Abstract

We probe the propagation of short electromagnetic pulses of finite bandwidth through a one-dimensional nonlinear photonic crystal. The theoretical scheme is tested in numerical simulations of the reflection and transmission spectra for a sample of recent experimental interest. The study is important for understanding of the nonlinear phase shifts and other active spectral modifications in photonic crystals, which have potential applications in all-optical signal processing.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  5. R.E.Slusher and B.J.Eggleton, eds., Nonlinear Photonic Crystals (Springer-Verlag, 2003).
  6. M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, "Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56, 3166-3174 (1997).
    [CrossRef]
  7. Y. Dumeige, P. Vidakovic, S. Sauvage, 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]
  8. Y. Dumeige, I. Sagnes, P. Monnier, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at the photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
    [CrossRef] [PubMed]
  9. R. Ghosh, A. K. Hafiz, P. Monnier, C. Cojocaru, F. Rainery, A. Levenson, and R. Raj, "Blue shift in a one-dimensional photonic crystal due to interference of second- and third-order nonlinearities," in Proceedings of the Seventh International Conference on Optoelectronics, Fiber Optics and Photonics: Photonics-2004, Kochi, India, December 9-11, 2004.
    [PubMed]
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    [CrossRef]
  15. C. Simonneau, J. P. Debray, J. C. Harmand, P. Vidakovic, D. J. Lovering, and J. A. Levenson, "Second-harmonic generation in a doubly resonant semiconductor microcavity," Opt. Lett. 22, 1775-1777 (1997).
    [CrossRef]
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    [CrossRef]

2004

W. Li-gang, L. Nian-hua, L. Qiang, and Z. Shi-yao, "Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals," Phys. Rev. E 70, 016601 (2004).
[CrossRef]

2002

Y. Dumeige, I. Sagnes, P. Monnier, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at the photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

2001

Y. Dumeige, P. Vidakovic, S. Sauvage, 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]

2000

M. Centini, C. Sibilia, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Reflectivity control via second order interaction process in one-dimensional photonic bandgap structures," Opt. Commun. 184, 283-288 (2000).
[CrossRef]

1999

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

1997

C. Simonneau, J. P. Debray, J. C. Harmand, P. Vidakovic, D. J. Lovering, and J. A. Levenson, "Second-harmonic generation in a doubly resonant semiconductor microcavity," Opt. Lett. 22, 1775-1777 (1997).
[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 in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

1995

1994

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

1989

1987

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

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

Abram, I.

Y. Dumeige, I. Sagnes, P. Monnier, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at the photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Bertolatti, M.

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Bertolotti, M.

M. Centini, C. Sibilia, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Reflectivity control via second order interaction process in one-dimensional photonic bandgap structures," Opt. Commun. 184, 283-288 (2000).
[CrossRef]

Bethune, D. S.

Bloemer, M. J.

M. Centini, C. Sibilia, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Reflectivity control via second order interaction process in one-dimensional photonic bandgap structures," Opt. Commun. 184, 283-288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap 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 in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

Bowden, C. M.

M. Centini, C. Sibilia, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Reflectivity control via second order interaction process in one-dimensional photonic bandgap structures," Opt. Commun. 184, 283-288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap 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 in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

Centini, M.

Y. Dumeige, P. Vidakovic, S. Sauvage, 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, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Reflectivity control via second order interaction process in one-dimensional photonic bandgap structures," Opt. Commun. 184, 283-288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Cojocaru, C.

R. Ghosh, A. K. Hafiz, P. Monnier, C. Cojocaru, F. Rainery, A. Levenson, and R. Raj, "Blue shift in a one-dimensional photonic crystal due to interference of second- and third-order nonlinearities," in Proceedings of the Seventh International Conference on Optoelectronics, Fiber Optics and Photonics: Photonics-2004, Kochi, India, December 9-11, 2004.
[PubMed]

D'Aguanno, G.

Y. Dumeige, P. Vidakovic, S. Sauvage, 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, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Reflectivity control via second order interaction process in one-dimensional photonic bandgap structures," Opt. Commun. 184, 283-288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Debray, J. P.

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 in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

Dumeige, Y.

Y. Dumeige, I. Sagnes, P. Monnier, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at the photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Y. Dumeige, P. Vidakovic, S. Sauvage, 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]

Ghosh, R.

R. Ghosh, A. K. Hafiz, P. Monnier, C. Cojocaru, F. Rainery, A. Levenson, and R. Raj, "Blue shift in a one-dimensional photonic crystal due to interference of second- and third-order nonlinearities," in Proceedings of the Seventh International Conference on Optoelectronics, Fiber Optics and Photonics: Photonics-2004, Kochi, India, December 9-11, 2004.
[PubMed]

Hafiz, A. K.

R. Ghosh, A. K. Hafiz, P. Monnier, C. Cojocaru, F. Rainery, A. Levenson, and R. Raj, "Blue shift in a one-dimensional photonic crystal due to interference of second- and third-order nonlinearities," in Proceedings of the Seventh International Conference on Optoelectronics, Fiber Optics and Photonics: Photonics-2004, Kochi, India, December 9-11, 2004.
[PubMed]

Harmand, J. C.

Hashizume, N.

Haus, J. W.

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

Ito, R.

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

John, S.

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

Kondo, T.

Levenson, A.

Y. Dumeige, I. Sagnes, P. Monnier, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at the photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

R. Ghosh, A. K. Hafiz, P. Monnier, C. Cojocaru, F. Rainery, A. Levenson, and R. Raj, "Blue shift in a one-dimensional photonic crystal due to interference of second- and third-order nonlinearities," in Proceedings of the Seventh International Conference on Optoelectronics, Fiber Optics and Photonics: Photonics-2004, Kochi, India, December 9-11, 2004.
[PubMed]

Levenson, J. A.

Y. Dumeige, P. Vidakovic, S. Sauvage, 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]

C. Simonneau, J. P. Debray, J. C. Harmand, P. Vidakovic, D. J. Lovering, and J. A. Levenson, "Second-harmonic generation in a doubly resonant semiconductor microcavity," Opt. Lett. 22, 1775-1777 (1997).
[CrossRef]

Li-gang, W.

W. Li-gang, L. Nian-hua, L. Qiang, and Z. Shi-yao, "Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals," Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Lovering, D. J.

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 in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Mériadec, C.

Y. Dumeige, I. Sagnes, P. Monnier, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at the photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Monnier, P.

Y. Dumeige, I. Sagnes, P. Monnier, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at the photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

R. Ghosh, A. K. Hafiz, P. Monnier, C. Cojocaru, F. Rainery, A. Levenson, and R. Raj, "Blue shift in a one-dimensional photonic crystal due to interference of second- and third-order nonlinearities," in Proceedings of the Seventh International Conference on Optoelectronics, Fiber Optics and Photonics: Photonics-2004, Kochi, India, December 9-11, 2004.
[PubMed]

Nefedov, I.

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Nian-hua, L.

W. Li-gang, L. Nian-hua, L. Qiang, and Z. Shi-yao, "Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals," Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Ohashi, M.

Qiang, L.

W. Li-gang, L. Nian-hua, L. Qiang, and Z. Shi-yao, "Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals," Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Rainery, F.

R. Ghosh, A. K. Hafiz, P. Monnier, C. Cojocaru, F. Rainery, A. Levenson, and R. Raj, "Blue shift in a one-dimensional photonic crystal due to interference of second- and third-order nonlinearities," in Proceedings of the Seventh International Conference on Optoelectronics, Fiber Optics and Photonics: Photonics-2004, Kochi, India, December 9-11, 2004.
[PubMed]

Raj, R.

R. Ghosh, A. K. Hafiz, P. Monnier, C. Cojocaru, F. Rainery, A. Levenson, and R. Raj, "Blue shift in a one-dimensional photonic crystal due to interference of second- and third-order nonlinearities," in Proceedings of the Seventh International Conference on Optoelectronics, Fiber Optics and Photonics: Photonics-2004, Kochi, India, December 9-11, 2004.
[PubMed]

Sagnes, I.

Y. Dumeige, I. Sagnes, P. Monnier, I. Abram, C. Mériadec, and A. Levenson, "Phase-matched frequency doubling at the photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Y. Dumeige, P. Vidakovic, S. Sauvage, 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]

Sauvage, S.

Y. Dumeige, P. Vidakovic, S. Sauvage, 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. Sauvage, 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, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Reflectivity control via second order interaction process in one-dimensional photonic bandgap structures," Opt. Commun. 184, 283-288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap 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 in nonlinear, one-dimensional, periodic structures," Phys. Rev. A 56, 3166-3174 (1997).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef] [PubMed]

Shi-yao, Z.

W. Li-gang, L. Nian-hua, L. Qiang, and Z. Shi-yao, "Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals," Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Sibilia, C.

Y. Dumeige, P. Vidakovic, S. Sauvage, 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, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Reflectivity control via second order interaction process in one-dimensional photonic bandgap structures," Opt. Commun. 184, 283-288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Simonneau, C.

Vidakovic, P.

Y. Dumeige, P. Vidakovic, S. Sauvage, 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]

C. Simonneau, J. P. Debray, J. C. Harmand, P. Vidakovic, D. J. Lovering, and J. A. Levenson, "Second-harmonic generation in a doubly resonant semiconductor microcavity," Opt. Lett. 22, 1775-1777 (1997).
[CrossRef]

Viswanathan, R.

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

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Yablonovitch, E.

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

Appl. Phys. Lett.

Y. Dumeige, P. Vidakovic, S. Sauvage, 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]

J. Opt. Soc. Am. B

Opt. Commun.

M. Centini, C. Sibilia, G. D'Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, "Reflectivity control via second order interaction process in one-dimensional photonic bandgap structures," Opt. Commun. 184, 283-288 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. E

M. Centini, C. Sibilia, M. Scalora, G. D'Aguanno, M. Bertolatti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, "Dispersive properties of a finite, one-dimensional photonic bandgap structures: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

W. Li-gang, L. Nian-hua, L. Qiang, and Z. Shi-yao, "Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals," Phys. Rev. E 70, 016601 (2004).
[CrossRef]

Phys. Rev. Lett.

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Figures (10)

Fig. 1
Fig. 1

Plot of the transmission profile of the 18-period structure with n L = 1.5 and n NL given by the Sellmeir equation. The angle of incidence is taken to be 42°, and a TM wave is assumed.

Fig. 2
Fig. 2

Plots of the FF spectra: incident FF (solid curve), reflected FF (dashed curve), and transmitted FF (dotted curve).

Fig. 3
Fig. 3

Plots of the SHF spectra: incident SHF (solid curve), reflected SHF (dashed curve), and transmitted SHF (dotted curve).

Fig. 4
Fig. 4

Plots of the FF spectra for the peak SHF value of 3 × 10 7 V m : reflected FF (solid curve) and transmitted FF (dotted curve).

Fig. 5
Fig. 5

Plots of the reflected FF spectra for different values of the peak SHF: 3.19 × 10 7 V m (solid curve), 3.20 × 10 7 V m (dotted curve), 3.21 × 10 7 V m (small-dashed curve), 3.22 × 10 7 V m (dotted–dashed curve), 3.23 × 10 7 V m (three-dotted curve), and 3.24 × 10 7 V m (long-dashed curve).

Fig. 6
Fig. 6

Plots of the transmitted FF spectra for different values of the peak SHF as in Fig. 5: 3.19 × 10 7 V m (solid curve), 3.20 × 10 7 V m (dotted curve), 3.21 × 10 7 V m (small-dashed curve), 3.22 × 10 7 V m (dotted–dashed curve), 3.23 × 10 7 V m (three-dotted curve), and 3.24 × 10 7 V m (long-dashed curve).

Fig. 7
Fig. 7

Plots of the reflected FF spectra for different peak values of the incident FF: 1.09 × 10 8 V m (dotted curve), 1.10 × 10 8 V m (dashed curve), and 1.11 × 10 8 V m (solid curve).

Fig. 8
Fig. 8

Plots of the transmitted FF spectra for different peak values of the incident FF as in Fig. 7: 1.09 × 10 8 V m (dotted curve), 1.10 × 10 8 V m (dashed curve), and 1.11 × 10 8 V m (solid curve).

Fig. 9
Fig. 9

Plots of the reflected FF spectra for different peak values of the incident FF: 1.725 × 10 8 V m (dotted curve), 1.7275 × 10 8 V m (dotted–dashed curve), 1.73 × 10 8 V m (dashed curve), and 1.735 × 10 8 V m (solid curve).

Fig. 10
Fig. 10

Plots of the transmitted FF spectra for different peak values of the incident FF, as in Fig. 9: 1.725 × 10 8 V m (dotted curve), 1.7275 × 10 8 V m (dotted–dashed curve), 1.73 × 10 8 V m (dashed curve), and 1.735 × 10 8 V m (solid curve).

Equations (34)

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B = μ 0 H ,
D = ϵ ¯ E + P NL ,
2 E ( E ) 2 E s z 2 ,
P NL = z ̂ P p ( NL ) + P s ( NL ) = z ̂ P p ( NL ) + x ̂ ( x ̂ P s ( NL ) ) + y ̂ ( y ̂ P s ( NL ) ) ,
E P ( ω , z ) = P p ( NL ) ( ω , z ) ϵ p ,
2 E s z 2 + ω 2 μ 0 ϵ s E s + μ 0 ω 2 P s ( NL ) = 0 .
K i = z ̂ k i + x ̂ β ,
E i x ( ω , z , t ) = [ E i x f ( ω , z ) exp ( i k i z ) + E i x b ( ω , z ) exp ( i k i z ) ] exp [ i ( β x ω t ) ] + c.c.
E i ( ω , z ) = i ω 2 2 ϵ 0 c 2 k i [ x ̂ x ̂ + y ̂ y ̂ ] { [ z i 1 z P i + ( z ) exp ( i k i d z ) d z ] exp ( i k i z ) + [ z z i P i ( z ) exp ( i k i z ) d z ] exp ( i k i z ) } ,
E i ( gen ) ( r ) = E i ( gen ) ( z ) exp ( i β x ) ,
E i x f ( ω , x , z ) = [ E i x f ( ω , z i 1 ) + i ω 2 2 ϵ 0 c 2 k i x ̂ z i 1 z P i + ( z ) exp ( i k i z ) d z ] exp ( i k i z ) exp ( i β x ) ,
E i x b ( ω , x , z ) = [ E i x b ( ω , z i 1 ) i ω 2 2 ϵ 0 c 2 k i x ̂ z i 1 z P i ( z ) exp ( i k i z ) d z ] exp ( i k i z ) exp ( i β x ) .
M j i = 1 t j i [ 1 r j i r j i 1 ] ,
r j i = n j 2 tan θ j n i 2 tan θ i n j 2 tan θ j + n i 2 tan θ i ,
t j i = 2 n j 2 tan θ j n i 2 tan θ i + n j 2 tan θ j .
Q L ( ω ) = [ exp ( i k D ω d L ) 0 0 exp ( i k L ω d L ) ] ,
P NL χ ( 2 ) ( ω 2 ) = χ ( 2 ) : E ( ω 1 ) E ( ω 1 ) .
P NL χ ( 2 ) ( ω 1 ) = χ ( 2 ) : E ( ω 2 ) E * ( ω 1 )
P NL χ ( 3 ) ( ω 1 ) = χ ( 3 ) : E * ( ω 2 ) E ( ω 2 ) E ( ω 1 ) + χ ( 3 ) : E * ( ω 1 ) E ( ω 1 ) E ( ω 1 ) .
E ( ω i ) = α i E i 0 α i 2 + ( ω i ω i 0 ) 2 ,
n NL ( λ ) = 1 + A λ 2 λ 2 B ,
E NL f ( ω 1 , z + Δ , N ) exp [ i k NL ω 1 ( z + Δ ) ] = E NL f ( ω 1 , z , N ) exp [ i k NL ω 1 ( z + Δ ) ] + i ω 1 2 c n NL ω 1 cos θ ω 1 ( { χ ( 2 ) z z + Δ ω 1 ω 2 [ α 1 E 10 f ( z , N ) exp ( i k NL ω 1 z ) α 1 2 + ( ω 1 ω 10 ) 2 ] * exp ( i k NL ω 1 z ) α 2 E 20 f ( z , N ) exp ( i k NL ω 2 z ) α 2 2 + ( ω 2 ω 20 ) 2 δ ( ω 2 ω 1 ω 1 ) d ω 1 α 1 d ω 2 α 2 d z } + [ χ ( 3 ) z z + Δ ω 2 E 20 f α 2 α 2 2 + ( ω 2 ω 20 ) 2 2 E NL f ( ω 1 , z , N ) exp ( i k ω NL ω 1 z ) × exp ( i k NL ω 1 z ) d ω z α 2 d z ] + [ χ ( 3 ) z z + Δ ω 1 α 1 E 10 f α 1 2 + ( ω 1 ω 10 ) 2 2 E NL f ( ω 1 , z , N ) exp ( i k NL ω 1 z ) exp ( i k NL ω 1 z ) d ω 1 α 1 d z ] ) exp [ i k NL ω 1 ( z + Δ ) ] ,
E NL b ( ω 1 , z + Δ , N ) exp [ i k NL ω 1 ( z + Δ ) ] = E NL b ( ω 1 , z , N ) exp [ i k NL ω 1 ( z + Δ ) ] i ω 1 2 c n NL ω 1 cos θ ω 1 ( { χ ( 2 ) z z + Δ ω 1 ω 2 [ α 1 E 10 b ( z , N ) exp ( i k NL ω 1 z ) α 1 2 + ( ω 1 ω 10 ) 2 ] * exp ( i k NL ω 1 z ) α 2 E 20 b ( z , N ) exp ( i k NL ω 2 z ) α 2 2 + ( ω 2 ω 20 ) 2 δ ( ω 2 ω 1 ω 1 ) d ω 2 α 2 d ω 1 α 1 d z } + [ χ ( 3 ) z z + Δ ω 2 E 20 b α 2 α 2 + ( ω 2 ω 20 ) 2 2 E NL b ( ω 1 , z , N ) exp ( i k NL ω 1 z ) × exp ( i k NL ω 1 z ) d ω 2 α 2 d z ] + [ χ ( 3 ) z z + Δ ω 1 α 1 E 10 b ( z , N ) α 1 2 + ( ω 1 ω 10 ) 2 2 E NL b ( ω 1 , z , N ) exp ( i k NL ω 1 z ) exp ( i k NL ω 1 z ) d ω 1 α 1 d z ] ) exp [ i k NL ω 1 ( z + Δ ) ] .
E gen ( ω 2 , z , N ) = E + ( ω 2 , N ) exp ( i k NL ω 2 z ) + E ( ω 2 , N ) exp ( i k NL ω 2 z ) ,
E ( ω 2 , z i , N ) = ( E L f ( ω 2 , z i , N ) exp ( i k L ω 2 z i ) E L b ( ω 2 , z i , N ) exp ( i k L ω 2 z i ) ) .
Q NL ( ω 2 ) = [ exp ( i k NL ω 2 d NL ) 0 0 exp ( i k NL ω 2 d NL ) ] ,
( E L f ( ω 2 , z i + 2 N + 1 ) exp ( i k L ω 2 z i + 2 ) E L b ( ω 2 , z i + 2 N + 1 ) exp ( i k L ω 2 z i + 2 ) ) = M 12 [ Q NL M 21 Q L ( E L f ( ω 2 , z i , N ) exp ( i k L ω 2 z i ) E L b ( ω 2 , z i , N ) exp ( i k L ω 2 z i ) ) + ( E + ( ω 2 , N ) exp ( i k NL ω 2 z i + 2 ) E ( ω 2 , N ) exp ( i k NL ω 2 z i + 2 ) ) ] .
E o ( ω 2 ) = ( E o f ( ω 2 ) exp ( i k o z o ) E o b ( ω 2 ) exp ( i k o z o ) ) ,
E s ( ω 2 ) = ( E s f ( ω 2 ) exp ( i k s z i ) E s b ( ω 2 ) exp ( i k s z i ) ) ,
Q = M 12 Q NL M 21 Q L .
( E s f ( ω 2 ) exp ( i k s z s ) E s b ( ω 2 ) exp ( i k s z s ) ) = M s Q NL M 21 Q L Q N 1 M o ( E o f ( ω 2 ) exp ( i k o z o ) E o b ( ω 2 ) exp ( i k o z o ) ) + M s Q NL M 21 Q L Q N 2 M 12 ( E + ( ω 2 , 1 ) exp ( i k NL ω 2 z 2 ) E ( ω 2 , 1 ) exp ( i k NL ω 2 z 2 ) ) + M s Q NL M 21 Q L Q N 3 M 12 ( E + ( ω 2 , 2 ) exp ( i k NL ω 2 z 4 ) E ( ω 2 , 2 ) exp ( i k NL ω 2 z 4 ) ) + M s Q NL M 21 Q L M 12 ( E + ( ω 2 , N 1 ) exp ( i k NL ω 2 z 2 N 2 ) E ( ω 2 , N 1 ) exp ( i k NL ω 2 z 2 N 2 ) ) + M s ( E + ( ω 2 , N ) exp ( i k NL ω 2 z s ) E ( ω 2 , N ) exp ( i k NL ω 2 z s ) ) .
P NL χ ( 3 ) ( ω 1 ) = χ ( 3 ) : E * ( ω 2 ) E ( ω 2 ) E ( ω 1 ) .
E NL f ( ω 1 , z + Δ , N ) exp [ i k NL ω 1 ( z + Δ ) ] = E NL f ( ω 1 , z , N ) exp [ i k NL ω 1 ( z + Δ ) ] + i ω 1 2 c n NL ω 1 cos θ ω 1 { [ χ ( 3 ) z z + Δ ω 2 E NL f ( ω 2 , z , N ) 2 × E NL f ( ω 1 , z , N ) exp ( i k NL ω 1 z ) exp ( i k NL ω 1 z ) d ω 2 d z ] } exp [ i k NL ω 1 ( z + Δ ) ] ,
E NL b ( ω 1 , z + Δ , N ) exp [ i k NL ω 1 ( z + Δ ) ] = E NL b ( ω 1 , z , N ) exp [ i k NL ω 1 ( z + Δ ) ] i ω 1 2 c n NL ω 1 cos θ ω 1 { [ χ ( 3 ) z z + Δ ω 2 E NL b ( ω 2 , z , N ) 2 E NL b ( ω 1 , z , N ) exp ( i k NL ω 1 z ) exp ( i k NL ω 1 z ) d ω 2 d z ] } exp [ i k NL ω 1 ( z + Δ ) ] .

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