Abstract

We present an adaptation of the fast Fourier factorization method to the simulation of two-dimensional (2D) photonic crystals with a third-order nonlinearity. The algorithm and its performance are detailed and illustrated via the simulation of a Kerr 2D photonic crystal. A change in the transmission spectrum at high intensity is observed. We explain why the change does not reduce to a translation (redshift) but rather consists in a deformation and why one side of the bandgap is more suited to a switching application than the other one.

© 2006 Optical Society of America

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  1. J. Joannopoulos, Photonic Crystals, Molding the Flow of Light (Princeton U. Press, 1995).
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    [CrossRef] [PubMed]
  3. A. Priou and T. Itoh, eds., Progress in Electromagnetic Research (Universita di Pisa, 2004), Vol. 43.
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    [CrossRef]
  5. D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
    [CrossRef]
  6. P. Halevi and F. R. Mendieta, "Tunable photonic crystals with semiconducting constituents," Phys. Rev. Lett. 85, 1875-1878 (2000).
    [CrossRef] [PubMed]
  7. W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
    [CrossRef] [PubMed]
  8. S. John and N. Akozbek, "Nonlinear optical solitary waves in a photonic band gap," Phys. Rev. Lett. 71, 1168-1171 (1993).
    [CrossRef] [PubMed]
  9. M. Scarola, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashortpulses in nonlinear photonic bandgap material," Phys. Rev. Lett. 73, 1368-1371 (1994).
    [CrossRef]
  10. H. Y. Ryu and M. Notomi, "Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab," Phys. Rev. B 68, 5209-5217 (2003).
    [CrossRef]
  11. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).
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    [CrossRef]
  13. V. Lousse and J. P. Vigneron, "Bistable behaviour of a photonic crystal nonlinear cavity," Physica B 338, 171-177 (2003).
    [CrossRef]
  14. E. Lidorikis, Q. Li, and C. M. Soukoulis, "Wave propagation in nonlinear multilayer structures," Phys. Rev. B 54, 10249-10252 (1996).
    [CrossRef]
  15. N. Akozbek and S. John, "Optical solitary waves in two and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57, 2287-2319 (1998).
    [CrossRef]
  16. S. F. Mingaleev and Y. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86, 5474-5477 (2001).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  19. A. M. Kamtchatnoc, S. A. Darmanyan, and M. Nevière, "Polariton gap solitary waves in semiconductor microcavities," J. Lumin. 110, 373-377 (2004).
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  23. V. Lousse and J. P. Vigneron, "Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical material," Phys. Rev. E 63, 027602-027606 (2001).
    [CrossRef]
  24. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystal," Phys. Rev. E 66, 055601-055605 (2002).
    [CrossRef]
  25. E. Popov and M. Nevière, Light Propagation in Periodic Media (Marcel Dekker, 2003).
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    [CrossRef]
  27. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
    [CrossRef]
  28. N. Bonod, E. Popov, and M. Neviere, "Fourier factorization of nonlinear Maxwell equations in periodic media: application to the optical Kerr effect," Opt. Commun. 244, 389-398 (2005).
    [CrossRef]
  29. P. Vincent, N. Paraire, M. Nevière, A. Koster, and R. Reinisch, "Gratings in nonlinear optics and optical bistability," J. Opt. Soc. Am. B 2, 1106-1116 (1985).
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  30. V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystals films," Phys. Rev. B 69, 155106-155117 (2004).
    [CrossRef]
  31. D. Felbacq, G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A 11, 2526-2534 (1994).
    [CrossRef]
  32. E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
    [CrossRef]

2005

N. Bonod, E. Popov, and M. Neviere, "Fourier factorization of nonlinear Maxwell equations in periodic media: application to the optical Kerr effect," Opt. Commun. 244, 389-398 (2005).
[CrossRef]

2004

V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystals films," Phys. Rev. B 69, 155106-155117 (2004).
[CrossRef]

A. M. Kamtchatnoc, S. A. Darmanyan, and M. Nevière, "Polariton gap solitary waves in semiconductor microcavities," J. Lumin. 110, 373-377 (2004).
[CrossRef]

2003

P. Xie, Z. Q. Zhang, and X. Zhang, "Gap solitons and soliton trains in finite-size two-dimensional periodic and quasiperiodic photonic crystals," Phys. Rev. E 67, 026607-026612 (2003).
[CrossRef]

V. Lousse and J. P. Vigneron, "Bistable behaviour of a photonic crystal nonlinear cavity," Physica B 338, 171-177 (2003).
[CrossRef]

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

H. Y. Ryu and M. Notomi, "Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab," Phys. Rev. B 68, 5209-5217 (2003).
[CrossRef]

B. Y. Soon, J. W. Haus, M. Scalora, and C. Sibilia, "One-dimensional photonic crystal limiter," Opt. Express 11, 2007-2018 (2003).
[CrossRef] [PubMed]

2002

S. Pereira, P. Chark, and J. E. Sipe, "Gap-soliton switching in short microresonator structures," J. Opt. Soc. Am. B 19, 2191-2202 (2002).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystal," Phys. Rev. E 66, 055601-055605 (2002).
[CrossRef]

2001

V. Lousse and J. P. Vigneron, "Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical material," Phys. Rev. E 63, 027602-027606 (2001).
[CrossRef]

S. F. Mingaleev and Y. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86, 5474-5477 (2001).
[CrossRef] [PubMed]

2000

P. Halevi and F. R. Mendieta, "Tunable photonic crystals with semiconducting constituents," Phys. Rev. Lett. 85, 1875-1878 (2000).
[CrossRef] [PubMed]

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
[CrossRef]

E. Popov and M. Nevière, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A 17, 1773-1784 (2000).
[CrossRef]

L. Brzozowski and E. H. Sargent, "Nonlinear distributed-feedback structures as passive optical limiters," J. Opt. Soc. Am. B 17, 1360-1365 (2000).
[CrossRef]

1999

K. Bush and S. John, "Liquid crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

1998

N. Akozbek and S. John, "Optical solitary waves in two and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57, 2287-2319 (1998).
[CrossRef]

1997

R. Wang, J. Dong, and D. Y. Xing, "Dispersive optical bistability in one-dimensional doped photonic band gap structure," Phys. Rev. E 55, 6301-6304 (1997).
[CrossRef]

P. Tran, "Optical limiting and switching of short pulses by use of a nonlinear photonic bandgap structure with a defect," J. Opt. Soc. Am. B 14, 2589-2595 (1997).
[CrossRef]

1996

L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
[CrossRef]

E. Lidorikis, Q. Li, and C. M. Soukoulis, "Wave propagation in nonlinear multilayer structures," Phys. Rev. B 54, 10249-10252 (1996).
[CrossRef]

1994

M. Scarola, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashortpulses in nonlinear photonic bandgap material," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef]

D. Felbacq, G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A 11, 2526-2534 (1994).
[CrossRef]

1993

S. John and N. Akozbek, "Nonlinear optical solitary waves in a photonic band gap," Phys. Rev. Lett. 71, 1168-1171 (1993).
[CrossRef] [PubMed]

1987

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

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
[CrossRef] [PubMed]

1985

Akozbek, N.

N. Akozbek and S. John, "Optical solitary waves in two and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57, 2287-2319 (1998).
[CrossRef]

S. John and N. Akozbek, "Nonlinear optical solitary waves in a photonic band gap," Phys. Rev. Lett. 71, 1168-1171 (1993).
[CrossRef] [PubMed]

Bloemer, M. J.

M. Scarola, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashortpulses in nonlinear photonic bandgap material," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef]

Bonod, N.

N. Bonod, E. Popov, and M. Neviere, "Fourier factorization of nonlinear Maxwell equations in periodic media: application to the optical Kerr effect," Opt. Commun. 244, 389-398 (2005).
[CrossRef]

Bowden, C. M.

M. Scarola, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashortpulses in nonlinear photonic bandgap material," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef]

Brzozowski, L.

Bush, K.

K. Bush and S. John, "Liquid crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

Centeno, E.

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
[CrossRef]

Chark, P.

Chen, W.

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
[CrossRef] [PubMed]

Darmanyan, S. A.

A. M. Kamtchatnoc, S. A. Darmanyan, and M. Nevière, "Polariton gap solitary waves in semiconductor microcavities," J. Lumin. 110, 373-377 (2004).
[CrossRef]

Dong, J.

R. Wang, J. Dong, and D. Y. Xing, "Dispersive optical bistability in one-dimensional doped photonic band gap structure," Phys. Rev. E 55, 6301-6304 (1997).
[CrossRef]

Dowling, J. P.

M. Scarola, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashortpulses in nonlinear photonic bandgap material," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef]

Felbacq, D.

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
[CrossRef]

D. Felbacq, G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A 11, 2526-2534 (1994).
[CrossRef]

Fink, Y.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystal," Phys. Rev. E 66, 055601-055605 (2002).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

Gopalan, V.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Halevi, P.

P. Halevi and F. R. Mendieta, "Tunable photonic crystals with semiconducting constituents," Phys. Rev. Lett. 85, 1875-1878 (2000).
[CrossRef] [PubMed]

Haus, J. W.

Ibanescu, M.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystal," Phys. Rev. E 66, 055601-055605 (2002).
[CrossRef]

Itoh, T.

A. Priou and T. Itoh, eds., Progress in Electromagnetic Research (Universita di Pisa, 2004), Vol. 43.

Joannopoulos, J.

J. Joannopoulos, Photonic Crystals, Molding the Flow of Light (Princeton U. Press, 1995).

Joannopoulos, J. D.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystal," Phys. Rev. E 66, 055601-055605 (2002).
[CrossRef]

John, S.

K. Bush and S. John, "Liquid crystal photonic-band-gap materials: the tunable electromagnetic vacuum," Phys. Rev. Lett. 83, 967-970 (1999).
[CrossRef]

N. Akozbek and S. John, "Optical solitary waves in two and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57, 2287-2319 (1998).
[CrossRef]

S. John and N. Akozbek, "Nonlinear optical solitary waves in a photonic band gap," Phys. Rev. Lett. 71, 1168-1171 (1993).
[CrossRef] [PubMed]

Johnson, S. G.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystal," Phys. Rev. E 66, 055601-055605 (2002).
[CrossRef]

Kamtchatnoc, A. M.

A. M. Kamtchatnoc, S. A. Darmanyan, and M. Nevière, "Polariton gap solitary waves in semiconductor microcavities," J. Lumin. 110, 373-377 (2004).
[CrossRef]

Kim, S.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Kivshar, Y. S.

S. F. Mingaleev and Y. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86, 5474-5477 (2001).
[CrossRef] [PubMed]

Koster, A.

Li, L.

Li, Q.

E. Lidorikis, Q. Li, and C. M. Soukoulis, "Wave propagation in nonlinear multilayer structures," Phys. Rev. B 54, 10249-10252 (1996).
[CrossRef]

Lidorikis, E.

E. Lidorikis, Q. Li, and C. M. Soukoulis, "Wave propagation in nonlinear multilayer structures," Phys. Rev. B 54, 10249-10252 (1996).
[CrossRef]

Lousse, V.

V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystals films," Phys. Rev. B 69, 155106-155117 (2004).
[CrossRef]

V. Lousse and J. P. Vigneron, "Bistable behaviour of a photonic crystal nonlinear cavity," Physica B 338, 171-177 (2003).
[CrossRef]

V. Lousse and J. P. Vigneron, "Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical material," Phys. Rev. E 63, 027602-027606 (2001).
[CrossRef]

Malkova, N.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Maystre, D.

Mendieta, F. R.

P. Halevi and F. R. Mendieta, "Tunable photonic crystals with semiconducting constituents," Phys. Rev. Lett. 85, 1875-1878 (2000).
[CrossRef] [PubMed]

Mills, D. L.

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
[CrossRef] [PubMed]

Mingaleev, S. F.

S. F. Mingaleev and Y. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86, 5474-5477 (2001).
[CrossRef] [PubMed]

Neviere, M.

N. Bonod, E. Popov, and M. Neviere, "Fourier factorization of nonlinear Maxwell equations in periodic media: application to the optical Kerr effect," Opt. Commun. 244, 389-398 (2005).
[CrossRef]

Nevière, M.

Notomi, M.

H. Y. Ryu and M. Notomi, "Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab," Phys. Rev. B 68, 5209-5217 (2003).
[CrossRef]

Paraire, N.

Pereira, S.

Popov, E.

N. Bonod, E. Popov, and M. Neviere, "Fourier factorization of nonlinear Maxwell equations in periodic media: application to the optical Kerr effect," Opt. Commun. 244, 389-398 (2005).
[CrossRef]

E. Popov and M. Nevière, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A 17, 1773-1784 (2000).
[CrossRef]

E. Popov and M. Nevière, Light Propagation in Periodic Media (Marcel Dekker, 2003).

Priou, A.

A. Priou and T. Itoh, eds., Progress in Electromagnetic Research (Universita di Pisa, 2004), Vol. 43.

Reinisch, R.

Ryu, H. Y.

H. Y. Ryu and M. Notomi, "Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab," Phys. Rev. B 68, 5209-5217 (2003).
[CrossRef]

Sargent, E. H.

Scalora, M.

Scarola, M.

M. Scarola, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, "Optical limiting and switching of ultrashortpulses in nonlinear photonic bandgap material," Phys. Rev. Lett. 73, 1368-1371 (1994).
[CrossRef]

Scrymgeour, D.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

Sibilia, C.

Sipe, J. E.

Soljacic, M.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystal," Phys. Rev. E 66, 055601-055605 (2002).
[CrossRef]

Soon, B. Y.

Soukoulis, C. M.

E. Lidorikis, Q. Li, and C. M. Soukoulis, "Wave propagation in nonlinear multilayer structures," Phys. Rev. B 54, 10249-10252 (1996).
[CrossRef]

Tayeb, G.

Tran, P.

Vigneron, J. P.

V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystals films," Phys. Rev. B 69, 155106-155117 (2004).
[CrossRef]

V. Lousse and J. P. Vigneron, "Bistable behaviour of a photonic crystal nonlinear cavity," Physica B 338, 171-177 (2003).
[CrossRef]

V. Lousse and J. P. Vigneron, "Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical material," Phys. Rev. E 63, 027602-027606 (2001).
[CrossRef]

Vincent, P.

Wang, R.

R. Wang, J. Dong, and D. Y. Xing, "Dispersive optical bistability in one-dimensional doped photonic band gap structure," Phys. Rev. E 55, 6301-6304 (1997).
[CrossRef]

Xie, P.

P. Xie, Z. Q. Zhang, and X. Zhang, "Gap solitons and soliton trains in finite-size two-dimensional periodic and quasiperiodic photonic crystals," Phys. Rev. E 67, 026607-026612 (2003).
[CrossRef]

Xing, D. Y.

R. Wang, J. Dong, and D. Y. Xing, "Dispersive optical bistability in one-dimensional doped photonic band gap structure," Phys. Rev. E 55, 6301-6304 (1997).
[CrossRef]

Yablonovitch, E.

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

Zhang, X.

P. Xie, Z. Q. Zhang, and X. Zhang, "Gap solitons and soliton trains in finite-size two-dimensional periodic and quasiperiodic photonic crystals," Phys. Rev. E 67, 026607-026612 (2003).
[CrossRef]

Zhang, Z. Q.

P. Xie, Z. Q. Zhang, and X. Zhang, "Gap solitons and soliton trains in finite-size two-dimensional periodic and quasiperiodic photonic crystals," Phys. Rev. E 67, 026607-026612 (2003).
[CrossRef]

Appl. Phys. Lett.

D. Scrymgeour, N. Malkova, S. Kim, and V. Gopalan, "Electro-optic control of the superprism effect in photonic crystals," Appl. Phys. Lett. 82, 3176-3178 (2003).
[CrossRef]

J. Lumin.

A. M. Kamtchatnoc, S. A. Darmanyan, and M. Nevière, "Polariton gap solitary waves in semiconductor microcavities," J. Lumin. 110, 373-377 (2004).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

N. Bonod, E. Popov, and M. Neviere, "Fourier factorization of nonlinear Maxwell equations in periodic media: application to the optical Kerr effect," Opt. Commun. 244, 389-398 (2005).
[CrossRef]

Opt. Express

Phys. Rev. B

V. Lousse and J. P. Vigneron, "Use of Fano resonances for bistable optical transfer through photonic crystals films," Phys. Rev. B 69, 155106-155117 (2004).
[CrossRef]

E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, 7683-7686 (2000).
[CrossRef]

E. Lidorikis, Q. Li, and C. M. Soukoulis, "Wave propagation in nonlinear multilayer structures," Phys. Rev. B 54, 10249-10252 (1996).
[CrossRef]

H. Y. Ryu and M. Notomi, "Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab," Phys. Rev. B 68, 5209-5217 (2003).
[CrossRef]

Phys. Rev. E

R. Wang, J. Dong, and D. Y. Xing, "Dispersive optical bistability in one-dimensional doped photonic band gap structure," Phys. Rev. E 55, 6301-6304 (1997).
[CrossRef]

V. Lousse and J. P. Vigneron, "Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical material," Phys. Rev. E 63, 027602-027606 (2001).
[CrossRef]

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystal," Phys. Rev. E 66, 055601-055605 (2002).
[CrossRef]

N. Akozbek and S. John, "Optical solitary waves in two and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57, 2287-2319 (1998).
[CrossRef]

P. Xie, Z. Q. Zhang, and X. Zhang, "Gap solitons and soliton trains in finite-size two-dimensional periodic and quasiperiodic photonic crystals," Phys. Rev. E 67, 026607-026612 (2003).
[CrossRef]

Phys. Rev. Lett.

S. F. Mingaleev and Y. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86, 5474-5477 (2001).
[CrossRef] [PubMed]

P. Halevi and F. R. Mendieta, "Tunable photonic crystals with semiconducting constituents," Phys. Rev. Lett. 85, 1875-1878 (2000).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Structure of the PC and mesh used for its simulation.

Fig. 2
Fig. 2

Field map at a 968 nm wavelength of our structure illuminated with intensity (a) 0.5320 and (b) 0.5321 (arbitrary units). The inhomogeneities in the rods are obvious.

Fig. 3
Fig. 3

Transmission versus λ for different values of the intensity I (arbitrary units) of the incident field.

Fig. 4
Fig. 4

Evolution of the transmission map for an increasing value of the magnitude of the incident field.

Fig. 5
Fig. 5

(a) and (b) Hysteresis phenomenon obtained at λ = 968 nm .

Equations (1)

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d d y ( [ E x ] [ E z ] [ H x ] [ H z ] ) = M ( y ) ( [ E x ] [ E z ] [ H x ] [ H z ] ) .

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