Abstract

We consider the optical response of a one-dimensional photonic crystal with a dense resonant medium as a defect. Using the iteration matrix approach, we calculate the intensity distribution in this structure and the reflection and transmission properties of it. We discuss the influence of photonic crystal on the bistable behavior of a dense resonant medium both within and outside the region of intrinsic optical bistability. Finally we compare our results with the case without taking into account near dipole–dipole interaction.

© 2008 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
    [Crossref] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987).
    [Crossref] [PubMed]
  3. E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173-194 (1994).
    [Crossref]
  4. T. F. Krauss and R. M. De La Rue, “Photonic crystals in the optical regime--past, present and future,” Prog. Quantum Electron. 23, 51-96 (1999).
    [Crossref]
  5. M. Bertolotti, “Wave interactions in photonic band structures: an overview,” J. Opt. A, Pure Appl. Opt. 8, S9-S32 (2006).
    [Crossref]
  6. Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B 53, 15577-15585 (1996).
    [Crossref]
  7. E. Lidorikis, K. Busch, Q. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090-15099 (1997).
    [Crossref]
  8. S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E 62, 5777-5782 (2000).
    [Crossref]
  9. S. F. Mingaleev and Yu. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19, 2241-2249 (2002).
    [Crossref]
  10. M. F. Yanik, S. Fan, and M. Soljačić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739-2741 (2003).
    [Crossref]
  11. S. F. Mingaleev, A. E. Miroshnichenko, Yu. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E 74, 046603 (2006).
    [Crossref]
  12. M. Soljačić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637-639 (2003).
    [Crossref] [PubMed]
  13. M. F. Yanik, S. Fan, M. Soljačić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28, 2506-2508 (2003).
    [Crossref] [PubMed]
  14. M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
    [Crossref]
  15. P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801-820 (2005).
    [Crossref] [PubMed]
  16. S. Hansmann, “Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures,” IEEE J. Quantum Electron. 28, 2589-2595 (1992).
    [Crossref]
  17. S. Luo, K. L. Yao, J. V. Xu, Z. L. Liu, F. Li, and L. Zhao, “Effect of absorption on photonic band gap,” Proc. SPIE 4595, 174-182 (2001).
    [Crossref]
  18. L. Diao and S. Blair, “Optical bistability and multistability in one-dimensional photonic band gap structures,” J. Opt. A, Pure Appl. Opt. 9, 972-981 (2007).
    [Crossref]
  19. C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
    [Crossref] [PubMed]
  20. A. A. Afanas'ev, A. G. Cherstvy, and R. A. Vlasov, “Hysteresis phenomena in the light self-diffraction in a dense resonant medium,” Opt. Quantum Electron. 31, 605-614 (1999).
    [Crossref]
  21. V. Malyshev and E. C. Jarque, “Optical hysteresis and instabilities inside the polariton band gap,” J. Opt. Soc. Am. B 12, 1868-1877 (1995).
    [Crossref]
  22. A. I. Frank, “Optics of ultracold neutrons and the neutron-microscope problem,” Sov. Phys. Usp. 30, 110-133 (1987).
    [Crossref]
  23. F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
    [Crossref]
  24. Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917-3926 (1986).
    [Crossref] [PubMed]
  25. V. Malyshev and E. C. Jarque, “Spatial effects in nonlinear resonant reflection from the boundary of a dense semi-infinite two-level medium: normal incidence,” J. Opt. Soc. Am. B 14, 1167-1178 (1997).
    [Crossref]
  26. A. A. Afanas'ev, R. A. Vlasov, N. B. Gubar, and V. M. Volkov, “Hysteresis behavior in light reflection from a dense resonant medium with intrinsic optical bistability,” J. Opt. Soc. Am. B 15, 1160-1167 (1998).
    [Crossref]
  27. E. Lidorikis and C. M. Soukoulis, “Pulse-driven switching in one-dimensional nonlinear photonic band gap materials: a numerical study,” Phys. Rev. E 61, 5825-5829 (2000).
    [Crossref]

2007 (1)

L. Diao and S. Blair, “Optical bistability and multistability in one-dimensional photonic band gap structures,” J. Opt. A, Pure Appl. Opt. 9, 972-981 (2007).
[Crossref]

2006 (2)

M. Bertolotti, “Wave interactions in photonic band structures: an overview,” J. Opt. A, Pure Appl. Opt. 8, S9-S32 (2006).
[Crossref]

S. F. Mingaleev, A. E. Miroshnichenko, Yu. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E 74, 046603 (2006).
[Crossref]

2005 (1)

2003 (3)

2002 (2)

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

S. F. Mingaleev and Yu. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19, 2241-2249 (2002).
[Crossref]

2001 (1)

S. Luo, K. L. Yao, J. V. Xu, Z. L. Liu, F. Li, and L. Zhao, “Effect of absorption on photonic band gap,” Proc. SPIE 4595, 174-182 (2001).
[Crossref]

2000 (2)

E. Lidorikis and C. M. Soukoulis, “Pulse-driven switching in one-dimensional nonlinear photonic band gap materials: a numerical study,” Phys. Rev. E 61, 5825-5829 (2000).
[Crossref]

S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E 62, 5777-5782 (2000).
[Crossref]

1999 (2)

T. F. Krauss and R. M. De La Rue, “Photonic crystals in the optical regime--past, present and future,” Prog. Quantum Electron. 23, 51-96 (1999).
[Crossref]

A. A. Afanas'ev, A. G. Cherstvy, and R. A. Vlasov, “Hysteresis phenomena in the light self-diffraction in a dense resonant medium,” Opt. Quantum Electron. 31, 605-614 (1999).
[Crossref]

1998 (1)

1997 (2)

V. Malyshev and E. C. Jarque, “Spatial effects in nonlinear resonant reflection from the boundary of a dense semi-infinite two-level medium: normal incidence,” J. Opt. Soc. Am. B 14, 1167-1178 (1997).
[Crossref]

E. Lidorikis, K. Busch, Q. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090-15099 (1997).
[Crossref]

1996 (1)

Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B 53, 15577-15585 (1996).
[Crossref]

1995 (1)

1994 (1)

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173-194 (1994).
[Crossref]

1993 (1)

C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
[Crossref] [PubMed]

1992 (1)

S. Hansmann, “Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures,” IEEE J. Quantum Electron. 28, 2589-2595 (1992).
[Crossref]

1987 (3)

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]

A. I. Frank, “Optics of ultracold neutrons and the neutron-microscope problem,” Sov. Phys. Usp. 30, 110-133 (1987).
[Crossref]

1986 (1)

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917-3926 (1986).
[Crossref] [PubMed]

1984 (1)

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[Crossref]

Afanas'ev, A. A.

A. A. Afanas'ev, A. G. Cherstvy, and R. A. Vlasov, “Hysteresis phenomena in the light self-diffraction in a dense resonant medium,” Opt. Quantum Electron. 31, 605-614 (1999).
[Crossref]

A. A. Afanas'ev, R. A. Vlasov, N. B. Gubar, and V. M. Volkov, “Hysteresis behavior in light reflection from a dense resonant medium with intrinsic optical bistability,” J. Opt. Soc. Am. B 15, 1160-1167 (1998).
[Crossref]

Barclay, P. E.

Ben-Aryeh, Y.

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917-3926 (1986).
[Crossref] [PubMed]

Bertolotti, M.

M. Bertolotti, “Wave interactions in photonic band structures: an overview,” J. Opt. A, Pure Appl. Opt. 8, S9-S32 (2006).
[Crossref]

Blair, S.

L. Diao and S. Blair, “Optical bistability and multistability in one-dimensional photonic band gap structures,” J. Opt. A, Pure Appl. Opt. 9, 972-981 (2007).
[Crossref]

Bowden, C.

C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
[Crossref] [PubMed]

Bowden, C. M.

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917-3926 (1986).
[Crossref] [PubMed]

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[Crossref]

Busch, K.

S. F. Mingaleev, A. E. Miroshnichenko, Yu. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E 74, 046603 (2006).
[Crossref]

E. Lidorikis, K. Busch, Q. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090-15099 (1997).
[Crossref]

Chan, C. T.

E. Lidorikis, K. Busch, Q. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090-15099 (1997).
[Crossref]

Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B 53, 15577-15585 (1996).
[Crossref]

Cherstvy, A. G.

A. A. Afanas'ev, A. G. Cherstvy, and R. A. Vlasov, “Hysteresis phenomena in the light self-diffraction in a dense resonant medium,” Opt. Quantum Electron. 31, 605-614 (1999).
[Crossref]

De La Rue, R. M.

T. F. Krauss and R. M. De La Rue, “Photonic crystals in the optical regime--past, present and future,” Prog. Quantum Electron. 23, 51-96 (1999).
[Crossref]

Diao, L.

L. Diao and S. Blair, “Optical bistability and multistability in one-dimensional photonic band gap structures,” J. Opt. A, Pure Appl. Opt. 9, 972-981 (2007).
[Crossref]

Dowling, J. P.

C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
[Crossref] [PubMed]

Englund, J. C.

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917-3926 (1986).
[Crossref] [PubMed]

Fan, S.

Fink, Y.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

Frank, A. I.

A. I. Frank, “Optics of ultracold neutrons and the neutron-microscope problem,” Sov. Phys. Usp. 30, 110-133 (1987).
[Crossref]

Gubar, N. B.

Hansmann, S.

S. Hansmann, “Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures,” IEEE J. Quantum Electron. 28, 2589-2595 (1992).
[Crossref]

Ho, K. M.

Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B 53, 15577-15585 (1996).
[Crossref]

Hopf, F. A.

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[Crossref]

Ibanescu, M.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

Jarque, E. C.

Joannopoulos, J. D.

John, S.

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

Johnson, S. G.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

Kivshar, Yu. S.

S. F. Mingaleev, A. E. Miroshnichenko, Yu. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E 74, 046603 (2006).
[Crossref]

S. F. Mingaleev and Yu. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19, 2241-2249 (2002).
[Crossref]

S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E 62, 5777-5782 (2000).
[Crossref]

Krauss, T. F.

T. F. Krauss and R. M. De La Rue, “Photonic crystals in the optical regime--past, present and future,” Prog. Quantum Electron. 23, 51-96 (1999).
[Crossref]

Li, F.

S. Luo, K. L. Yao, J. V. Xu, Z. L. Liu, F. Li, and L. Zhao, “Effect of absorption on photonic band gap,” Proc. SPIE 4595, 174-182 (2001).
[Crossref]

Li, Q.

E. Lidorikis, K. Busch, Q. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090-15099 (1997).
[Crossref]

Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B 53, 15577-15585 (1996).
[Crossref]

Lidorikis, E.

E. Lidorikis and C. M. Soukoulis, “Pulse-driven switching in one-dimensional nonlinear photonic band gap materials: a numerical study,” Phys. Rev. E 61, 5825-5829 (2000).
[Crossref]

E. Lidorikis, K. Busch, Q. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090-15099 (1997).
[Crossref]

Liu, Z. L.

S. Luo, K. L. Yao, J. V. Xu, Z. L. Liu, F. Li, and L. Zhao, “Effect of absorption on photonic band gap,” Proc. SPIE 4595, 174-182 (2001).
[Crossref]

Louisell, W. H.

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[Crossref]

Luo, C.

Luo, S.

S. Luo, K. L. Yao, J. V. Xu, Z. L. Liu, F. Li, and L. Zhao, “Effect of absorption on photonic band gap,” Proc. SPIE 4595, 174-182 (2001).
[Crossref]

Malyshev, V.

Mingaleev, S. F.

S. F. Mingaleev, A. E. Miroshnichenko, Yu. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E 74, 046603 (2006).
[Crossref]

S. F. Mingaleev and Yu. S. Kivshar, “Nonlinear transmission and light localization in photonic-crystal waveguides,” J. Opt. Soc. Am. B 19, 2241-2249 (2002).
[Crossref]

S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E 62, 5777-5782 (2000).
[Crossref]

Miroshnichenko, A. E.

S. F. Mingaleev, A. E. Miroshnichenko, Yu. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E 74, 046603 (2006).
[Crossref]

Painter, O.

Sammut, R. A.

S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E 62, 5777-5782 (2000).
[Crossref]

Soljacic, M.

M. F. Yanik, S. Fan, and M. Soljačić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739-2741 (2003).
[Crossref]

M. Soljačić, C. Luo, J. D. Joannopoulos, and S. Fan, “Nonlinear photonic crystal microdevices for optical integration,” Opt. Lett. 28, 637-639 (2003).
[Crossref] [PubMed]

M. F. Yanik, S. Fan, M. Soljačić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28, 2506-2508 (2003).
[Crossref] [PubMed]

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[Crossref]

Soukoulis, C. M.

E. Lidorikis and C. M. Soukoulis, “Pulse-driven switching in one-dimensional nonlinear photonic band gap materials: a numerical study,” Phys. Rev. E 61, 5825-5829 (2000).
[Crossref]

E. Lidorikis, K. Busch, Q. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090-15099 (1997).
[Crossref]

Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B 53, 15577-15585 (1996).
[Crossref]

Srinivasan, K.

Vlasov, R. A.

A. A. Afanas'ev, A. G. Cherstvy, and R. A. Vlasov, “Hysteresis phenomena in the light self-diffraction in a dense resonant medium,” Opt. Quantum Electron. 31, 605-614 (1999).
[Crossref]

A. A. Afanas'ev, R. A. Vlasov, N. B. Gubar, and V. M. Volkov, “Hysteresis behavior in light reflection from a dense resonant medium with intrinsic optical bistability,” J. Opt. Soc. Am. B 15, 1160-1167 (1998).
[Crossref]

Volkov, V. M.

Xu, J. V.

S. Luo, K. L. Yao, J. V. Xu, Z. L. Liu, F. Li, and L. Zhao, “Effect of absorption on photonic band gap,” Proc. SPIE 4595, 174-182 (2001).
[Crossref]

Yablonovitch, E.

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173-194 (1994).
[Crossref]

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

Yanik, M. F.

M. F. Yanik, S. Fan, and M. Soljačić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739-2741 (2003).
[Crossref]

M. F. Yanik, S. Fan, M. Soljačić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28, 2506-2508 (2003).
[Crossref] [PubMed]

Yao, K. L.

S. Luo, K. L. Yao, J. V. Xu, Z. L. Liu, F. Li, and L. Zhao, “Effect of absorption on photonic band gap,” Proc. SPIE 4595, 174-182 (2001).
[Crossref]

Zhao, L.

S. Luo, K. L. Yao, J. V. Xu, Z. L. Liu, F. Li, and L. Zhao, “Effect of absorption on photonic band gap,” Proc. SPIE 4595, 174-182 (2001).
[Crossref]

Appl. Phys. Lett. (1)

M. F. Yanik, S. Fan, and M. Soljačić, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739-2741 (2003).
[Crossref]

IEEE J. Quantum Electron. (1)

S. Hansmann, “Transfer matrix analysis of the spectral properties of complex distributed feedback laser structures,” IEEE J. Quantum Electron. 28, 2589-2595 (1992).
[Crossref]

J. Mod. Opt. (1)

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173-194 (1994).
[Crossref]

J. Opt. A, Pure Appl. Opt. (2)

M. Bertolotti, “Wave interactions in photonic band structures: an overview,” J. Opt. A, Pure Appl. Opt. 8, S9-S32 (2006).
[Crossref]

L. Diao and S. Blair, “Optical bistability and multistability in one-dimensional photonic band gap structures,” J. Opt. A, Pure Appl. Opt. 9, 972-981 (2007).
[Crossref]

J. Opt. Soc. Am. B (4)

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. A. Afanas'ev, A. G. Cherstvy, and R. A. Vlasov, “Hysteresis phenomena in the light self-diffraction in a dense resonant medium,” Opt. Quantum Electron. 31, 605-614 (1999).
[Crossref]

Phys. Rev. A (3)

F. A. Hopf, C. M. Bowden, and W. H. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591-2596 (1984).
[Crossref]

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917-3926 (1986).
[Crossref] [PubMed]

C. Bowden and J. P. Dowling, “Near dipole-dipole effects in dense media: Generalized Maxwell-Bloch equations,” Phys. Rev. A 47, 1247-1251 (1993).
[Crossref] [PubMed]

Phys. Rev. B (2)

Q. Li, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Wave propagation in nonlinear photonic band-gap materials,” Phys. Rev. B 53, 15577-15585 (1996).
[Crossref]

E. Lidorikis, K. Busch, Q. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090-15099 (1997).
[Crossref]

Phys. Rev. E (4)

S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, “Long-range interaction and nonlinear localized modes in photonic crystal waveguides,” Phys. Rev. E 62, 5777-5782 (2000).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1

Distribution of normalized radiation intensity Ω 2 Ω 0 2 in a photonic structure with a defect described by Eqs. (10, 12) at input intensity (a) Ω 0 2 = 0.3 , (b) Ω 0 2 = 0.6 . Parameters: n 1 = 1 , a 1 = 0.4 μ m , n 2 = 3.5 , a 2 = 0.137 μ m , a 3 = 0.5 μ m ; number of linear periods k = 4 , l = 4 ; δ = 4 , b = 8 , ε 0 = 4.5 , γ 2 γ 1 = 100 ; wavelength λ = 0.5 μ m .

Fig. 2
Fig. 2

The threshold permittivity versus (a) the constant b (at N = 1 ), (b) the population difference N (at δ = 4 ).

Fig. 3
Fig. 3

The population difference [calculated by Eq. (10)] versus intensity Ω 2 at different values of near dipole–dipole constant b. Parameters: δ = 4 , γ 2 γ 1 = 100 .

Fig. 4
Fig. 4

Reflection versus input intensity for the photonic structure with the defect at different values of (a) wavelength λ and (b) linear permittivity ε 0 . Parameters: n 1 = 1 , a 1 = 0.4 μ m , n 2 = 3.5 , a 2 = 0.137 μ m , a 3 = 0.5 μ m ; number of linear periods k = 4 , l = 4 ; δ = 4 , b = 8 , γ 2 γ 1 = 100 ; (a) ε 0 = 4.5 ; (b) λ = 0.5 μ m .

Fig. 5
Fig. 5

(a) Reflection and (b) transmission versus input intensity for the photonic structure with the defect at different values of the constant of near dipole–dipole interaction b. Parameters: n 1 = 1 , a 1 = 0.4 μ m , n 2 = 3.5 , a 2 = 0.137 μ m , a 3 = 0.5 μ m ; number of linear periods k = 4 , l = 4 ; δ = 4 , ε 0 = 4.5 , γ 2 γ 1 = 100 ; wavelength λ = 0.5 μ m .

Fig. 6
Fig. 6

Curve of the IOB boundary.

Fig. 7
Fig. 7

Reflection and transmission versus input intensity for the photonic structure (a, b) with the defect and (c, d) for the defect itself at different values of the constant of near dipole–dipole interaction b. Parameters: n 1 = 1 , a 1 = 0.4 μ m , n 2 = 3.5 , a 2 = 0.137 μ m , a 3 = 0.5 μ m ; number of linear periods k = 4 , l = 4 ; δ = 1 , ε 0 = 4.5 , γ 2 γ 1 = 100 ; wavelength λ = 0.5 μ m .

Fig. 8
Fig. 8

(a) Reflection and (b) transmission versus input intensity for the photonic structure with the defect at different values of the defect thickness. Parameters: n 1 = 1 , a 1 = 0.4 μ m , n 2 = 3.5 , a 2 = 0.137 μ m ; number of linear periods k = 4 , l = 4 ; δ = 4 , b = 8 , ε 0 = 4.5 , γ 2 γ 1 = 100 ; wavelength λ = 0.5 μ m .

Fig. 9
Fig. 9

(a) Reflection and (b) transmission versus input intensity for the layer of dense resonant medium at different values of its thickness. Parameters: δ = 4 , b = 8 , ε 0 = 4.5 , γ 2 γ 1 = 100 ; wavelength λ = 0.5 μ m .

Fig. 10
Fig. 10

Reflection and transmission versus input intensity (a) for the layer described by Eq. (17), (b) for the photonic structure with the defect. Parameters: n 1 = 1 , a 1 = 0.4 μ m , n 2 = 3.5 , a 2 = 0.137 μ m , a 3 = 0.5 μ m ; number of linear periods k = 4 , l = 4 ; b = 8 , δ = 4 , ε 0 = 4.5 , γ 2 γ 1 = 100 ; wavelength λ = 0.5 μ m .

Equations (22)

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( Ω 0 r 0 ) = M ( t 0 r 0 ) ,
t 0 = Ω 0 M 11 , r 0 = Ω 0 M 21 M 11 .
Δ i j = ( δ i j + δ i j δ i j δ i j + ) , δ i j ± = 1 2 ( 1 ± n j n i ) .
Π i = ( exp i p i 0 0 exp i p i ) , p i = n i w c a i ,
M = M 1 M nl M 2 .
M 1 = Δ 01 Π 1 S 2 ( S 1 S 2 ) k 1 ,
M 2 = Π 1 S 2 ( S 1 S 2 ) l 1 Δ 20 ,
( Ω 0 r 0 ) = Φ i ( t i r i ) ,
r i = Φ i 11 r 0 Φ i 21 Ω 0 Φ i 11 Φ i 22 Φ i 12 Φ i 21 ,
t i = Φ i 12 r 0 Φ i 22 Ω 0 Φ i 11 Φ i 22 Φ i 12 Φ i 21 .
d P d t = i γ 2 Ω N γ 2 P [ 1 i ( δ + b N ) ] ,
d N d t = 2 i γ 2 ( Ω * P P * Ω ) γ 1 ( N N eq ) ,
[ 1 + ( δ + b N ) 2 ] ( 1 N ) = 4 γ 2 γ 1 Ω 2 N .
P = i Ω N 1 i ( δ + b N ) .
ϵ = ϵ 0 + 4 π μ 2 C γ 2 i N 1 i ( δ + b N ) = ϵ 0 + 3 i b N 1 i ( δ + b N ) ,
ϵ 0 < ϵ th = 3 b N ( δ + b N ) 1 + ( δ + b N ) 2 .
2 b 2 N 3 + b ( 2 δ b ) N 2 + 1 + δ 2 = 0 .
b = 2 δ + 6 ( 1 + δ 2 ) 1 3 Re ( δ + i ) 1 3 .
N = 1 + δ 2 1 + δ 2 + 4 γ 2 γ 1 Ω 2 ,
P = i δ 1 + δ 2 + 4 γ 2 γ 1 Ω 2 Ω .
ϵ = ϵ 0 + 3 b i δ 1 + δ 2 + 4 γ 2 γ 1 Ω 2 ,
I = c 2 π E 2 = c 2 π ( γ 2 μ ) 2 Ω 2 .

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