Abstract

We examine in detail the quasi-phase-matching process obtained as a stationary modulation of the fundamental field at the band edge of a finite one-dimensional photonic crystal. The treatment is carried out in terms of the structure Bloch waves and fully explains the behavior of second-harmonic generation in the grating. An integrated microstructured AlGaAs mesa waveguide is proposed that gives efficient second-harmonic and difference-frequency generation in virtue of the combined presence of a periodic modulation of the fundamental-field amplitude and of the photonic bandgap edge.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. C. Conti, G. Assanto, and S. Trillo, “Cavityless oscillation through backward quasiphase-matched second-harmonic generation,” Opt. Lett. 24, 1139–1141 (1999).
    [CrossRef]
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    [CrossRef]
  16. J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
    [CrossRef]
  17. 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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
    [CrossRef]
  18. Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. Meriadec, and A. Levenson, “χ(2) semiconductor photonic crystals,” J. Opt. Soc. Am. B 9, 2094–2101 (2002).
    [CrossRef]
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  22. Fimmwave, PhotonDesign Ltd, UK.
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    [CrossRef]
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    [CrossRef]

2002 (3)

2001 (2)

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609 (2001).
[CrossRef]

1999 (5)

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]

C. Conti, G. Assanto, and S. Trillo, “Cavityless oscillation through backward quasiphase-matched second-harmonic generation,” Opt. Lett. 24, 1139–1141 (1999).
[CrossRef]

C. Conti, G. Assanto, and S. Trillo, “Energy localization through Bragg gratings in quadratic media for second harmonic generation,” Acta Phys. Pol. 95, 719–726 (1999).

Y. Jeong and B. Lee, “Matrix analysis for layered quasi-phase-matched media considering multiple reflection and pump wave depletion,” IEEE J. Quantum Electron. 35, 162–172 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

1998 (2)

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

1997 (1)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation on nolinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 278, 2631–2654 (1992).
[CrossRef]

1989 (1)

1977 (1)

1973 (1)

C. L. Tang and P. P. Bey, “Phase matching in second harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. 9, 9–17 (1973).
[CrossRef]

1972 (1)

S. Somekh and A. Yariv, “Phase matching by periodic modulation of the nonlinear optical properties,” Opt. Commun. 6, 301–304 (1972).
[CrossRef]

1970 (1)

N. Bloembergen and A. J. Sievers, “Nonlinear properties of laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970).
[CrossRef]

1962 (2)

J. A. Giordmaine, “Mixing of light beams in crystals,” Phys. Rev. Lett. 8, 19–20 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Assanto, G.

C. Conti, G. Assanto, and S. Trillo, “Cavityless oscillation through backward quasiphase-matched second-harmonic generation,” Opt. Lett. 24, 1139–1141 (1999).
[CrossRef]

C. Conti, G. Assanto, and S. Trillo, “Energy localization through Bragg gratings in quadratic media for second harmonic generation,” Acta Phys. Pol. 95, 719–726 (1999).

Balakin, A. V.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609 (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]

Berger, V.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Bethune, D. S.

Bey, P. P.

C. L. Tang and P. P. Bey, “Phase matching in second harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. 9, 9–17 (1973).
[CrossRef]

Bloembergen, N.

N. Bloembergen and A. J. Sievers, “Nonlinear properties of laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970).
[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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation on nolinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Boucher, D.

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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation on nolinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Bravetti, P.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Bushuev, V. A.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609 (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]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 278, 2631–2654 (1992).
[CrossRef]

Centini, M.

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Cole, J. D.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

Conti, C.

C. Conti, G. Assanto, and S. Trillo, “Energy localization through Bragg gratings in quadratic media for second harmonic generation,” Acta Phys. Pol. 95, 719–726 (1999).

C. Conti, G. Assanto, and S. Trillo, “Cavityless oscillation through backward quasiphase-matched second-harmonic generation,” Opt. Lett. 24, 1139–1141 (1999).
[CrossRef]

D’Aguanno, G.

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation on nolinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Dumeige, Y.

F. Ranieri, Y. Dumeige, A. Levenson, and X. Letartre, “Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal,” Electron. Lett. 38, 1704–1706 (2002).
[CrossRef]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. Meriadec, and A. Levenson, “χ(2) semiconductor photonic crystals,” J. Opt. Soc. Am. B 9, 2094–2101 (2002).
[CrossRef]

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 278, 2631–2654 (1992).
[CrossRef]

Fiore, A.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine, “Mixing of light beams in crystals,” Phys. Rev. Lett. 8, 19–20 (1962).
[CrossRef]

Haus, J. W.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation on nolinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Jeong, Y.

Y. Jeong and B. Lee, “Matrix analysis for layered quasi-phase-matched media considering multiple reflection and pump wave depletion,” IEEE J. Quantum Electron. 35, 162–172 (1999).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 278, 2631–2654 (1992).
[CrossRef]

Kalocsai, A. G.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

Koroteev, N. I.

Lee, B.

Y. Jeong and B. Lee, “Matrix analysis for layered quasi-phase-matched media considering multiple reflection and pump wave depletion,” IEEE J. Quantum Electron. 35, 162–172 (1999).
[CrossRef]

Letartre, X.

F. Ranieri, Y. Dumeige, A. Levenson, and X. Letartre, “Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal,” Electron. Lett. 38, 1704–1706 (2002).
[CrossRef]

Levenson, A.

F. Ranieri, Y. Dumeige, A. Levenson, and X. Letartre, “Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal,” Electron. Lett. 38, 1704–1706 (2002).
[CrossRef]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. Meriadec, and A. Levenson, “χ(2) semiconductor photonic crystals,” J. Opt. Soc. Am. B 9, 2094–2101 (2002).
[CrossRef]

Levenson, J. A.

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 278, 2631–2654 (1992).
[CrossRef]

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation on nolinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Mantsyzov, B. I.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609 (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.

Meriadec, C.

Midrio, M.

Monnier, P.

Nagle, J.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Nisenhoff, M.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Ozheredov, I. A.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609 (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]

Petrov, E. V.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609 (2001).
[CrossRef]

Ranieri, F.

F. Ranieri, Y. Dumeige, A. Levenson, and X. Letartre, “Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal,” Electron. Lett. 38, 1704–1706 (2002).
[CrossRef]

Romagnoli, M.

Rosencher, E.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Sagnes, I.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. Meriadec, and A. Levenson, “χ(2) semiconductor photonic crystals,” J. Opt. Soc. Am. B 9, 2094–2101 (2002).
[CrossRef]

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Savauge, S.

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Scalora, M.

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation on nolinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Shkurinov, A. P.

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609 (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]

Sibilia, C.

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Sievers, A. J.

N. Bloembergen and A. J. Sievers, “Nonlinear properties of laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970).
[CrossRef]

Socci, L.

Somekh, S.

S. Somekh and A. Yariv, “Phase matching by periodic modulation of the nonlinear optical properties,” Opt. Commun. 6, 301–304 (1972).
[CrossRef]

Tang, C. L.

C. L. Tang and P. P. Bey, “Phase matching in second harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. 9, 9–17 (1973).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Theimer, J.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

Trillo, S.

C. Conti, G. Assanto, and S. Trillo, “Energy localization through Bragg gratings in quadratic media for second harmonic generation,” Acta Phys. Pol. 95, 719–726 (1999).

C. Conti, G. Assanto, and S. Trillo, “Cavityless oscillation through backward quasiphase-matched second-harmonic generation,” Opt. Lett. 24, 1139–1141 (1999).
[CrossRef]

Vidakovic, P.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, C. Meriadec, and A. Levenson, “χ(2) semiconductor photonic crystals,” J. Opt. Soc. Am. B 9, 2094–2101 (2002).
[CrossRef]

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Viswanathan, R.

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation on nolinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
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[CrossRef]

S. Somekh and A. Yariv, “Phase matching by periodic modulation of the nonlinear optical properties,” Opt. Commun. 6, 301–304 (1972).
[CrossRef]

Yeh, P.

Acta Phys. Pol. (1)

C. Conti, G. Assanto, and S. Trillo, “Energy localization through Bragg gratings in quadratic media for second harmonic generation,” Acta Phys. Pol. 95, 719–726 (1999).

Appl. Phys. Lett. (2)

N. Bloembergen and A. J. Sievers, “Nonlinear properties of laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970).
[CrossRef]

Y. Dumeige, P. Vidakovic, S. Savauge, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Electron. Lett. (1)

F. Ranieri, Y. Dumeige, A. Levenson, and X. Letartre, “Nonlinear decoupled FDTD code: phase-matching in 2D defective photonic crystal,” Electron. Lett. 38, 1704–1706 (2002).
[CrossRef]

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Y. Jeong and B. Lee, “Matrix analysis for layered quasi-phase-matched media considering multiple reflection and pump wave depletion,” IEEE J. Quantum Electron. 35, 162–172 (1999).
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[CrossRef]

C. L. Tang and P. P. Bey, “Phase matching in second harmonic generation using artificial periodic structures,” IEEE J. Quantum Electron. 9, 9–17 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (3)

Nature (1)

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[CrossRef]

Opt. Commun. (1)

S. Somekh and A. Yariv, “Phase matching by periodic modulation of the nonlinear optical properties,” Opt. Commun. 6, 301–304 (1972).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second harmonic generation on nolinear, one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

J. W. Haus, R. Viswanathan, M. Scalora, A. G. Kalocsai, J. D. Cole, and J. Theimer, “Enhanced second-harmonic generation in media with weak periodicity,” Phys. Rev. A 57, 2120–2128 (1998).
[CrossRef]

Phys. Rev. E (2)

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 band gap structures: applications to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

A. V. Balakin, V. A. Bushuev, B. I. Mantsyzov, I. A. Ozheredov, E. V. Petrov, and A. P. Shkurinov, “Enhancement of sum frequency generation near the photonic band gap edge under the quasiphase matching conditions,” Phys. Rev. E 63, 046609 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

J. A. Giordmaine, “Mixing of light beams in crystals,” Phys. Rev. Lett. 8, 19–20 (1962).
[CrossRef]

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Other (3)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

P. St. J. Russell, T. A. Birks, and F. D. Lloyd-Lucas, “Photonic Bloch waves and photonic band gaps,” in Confined Electrons and Photons, E. Burstein and C. Weisbuch (Plenum, New York, 1995), pp. 585–633.

Fimmwave, PhotonDesign Ltd, UK.

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Figures (8)

Fig. 1
Fig. 1

Numerical solution to Eq. (1) for the non-phase-matched case (dot curve) and for the QPM case (solid curve). The rescaled modulating function is also shown for reference (dashed curve).

Fig. 2
Fig. 2

One-dimensional grating structure realized in a mesa waveguide. All relevant dimensions and Al concentrations are as indicated. The unit cell is formed by six layers with thickness (1136–154–1136–154–1136–462) nm.

Fig. 3
Fig. 3

FF transmission of the 111-unit cell grating. The order of the PBG is indicated in the figure. The reflectivity (and thus the mode density) of the 16th band edge near λ=1585 nm has been optimized by use of λ/4 layers to construct the unit cell, as discussed in the text.

Fig. 4
Fig. 4

(a) Top graph: linear transmission of the FF field near the band edge. Middle and bottom graphs: SH efficiency in the forward and backward directions, respectively, with 111 unit cells and other parameters as indicated in the text. (b) FF (top graph) and SH (bottom graph) fields inside the grating.

Fig. 5
Fig. 5

Enlargement of Fig. 4(b) showing the local field distributions of the FF field (top graph) and SH field (bottom graph) for a grating with 111 unit cells. The Bloch-wave modulation is clearly visible in the FF field, whereas the oscillations in the SH field are related to the coherence length.

Fig. 6
Fig. 6

(a) Top graph: linear transmission of the FF field near the band edge. Middle and bottom graphs: SH efficiency in the forward and backward directions, respectively, with 222 unit cells and other parameters as indicated in the text. (b) FF (top graph) and SH (bottom graph) fields inside the grating.

Fig. 7
Fig. 7

Maximum SH conversion efficiency in %/mW versus total device length. Each point corresponds to an increase in L of 463 µm, i.e., L=m×463 µm, and therefore to a shift of the FF peak efficiency to the mth transmission peak from the PBG edge.

Fig. 8
Fig. 8

Idler conversion efficiency versus idler wavelength from the 111-unit cell structure by difference-frequency generation. Signal input power is 1 mW, and the 10-mW pump beam is tuned from 750 to 850 nm.

Equations (8)

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

E2ω(z)=const 0Lf(z)χ(2)Eω2exp(jΔβz)dz,
Eωstaz=Eω++Eω-=f+(z)exp(jβz)+f-(z)exp(-jβz),
Eωstaz=2p=-ρp cos[(β-pK)z+ϕp].
Eωstaz=4 cosβ-n+m2Kz+ψ×cosm-n2Kz+ξ,
β-n+m2KL=tπ,
m-n2K=c¯Δβ,
m=2nωλ-tL-c¯lcΛ2,
n=2nωλ-tL+c¯lcΛ2,

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