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 ω3=2ω1-ω2 is discussed and demonstrated.

© 2002 Optical Society of America

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    [CrossRef] [PubMed]

2001 (2)

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).
[CrossRef]

A. V. Andreev and A. B. Kozlov, “Excitation of waveguide modes in a one-dimensional photonic crystal,” Quantum Electron. 31, 443–447 (2001).
[CrossRef]

2000 (1)

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).
[CrossRef]

1999 (3)

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

1998 (1)

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).
[CrossRef]

1996 (1)

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).
[CrossRef] [PubMed]

1994 (1)

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).
[CrossRef]

1988 (1)

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7988 (1988).
[CrossRef]

1987 (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

1983 (1)

1963 (1)

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35, 23–39 (1963).
[CrossRef]

1962 (3)

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]

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

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).
[CrossRef]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–120 (1961).
[CrossRef]

1957 (1)

Andreev, A. V.

A. V. Andreev and A. B. Kozlov, “Excitation of waveguide modes in a one-dimensional photonic crystal,” Quantum Electron. 31, 443–447 (2001).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

Andreeva, O. A.

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).
[CrossRef]

Armstrong, J. A.

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]

Baker, W. M.

Balakin, A. V.

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

Bendickson, J. M.

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).
[CrossRef]

Bertolotti, M.

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).
[CrossRef]

Bloembergen, N.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

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]

Bloemer, M. J.

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).
[CrossRef]

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).
[CrossRef]

Boucher, D.

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).
[CrossRef]

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).
[CrossRef]

Bowden, C. M.

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).
[CrossRef]

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).
[CrossRef]

Bushuev, V. A.

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).
[CrossRef]

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).
[CrossRef]

Centini, M.

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).
[CrossRef]

Chen, J. C.

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).
[CrossRef] [PubMed]

Crane, R. C.

D’Aguanno, G.

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).
[CrossRef]

Dowling, J. P.

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).
[CrossRef]

Ducuing, J.

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]

Fan, S.

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).
[CrossRef] [PubMed]

Fogel, I. S.

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).
[CrossRef]

Fortenberry, R.

Franken, P. A.

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35, 23–39 (1963).
[CrossRef]

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–120 (1961).
[CrossRef]

Guyot-Sionnest, P.

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7988 (1988).
[CrossRef]

Hetherington III, W. M.

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–120 (1961).
[CrossRef]

Howe, J. B.

Joannopoulos, J. D.

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).
[CrossRef] [PubMed]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Jonusauskas, G.

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).
[CrossRef]

Karaguleff, C.

Koroteev, N. I.

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).
[CrossRef]

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).
[CrossRef]

Kozlov, A. B.

A. V. Andreev and A. B. Kozlov, “Excitation of waveguide modes in a one-dimensional photonic crystal,” Quantum Electron. 31, 443–447 (2001).
[CrossRef]

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).
[CrossRef]

Kurland, I.

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).
[CrossRef] [PubMed]

Maker, P. D.

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).
[CrossRef]

Mantsyzov, B. I.

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).
[CrossRef]

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).
[CrossRef]

Masselin, P.

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

Mekis, A.

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).
[CrossRef] [PubMed]

Moshrefzadeh, R.

Mouret, G.

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).
[CrossRef]

Nefedov, I.

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).
[CrossRef]

Nisenoff, M.

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).
[CrossRef]

Ozheredov, I. A.

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).
[CrossRef]

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).
[CrossRef]

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

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]

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–120 (1961).
[CrossRef]

Petrov, E. V.

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).
[CrossRef]

Prudnikov, I. R.

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).
[CrossRef]

Rulliere, C.

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).
[CrossRef]

Savage, C. M.

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).
[CrossRef]

Scalora, M.

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).
[CrossRef]

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).
[CrossRef]

Shen, Y. R.

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7988 (1988).
[CrossRef]

Shkurinov, A. P.

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

Sibilia, C.

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).
[CrossRef]

Sipe, J. E.

Stegeman, G. I.

Szyzak, S. J.

Terhune, R. W.

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).
[CrossRef]

Tocci, M. D.

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).
[CrossRef]

Van Wyck, N. E.

Villeneuve, P. R.

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).
[CrossRef] [PubMed]

Ward, J. F.

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35, 23–39 (1963).
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–120 (1961).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Chem. Phys. Lett. (1)

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).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Phys. Rev. (2)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

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]

Phys. Rev. B (1)

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7988 (1988).
[CrossRef]

Phys. Rev. E (2)

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).
[CrossRef]

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).
[CrossRef]

Phys. Rev. Lett. (5)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, “Generation of optical harmonics,” Phys. Rev. Lett. 7, 118–120 (1961).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

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).
[CrossRef]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Pure Appl. Opt. (1)

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).
[CrossRef]

Quantum Electron. (3)

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).
[CrossRef]

A. V. Andreev and A. B. Kozlov, “Excitation of waveguide modes in a one-dimensional photonic crystal,” Quantum Electron. 31, 443–447 (2001).
[CrossRef]

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).
[CrossRef]

Rev. Mod. Phys. (1)

P. A. Franken and J. F. Ward, “Optical harmonics and nonlinear phenomena,” Rev. Mod. Phys. 35, 23–39 (1963).
[CrossRef]

Other (6)

A. Yariv and P. Yeh, Optical Waves in Crystals. Propagation and Control of Laser Radiation (Wiley, New York, 1984).

V. D. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).

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).

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.

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.

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Figures (10)

Fig. 1
Fig. 1

Electronogram of the ZnS/SrF2 multilayer structure. The acceleration voltage is 75 kV, and the angle of incidence of the beam on the sample is 0.5°.

Fig. 2
Fig. 2

Transmission coefficients (a) T1 at λ1=736 nm, (b) T2 at λ2=813 nm, (c) T3 of the wave at the SF, and (d) the intensity ISFG of the transmitted wave at the SF plotted as functions of the angle of incidence θ1 of the first pump wave. The pump waves and the wave at the SF are s-, p-, and s-polarized, respectively. The angle between the wave vectors of the pump waves is ϕ=36.2°. The first-order transmission resonances coincide for all three interacting waves.

Fig. 3
Fig. 3

Transmission coefficients (a) T1 at λ1=736 nm, (b) T2 at λ2=813 nm, (c) T3 of the wave at the SF, and (d) the intensity ISFG of the transmitted wave at the SF plotted as functions of the angle of incidence θ1 of the first pump wave. The pump waves and the wave at the SF are s-, p-, and s-polarized, respectively. The angle between the wave vectors of the pump waves is ϕ=45°, and there is coincidence of the second-, the first-, and the second-order transmission resonances of the first and the second pump waves and the wave at the SF, respectively.

Fig. 4
Fig. 4

Transmission coefficients (a) T1 at λ1=736 nm, (b) T2 at λ2=813 nm, (c) T3 of the wave at the SF, and (d) the intensity ISFG of the transmitted wave at the SF, which is generated at the interfaces (solid curve) and in the bulk (dotted curve) of the layers, plotted as functions of the angle of incidence θ1 of the first pump wave. The pump waves and the wave at the SF are s-, p-, and s-polarized, respectively. The angle between the wave vectors of the pump waves is ϕ=28°.

Fig. 5
Fig. 5

Experimental setup: C, a mechanical chopper; M, dichroic mirrors; L, lenses; S, the PC sample; GSF, set of glass filters; GP, the Glan–Taylor polarizer; DFR, the double Fresnel rhombus; D, the diaphragm; and PMT, the photomultiplier tube.

Fig. 6
Fig. 6

Transmission coefficients (a) T1 at λ1=736 nm of the pump wave, (b) T2 at λ2=813 nm of the pump wave, (c) T3 and the reflection coefficient R3 of the wave at the SF, and (d) the intensity ISFG of the transmitted wave at the SF plotted as functions of the angle of incidence θ1 of the first pump wave. The graphs on the left-hand side represent the experimental results, and those on the right-hand side, the theoretical calculations. The signal at the SF is generated at the interfaces (solid curve) and in the bulk (dotted curve) of the layers. All interacting waves are p polarized. The angle between the wave vectors of the pump waves is ϕ=29°.

Fig. 7
Fig. 7

Transmission coefficients (a) T1 at λ1=736 nm of the pump wave, (b) T2 at λ2=813 nm of the pump wave, (c) T3 and the reflection coefficient R3 of the wave at the SF, and (d) the intensity ISFG of the transmitted wave at the SF plotted as functions of the angle of incidence θ1 of the first pump wave. The graphs on the left-hand side represent the experimental results, and those on the right-hand side, the theoretical calculations. The signal at the SF is generated at the interfaces (solid curve) and in the bulk (dotted curve) of the layers. The angle between the wave vectors of the pump waves is ϕ=38°.

Fig. 8
Fig. 8

Transmission coefficients (a) T1 at λ1=736 nm of the pump wave, (b) T2 at λ2=813 nm of the pump wave, (c) T3 and the reflection coefficient R3 of the wave at the SF, and (d) the intensity ISFG of the transmitted wave at the SF plotted as functions of the angle of incidence θ1 of the first pump wave. The graphs on the left-hand side represent the experimental results, and those on the right-hand side, the theoretical calculations. The signal at the SF is generated at the interfaces (solid curve) and in the bulk (dotted curve) of the layers. The angle between the wave vectors of the pump waves is ϕ=45°.

Fig. 9
Fig. 9

Transmission coefficients (a) T1 at λ1=690 nm of the pump wave, (b) T2 at λ2=817 nm of the pump wave, and (c) the intensity IFWM of the transmitted wave at the FWM frequency plotted as functions of the angle of incidence θ1 of the first pump wave. In (c), the curve of open circles represents the experimental results, and the solid curve, the theoretical fitting. The angle between the wave vectors of the pump waves is ϕ=6.5°.

Fig. 10
Fig. 10

Experimental (triangles) and theoretical (solid curve) transmitted FWM signals with an angle of ϕ=25° between λ1=690 nm and λ2=817 nm beams. The inset shows the measured (circles) and the calculated (solid curve) angles θFWM between the FWM transmitted beam and the normal of the sample plotted versus the angle of incidence θ on the PC structure.

Tables (1)

Tables Icon

Table 1 Polarization of the Wave at the SF as a Function of the Polarizations of the Pump Waves

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

ΔzEx+(k2-ky2)Ex=-iω4πc2Jx,
Gx=Hx/n,
ΔzGx+(k2-ky2)Gx+nzznn2Gx
=-4πcnikyJz-zJy.
Ex(z)=-iω4πc21wsEx(1)(z)0zEx(2)(z)Jx(z)dz+Ex(2)(z)zLEx(1)(z)Jx(z)dz,
Hx(z)=-4πc1wpikyHx(1)(z)0zHx(2)(z)Jz(z)(z)dz+Hx(2)(z)zLHx(1)(z)Jz(z)(z)dz+4πc1wpiωcHx(1)(z)0zEy(2)(z)Jy(z)dz+Hx(2)(z)zLEy(1)(z)Jy(z)dz,
Jα(ω3)=Jαs(ω3)+Jαb(ω3)
Jαs(ω3)=p(χ1pnαE1βE2β+χ2pE1αnβE2β+χ3pE2αnβE1β)δ(z-zp),
Jαb(ω3)=χω12ω02-ω12E1βαE2β+ω22ω02-ω22E2βαE1β-ω1ω3ω02-ω12E1ββE2α-ω2ω3ω02-ω22E2ββE1α,
χ=iNV2e|d|2ω0ω3mω1ω2(ω02-ω32),
Jxb(ω3)=iχω3cω1ω2ω02-ω12(E1yH2z-E1zH2y)+ω1ω2ω02-ω22(E2yH1z-E2zH1y),
Jyb(ω3)=iχω3cω1ω2ω02-ω12E1zH2x+ω1ω2ω02-ω22E2zH1x+k2yω12ω02-ω12+k1yω22ω02-ω22E1xE2x-k2yω1ω2ω02-ω12+k1yω1ω2ω02-ω22(E1yE2y+E1zE2z),
Jzb(ω3)=iχω2cω12ω02-ω12(E1xH2y-E1yH2x)+ω1cω22ω02-ω22(E2xH1y-E2yH1x)-k2yω1ω2ω02-ω12-k1yω1ω2ω02-ω22(E1yE2z-E1zE2y)+χω1ω2ω02-ω12z22+ω1ω2ω02-ω22z11E1zE2z,

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