## Nonlinear process in photonic crystals under the noncollinear interaction

JOSA B, Vol. 19, Issue 9, pp. 2083-2093 (2002)

http://dx.doi.org/10.1364/JOSAB.19.002083

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### Abstract

We analyzed theoretically and studied experimentally the sum-frequency generation and four-wave-mixing processes under the noncollinear geometry of interaction in finite-length periodic photonic crystals. The efficiency of the surface and the bulk mechanisms of sum-frequency generation are compared. It is shown that surface and bulk mechanisms cannot be separated on the polarization of the sum-frequency signal only but that the angular dependencies of the sum-frequency signal intensity enable us to separate them. The excitation of inhomogeneous waves at the four-wave-mixing frequency of ω_{3}=2ω_{1}−ω_{2} is discussed and demonstrated.

© 2002 Optical Society of America

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(130.2790) Integrated optics : Guided waves

(190.0190) Nonlinear optics : Nonlinear optics

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(260.0260) Physical optics : Physical optics

**Citation**

Anatoli V. Andreev, Alexei V. Balakin, Alexander B. Kozlov, Ilya A. Ozheredov, Ilya R. Prudnikov, Alexander P. Shkurinov, Pascal Masselin, and Gael Mouret, "Nonlinear process in photonic crystals under the noncollinear interaction," J. Opt. Soc. Am. B **19**, 2083-2093 (2002)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-9-2083

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### References

- P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–120 (1961).
- N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
- V. D. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
- P. D. Maker, R. W. Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21–23 (1962).
- E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
- A. Yariv and P. Yeh, Optical Waves in Crystals. Propagation and Control of Laser Radiation (Wiley, New York, 1984).
- 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).
- P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35, 23–39 (1963).
- S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
- M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
- I. S. Fogel, J. M. Bendickson, M. D. Tocci, M. J. Bloemer, M. Scalora, C. M. Bowden, and J. P. Dowling, “Spontaneous emission and nonlinear effects in photonic bandgap materials,” Pure Appl. Opt. 7, 393–407 (1998).
- A. V. Andreev, O. A. Andreeva, A. V. Balakin, D. Boucher, P. Masselin, I. A. Ozheredov, I. R. Prudnikov, and A. P. Shkurinov, “Mechanisms of second-harmonic generation in one-dimensional periodic media,” Quantum Electron. 29, 632–637 (1999).
- A. V. Balakin, V. A. Bushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “Enhancement of second-harmonic generation with femtosecond laser pulses near the photonic band edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999).
- Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
- G. A. Reider and T. F. Heinz, “Second-order nonlinear optical effects at surfaces: recent advances,” in Photonic Probes of Surfaces, P. Halevi, ed. (Elsevier Science B. V., Amsterdam, 1995), pp. 415–478.
- A. V. Andreev and A. B. Kozlov, “The influence of the spatial inhomogeneity of the field on the nonlinear-optical response of an atom,” Quantum Electron. 30, 979–985 (2000).
- S. J. Szyzak, W. M. Baker, R. C. Crane, and J. B. Howe, “Refractive indexes of single synthetic zinc sulfide and cadmium sulfide crystals,” J. Opt. Soc. Am. 47, 240–243 (1957).
- Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology. Groupe III: Crystals and Solid State Physics (Springer-Verlag, Berlin, 1973), Vol. 7 (Crystal Structure Data of Inorganic Compounds), Part A, p. 13.
- P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7988 (1988).
- A. P. Shkurinov, N. I. Koroteev, G. Jonusauskas, and C. Rulliere, “Subpicosecond anisotropic CARS studies of vibrational mode-selective photoexcitation and relaxation of trans-Stilbene: first few picoseconds,” Chem. Phys. Lett. 223, 573–580 (1994).
- A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, E. V. Petrov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Enhancement of sum-frequency generation near the photonic bandgap edge under the quasi-phase-matching conditions,” Phys. Rev. E 63, 046609–1–046609–10 (2001).
- A. V. Andreev and A. B. Kozlov, “Excitation of waveguide modes in a one-dimensional photonic crystal,” Quantum Electron. 31, 443–447 (2001).
- A. V. Andreev, A. V. Balakin, A. B. Kozlov, I. A. Ozheredov, R. Prudnikov, A. P. Shkurinov, P. Masselin, and G. Mouret, “Four-wave mixing in one-dimensional photonic crystals: inhomogeneous wave excitation,” J. Opt. Soc. Am. B (to be published).
- G. I. Stegeman, R. Fortenberry, C. Karaguleff, R. Moshrefzadeh, W. M. Hetherington III, N. E. Van Wyck, and J. E. Sipe, “Coherent anti-Stokes Raman scattering in thin-film dielectric waveguides,” Opt. Lett. 8, 295–297 (1983).
- A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).

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