. D. Volosov and A. G. Kalintsev, “Optimum optical second-harmonic generation in tandem crystals,” Sov. Tech. Phys. Lett. 2, 373–375 (1976).
  9. L. K. Samantha, T. Yanagawa, and Y. Yamamoto, “Technique for enhanced second harmonic output power,” Opt. Commun. 76, 250–252 (1993).
  10. J.-J. Zondy, M. Abed, and S. Khodja, “Twin-crystal walkoff-compensated type-II second-harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11, 2368–2379 (1994).
  11. J.-J. Zondy, “Experimental investigation of single and twin AgGaSe2 crystals for cw 10.2 μm SHG,” Opt. Commun. 119, 320–326 (1995).
  12. K. Stoll, J.-J. Zondy, and O. Acef, “Fourth-harmonic generation of a continuous-wave CO2 laser by use of an AgGaSe2/ZnGeP2 doubly resonant device,” Opt. Lett. 22, 1302–1304 (1997).
  13. D. J. Armstrong, W. J. Alford, T. D. Raymond, and A. V. Smith, “Parametric amplification and oscillation with walk-off-compensating crystals,” J. Opt. Soc. Am. B 14, 460–474 (1997).
  14. E. Roissé, E. Louradour, O. Gay, V. Couderc, and A. Barthélémy, “Walk-off and phase-compensated resonantly enhanced frequency-doubling of picosecond pulses using type-II nonlinear crystals,” Appl. Phys. B 69, 25–27 (1999).
  15. T. Kaing, J.-J. Zondy, A. P. Yelisseyev, S. I. Lobanov, and L. Isaenko, “Improving the power and spectral performance of a 27–33 Thz AgGaS2 difference-frequency spectrometer,” IEEE Trans. Instrum. Meas. 48, 592–595 (1999).
  16. R. B. Andreev, K. V. Vetrov, V. D. Volosov, and A. G. Kalimtsev, “Three-wave parametric processes in multicrystal nonlinear frequency converters,” Opt. Spectrosc. 65, 90–93 (1988).
  17. M. Brown, “Increased spectral bandwidths in nonlinear conversion processes by use of multicrystal designs,” Opt. Lett. 23, 1591–1593 (1998).
  18. A. V. Smith, D. J. Armstrong, and W. J. Alford, “Increased acceptance bandwidths in optical frequency conversion by use of multiple walk-off-compensating nonlinear crystals,” J. Opt. Soc. Am. B 15, 122–141 (1998).
  19. J.-J. Zondy, M. Abed, S. Khodja, C. Bonnin, B. Rainaud, H. Albrecht, and D. Lupinski, “Walk-off-compensated type-I and type-II SHG using twin-crystal AgGaSe2 and KTiOPO4 devices,” in Nonlinear Frequency Generation and Conversion, M. C. Gupta, W. J. Kozlovsky, and D. C. McPherson, eds., Proc. SPIE 2700, 66–72 (1996).
  20. J.-J. Zondy and Cristal-Laser SA, “Structure monolithique obtenue par contact optique de cristaux non linéaires en compensation de walk-off,” French patent (brevet d’invention 96 01 197; April 4, 1999).
  21. Custom KTP and RbTiOAsO4 OCWOC and diffusion-bonded WOC structures are commercially available at http://www.cristal-laser.fr.
  22. B. Ya. Zeldovitch, Yu. E. Kapitskii, and A. N. Chudinov, “Interference between second-harmonics generated in two different KTP crystals,” Sov. J. Quantum Electron. 20, 1120–1121 (1990).
  23. M. Vaupel, A. Mai⁁tre, and C. Fabre, “Observation of pattern formation in an optical parametric oscillator,” Phys. Rev. Lett. 83, 5278–5281 (1999).
  24. S. Ducci, N. Treps, A. Maitre, and C. Fabre, “Pattern formation in optical parametric oscillators,” Phys. Rev. A 64, 023803 (2001).
  25. J. P. Fève, J.-J. Zondy, B. Boulanger, R. Bonnenberger, X. Cabirol, B. Ménaert, and G. Marnier, “Optimized blue light generation in optically contacted walkoff-compensated RbTiOAsO4 and KTiOP1−yAsyO4,” Opt. Commun. 161, 359–369 (1999).
  26. R. F. Wu, P. B. Phua, K. S. Lai, Y. L. Lim, E. Lau, A. Chang, C. Bonnin, and D. Lupinski, “Compact 21-W 2-μm intracavity optical parametric oscillator,” Opt. Lett. 25, 1460–1462 (2000).
  27. R. F. Wu, K. S. Lai, E. Lau, H. F. Wong, W. J. Xie, Y. L. Lim, K. W. Lim, and L. Chia, “Multi-watt ZGP OPO based on diffusion-bonded walkoff compensated KTP OPO and Nd:YALO laser,” in Advanced Solid State Lasers, Vol. 34 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper TuA4.
  28. R. Lebrun, G. Mennerat, and P. George, “High-efficiency mid-IR nanosecond cascaded optical parametric oscillators based on diffusion-bonded walkoff-compensated KTP and ZGP crystals,” Advanced Solid State Lasers, Vol. 34 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper TuA5.
  29. L. Torner, “Guiding-center walking soliton,” Opt. Lett. 23, 1256–1258 (1998).
  30. J. A. Fleck and M. D. Feit, “Beam propagation in uniaxial anisotropic media,” J. Opt. Soc. Am. 73, 920–926 (1983).
  31. M. A. Dreger and J. K. McIver, “Second-harmonic generation in a nonlinear, anisotropic medium with diffraction and depletion,” J. Opt. Soc. Am. B 7, 776–784 (1990).
  32. D. Eimerl, J. M. Auerbach, and P. W. Milonni, “Paraxial-wave theory of second and third harmonic generation in uniaxial crystals. I. Narrowband pump fields,” J. Mod. Opt. 42, 1037–1067 (1995).
  33. H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1328 (1966).
  34. D. A. Kleinman, A. Ashkin, and G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” Phys. Rev. 145, 338–384 (1966).
  35. 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. B 14, 2481–2497 (1997).
  36. J.-J. Zondy, “The effects of focusing in type-I and type-II difference frequency generations,” Opt. Commun. 149, 181–206 (1998).
  37. A. Steinbach, M. Rauner, F. C. Cruz, and J. C. Berquist, “Cw second harmonic generation with elliptical Gaussian beams,” Opt. Commun. 123, 207–214 (1996).
  38. T. Freegarde, J. Coutts, J. Walz, D. Leibfried, and T. W. Hänsch, “General analysis of type-I second-harmonic generation with elliptical Gaussian beams,” J. Opt. Soc. Am. B 14, 2010–2016 (1997).
  39. J.-J. Zondy, D. Kolker, C. Bonnin, and D. Lupinski, “Second-harmonic generation with monolithic walk-off-compensating periodic structures. 2. Experiments,” J. Opt. Soc. Am. B 20, 1695–1707 (2003).
  40. M. D. Feit and J. A. Fleck, “Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams,” J. Opt. Soc. Am. B 5, 633–640 (1988).
  41. A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1993).
  42. F. Castaldo, G. Abbate, and E. Santamato, “Theory for a new vectorial beam-propagation method in anisotropic structures,” Appl. Opt. 38, 3904–3910 (1999).
  43. S. C. Sheng and A. E. Siegman, “Nonlinear optical calculations using fast transform methods: second-harmonic generation with depletion and diffraction,” Phys. Rev. A 21, 599–606 (1980).
  44. M. Nieto-Vesperinas and G. Lera, “Solution to nonlinear optical frequency mixing equations with depletion and diffraction,” Opt. Commun. 69, 329–333 (1989).
  45. A. V. Smith and M. S. Bowers, “Phase distortions in sum- and difference-frequency mixing in crystals,” J. Opt. Soc. Am. B 12, 49–57 (1995).
  46. G. Arisholm, “General numerical methods for simulating second-order nonlinear interactions in birefringent media,” J. Opt. Soc. Am. B 14, 2543–2549 (1997).
  47. P. Plizka and P. P. Banerjee, “Nonlinear transverse effects in second-harmonic generation,” J. Opt. Soc. Am. B 10, 1810–1819 (1993).
  48. P. Plizka and P. P. Banerjee, “Self-phase modulation in quadratically nonlinear media,” J. Mod. Opt. 40, 1909–1916 (1993).
  49. R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990).
  50. Ref. 2, Chap. 6, p. 155.
  51. G. Shabtay, E. Eidinger, Z. Zalevsky, D. Mendlovic, and E. Marom, “Tunable birefringent filters—optimal iterative design,” Opt. Express 10, 1534–1538 (2002), http://www.opticsexpress.org.
  52. K. Kato, “Parametric oscillation at 3.2 μm in KTP pumped at 1.064 μm,” IEEE J. Quantum Electron. 27, 1137–1140 (1991).

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