OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 21, Iss. 8 — Aug. 1, 2004
  • pp: 1522–1534

Fresnel phase matching for three-wave mixing in isotropic semiconductors

Riad Haïdar, Nicolas Forget, Philippe Kupecek, and Emmanuel Rosencher  »View Author Affiliations

JOSA B, Vol. 21, Issue 8, pp. 1522-1534 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (483 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We deal with phase matching of three-wave mixing by total internal reflection in isotropic semiconductors. This technique makes use of the large relative phase lag between the three interacting waves at total internal reflection, as described by Augustin Fresnel. This is why we denote this technique as Fresnel phase matching. The theory of Fresnel phase matching is developed with a propagation matrix method: It allows us to describe the conditions (sample thickness, polarization, tuning angles, etc.) for phase matching, the influence of surface roughness, and the walk-off effects due to Goos–Hänchen shifts. Moreover, we show that nonresonant phase matching strongly alleviates the phase-matching tolerance while keeping good conversion yields. The potential of this technique is demonstrated by largely tunable mid-infrared generation (between 7 and 13 µm with a single sample) by use of difference-frequency mixing of two near-infrared sources. Excellent agreement between the presented theory and experiments is demonstrated both in GaAs and ZnSe samples.

© 2004 Optical Society of America

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(260.6970) Physical optics : Total internal reflection

Riad Haïdar, Nicolas Forget, Philippe Kupecek, and Emmanuel Rosencher, "Fresnel phase matching for three-wave mixing in isotropic semiconductors," J. Opt. Soc. Am. B 21, 1522-1534 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. See, D. Richter, A. Fried, and F. K. Tittel, eds., Special issue on “Trends in Laser Sources, Spectroscopic Techniques and Their Applications to Trace Gas Detection,” Appl. Phys. B 75 (2002).
  2. A. N. Baranov, V. V. Sherstnev, C. Alibert, and A. Krier, “New III–V semiconductor lasers emitting near 2.6 μm,” J. Appl. Phys. 79, 3354–3356 (1996). [CrossRef]
  3. G. Springholz, T. Schwarzl, W. Heiss, G. Bauer, M. Aigle, H. Pascher, and I. Vavra, “Midinfrared surface-emitting PbSe/PbEuTe quantum-dot lasers,” Appl. Phys. Lett. 79, 1225–1227 (2001). [CrossRef]
  4. J. Faist, F. Capasso, C. Sirtori, D. L. Sivco, J. N. Baillargeon, A. L. Hutchinson, S.-N. G. Chu, and A. Y. Cho, “High power mid-infrared (λ~5 μm) quantum cascade lasers operating above room temperature,” Appl. Phys. Lett. 68, 3680–3682 (1996). [CrossRef]
  5. C. Sirtori, P. Kruck, S. Barbieri, Ph. Collot, J. Nagle, M. Beck, J. Faist, and U. Oesterle, “GaAs/AlxGa1−x As quantum cascade lasers,” Appl. Phys. Lett. 73, 3486–3488 (1998). [CrossRef]
  6. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).
  7. J. P. van der Ziel, “Phase-matched harmonic generation in a laminar structure with wave propagation in the plane of the layers,” Appl. Phys. Lett. 26, 60–62 (1975). [CrossRef]
  8. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear otpical materials,” Nature 391, 463–466 (1998). [CrossRef]
  9. A. Fiore, S. Janz, L. Delobel, P. Van der Meer, P. Bravetti, V. Berger, E. Rosencher, and J. Nagle, “Second harmonic generation at 1.6 μm in AlGaAs/AlOx waveguides using birefringence phase matching,” Appl. Phys. Lett. 72, 2942–2944 (1998). [CrossRef]
  10. J. B. Khurgin, “Second-order non-linear effects in asymetric quantum-well structures,” Phys. Rev. B 38, 4056–4066 (1988). [CrossRef]
  11. E. Rosencher and B. Vinter, Optoelectronics (Cambridge U. Press, New York, 2002).
  12. D. Yang, J. B. Khurgin, and Y. J. Ding, “Cascaded waveguide phase-matching arrangement,” Opt. Lett. 25, 496–498 (2000). [CrossRef]
  13. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962). [CrossRef]
  14. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995). [CrossRef]
  15. D. E. Thomson, J. D. McMullen, and D. B. Anderson, “Second-harmonic generation in GaAs stack of plates using high power CO2 laser radiation,” Appl. Phys. Lett. 29, 113–115 (1976). [CrossRef]
  16. E. Lallier, L. Becouarn, M. Brévignon, and J. Lehoux, “Efficient second-harmonic generation of a CO2 laser with a quasi-phase-matched GaAs crystal,” Opt. Lett. 23, 1511–1153 (1998). [CrossRef]
  17. M. J. Angell, M. L. Emerson, J. L. Hoyt, J. F. Gibbons, L. A. Eyres, M. L. Bortz, and M. M. Fejer, “Growth of alternating 〈100〉〈111〉-oriented II–VI regions for quasi-phase-matched nonlinear optical devices on GaAs substrates,” Appl. Phys. Lett. 64, 3107–3109 (1994). [CrossRef]
  18. O. Levi, T. J. Pinguet, T. Skauli, L. A. Eyres, K. R. Parameswaran, J. S. Harris, Jr., M. M. Fejer, T. J. Kulp, S. E. Bisson, B. Gerard, E. Lallier, and L. Becouarn, “Difference frequency generation of 8-μm radiation in orientation-patterned GaAs,” Opt. Lett. 27, 2091–2093 (2002). [CrossRef]
  19. G. D. Boyd and C. K. N. Patel, “Enhancement of optical second harmonic generation (SHG) by reflection phase matching in ZnS and GaAs,” Appl. Phys. Lett. 8, 313–315 (1966). [CrossRef]
  20. H. Komine, W. H. Long, J. W. Tully, Jr., and E. A. Stappaerts, “Quasi-phase-matched second-harmonic generation by use of a total-internal-reflection phase shift in gallium arsenide and zinc selenide plates,” Opt. Lett. 23, 661–663 (1998). [CrossRef]
  21. G. Bruhat, Optique (Masson, Paris, 1954).
  22. M. V. Klein and E. T. Furtak, Optics, 2nd ed. (Wiley, New York, 1998).
  23. R. Haïdar, Ph. Kupecek, E. Rosencher, Ph. Lemasson, and R. Triboulet, “Quasi-phase-matched difference frequency generation (8–13 μm) in isotropic semiconductors using total internal reflection,” Appl. Phys. Lett. 82, 1167–1169 (2003). [CrossRef]
  24. R. Haïdar, “New quasi-phase-matching scenarios in isotropic semiconductors,” Ph.D. thesis (Université Paris Sud, Paris, 2003).
  25. M. M. Fejer, M. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992). [CrossRef]
  26. R. Haïdar, Ph. Kupecek, and E. Rosencher, “Non-resonant quasi-phase matching in GaAs plates by Fresnel birefringence,” Appl. Phys. Lett. 83, 1506–1508 (2003). [CrossRef]
  27. R. Haïdar, A. Mustelier, Ph. Kupecek, E. Rosencher, R. Triboulet, Ph. Lemasson, and G. Mennerat, “Largely tunable mid-infrared (8–12 μm) difference frequency generation in isotropic semiconductors,” J. Appl. Phys. 91, 2550–2552 (2002). [CrossRef]
  28. R. Haïdar, Ph. Kupecek, E. Rosencher, Ph. Lemasson, and R. Triboulet, “New mid-infrared optical sources based on isotropic semiconductors (ZnSe and GaAs) using total internal reflection quasi-phase matching,” in International Conference on Solid State Crystals 2002, J. Rutkowski and A. Rogalski, eds., Proc. SPIE 5136, 335–343 (2003).
  29. H. H. Li, “Refractive index of ZnS, ZnSe and ZnTe and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 13, 103–150 (1984). [CrossRef]
  30. S. Adashi, “GaAs, AlAs and AlxGa1−xAs: material parameters for use in a research and device applications,” J. Appl. Phys. 58, R1–R29 (1985). [CrossRef]
  31. J. A. Giordmaine, “Mixing of light beams in crystals,” Phys. Rev. Lett. 8, 19–20 (1962). [CrossRef]
  32. E. Rzepka, J. P. Roger, Ph. Lemasson, and R. Triboulet, “Optical transmission of ZnSe crystals grown by solid phase recrystallisation,” J. Cryst. Growth 197, 480–484 (1999). [CrossRef]
  33. G. Mennerat and Ph. Kupecek, “High-energy narrow-linewidth tunable source in the mid infrared,” in Advanced Solid State Lasers, W. R. Bosenberg and M. M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 47–49.
  34. M. M. J. W. Van Herpen, S. E. Bisson, and F. J. M. Harren, “Continuous-wave operation of a single-frequency optical parametric oscillator at 4–5 μm based on periodically poled LiNbO3,” Opt. Lett. 28, 2497–2499 (2003). [CrossRef] [PubMed]
  35. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  36. A. Puri and J. L. Birman, “Goos–Hänchen beam shift at total internal reflection with application to spatially dispersive media,” J. Opt. Soc. Am. A 3, 543–549 (1986). [CrossRef]
  37. H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000). [CrossRef]
  38. P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. 10, 2395–2413 (1971). [CrossRef] [PubMed]
  39. P. Chavel, “Aberrations et diffraction,” in Cours de SupOptique (Institut d’Optique Théorique et Appliquée, Orsay, France, 1997).
  40. D. Chemla, Ph. Kupecek, Ch. Schwartz, C. Scwhab, and A. Goltzene, “Nonlinear properties of cuprous halides,” IEEE J. Quantum Electron. QE-7, 126–132 (1971). [CrossRef]
  41. H. Shih and N. Bloembergen, “Phase-matched critical total reflection and the Goos–Hänchen shift in second-harmonic generation,” Phys. Rev. A 3, 412–420 (1971). [CrossRef]
  42. R. Haïdar, N. Forget, and E. Rosencher, “Optical parametric oscillations in microcavities based on isotropic semiconductors: a theoretical study,” IEEE J. Quantum Electron. 39, 569–576 (2003). [CrossRef]
  43. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited