Abstract

We numerically study the characteristics of a nonlinear pulse that propagates through a one-dimensional photonic bandgap (PBG) structure uniformly doped with two-level atoms. The numerical model adopted is the coupled system of nonlinear coupled-mode equations and atomic Bloch equations. The simulation results show that a self-induced transparency (SIT) soliton and a gap soliton can coexist in a nonlinear PBG structure uniformly doped with resonant atoms. Although this mixed state, known as a SIT-gap soliton, near the PBG edge has been theoretically predicted, we numerically show that such a solitary wave still exists even if its central frequency is located deep inside the PBG. The propagating characteristics of the SIT-gap soliton are also discussed.

© 2003 Optical Society of America

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  1. S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
    [CrossRef]
  2. J. H. Eberly, “Optical pulse and pulse-train propagation in a resonant medium,” Phys. Rev. Lett. 22, 760–762 (1969).
    [CrossRef]
  3. M. D. Crisp, “Distortionless propagation of light through an optical medium,” Phys. Rev. Lett. 22, 820–823 (1969).
    [CrossRef]
  4. L. Matulic and J. H. Eberly, “Analytic study of pulse chirping in self-induced transparency,” Phys. Rev. A 6, 822–836 (1972).
    [CrossRef]
  5. M. Nakazawa, E. Yamada, and H. Kubota, “Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton,” Phys. Rev. Lett. 66, 2625–2628 (1991).
    [CrossRef] [PubMed]
  6. T. Y. Wang and S. Chi, “Self-induced transparency in a dispersive and nonlinear Kerr host medium,” Opt. Lett. 16, 1575–1577 (1991).
    [CrossRef] [PubMed]
  7. S. Chi, T. Y. Wang, and S. Wen, “Theory of self-induced transparency in a Kerr host medium beyond the slowly-varying-envelope approximation,” Phys. Rev. A 47, 3371–3379 (1993).
    [CrossRef] [PubMed]
  8. M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
    [CrossRef] [PubMed]
  9. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  10. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef] [PubMed]
  11. B. I. Mantsyzov, “Gap 2 pi pulse with an inhomogeneously broadened line and an oscillating solitary wave,” Phys. Rev. A 51, 4939–4943 (1995).
    [CrossRef] [PubMed]
  12. B. I. Mantsyzov, “Laue soliton in a resonantly absorbing photonic crystal,” Opt. Commun. 189, 275–280 (2001).
    [CrossRef]
  13. B. I. Mantsyzov and R. A. Sil’nikov, “Oscillating gap 2 pi pulse in resonantly absorbing lattice,” JETP Lett. 74, 456–459 (2001).
    [CrossRef]
  14. A. E. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
    [CrossRef] [PubMed]
  15. A. E. Kozhekin, G. Kurizki, and B. A. Malomed, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
    [CrossRef]
  16. M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
    [CrossRef]
  17. G. Kurizki, A. E. Kozhekin, T. Opatrný, and B. A. Malomed, “Optical solitons in periodic media with resonant and off-resonant nonlinearities,” Prog. Opt. 42, 93–146 (2000).
    [CrossRef]
  18. N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
    [CrossRef]
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  21. B. J. Eggleton, R. E. Slusher, and C. M. de Sterke, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
    [CrossRef] [PubMed]
  22. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
    [CrossRef]
  23. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Bragg solitons in the nonlinear Schrödinger limit: experiment and theory,” J. Opt. Soc. Am. B 16, 587–599 (1999).
    [CrossRef]
  24. C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E 59, 1267–1269 (1999).
    [CrossRef]
  25. S. Chi, B. Luo, and H.-Y. Tseng, “Ultrashort Bragg soliton in a fiber Bragg grating,” Opt. Commun. 206, 115–121 (2002).
    [CrossRef]
  26. G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).
  27. M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
    [CrossRef]
  28. M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass-fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2333 (1993).
    [CrossRef]
  29. M. Asobe, T. Ohara, I. Yokohama, and T. Kaino, “Fabrication of Bragg grating in chalcogenide glass fiber using the transverse holographic method,” Electron. Lett. 32, 1611–1613 (1996).
    [CrossRef]
  30. P. Millar, R. M. De La Rue, T. F. Krauss, J. S. Aitchison, N. G. R. Broderick, and D. J. Richardson, “Nonlinear propagation effects in an AlGaAs Bragg grating filter,” Opt. Lett. 24, 685–687 (1999).
    [CrossRef]

2002 (1)

S. Chi, B. Luo, and H.-Y. Tseng, “Ultrashort Bragg soliton in a fiber Bragg grating,” Opt. Commun. 206, 115–121 (2002).
[CrossRef]

2001 (2)

B. I. Mantsyzov, “Laue soliton in a resonantly absorbing photonic crystal,” Opt. Commun. 189, 275–280 (2001).
[CrossRef]

B. I. Mantsyzov and R. A. Sil’nikov, “Oscillating gap 2 pi pulse in resonantly absorbing lattice,” JETP Lett. 74, 456–459 (2001).
[CrossRef]

2000 (2)

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

G. Kurizki, A. E. Kozhekin, T. Opatrný, and B. A. Malomed, “Optical solitons in periodic media with resonant and off-resonant nonlinearities,” Prog. Opt. 42, 93–146 (2000).
[CrossRef]

1999 (3)

1998 (2)

N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
[CrossRef]

A. E. Kozhekin, G. Kurizki, and B. A. Malomed, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

1997 (1)

1996 (2)

M. Asobe, T. Ohara, I. Yokohama, and T. Kaino, “Fabrication of Bragg grating in chalcogenide glass fiber using the transverse holographic method,” Electron. Lett. 32, 1611–1613 (1996).
[CrossRef]

B. J. Eggleton, R. E. Slusher, and C. M. de Sterke, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

1995 (2)

B. I. Mantsyzov, “Gap 2 pi pulse with an inhomogeneously broadened line and an oscillating solitary wave,” Phys. Rev. A 51, 4939–4943 (1995).
[CrossRef] [PubMed]

A. E. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

1994 (1)

C. M. de Sterke and J. E. Sipe, “Map solitons,” Prog. Opt. 33, 203–259 (1994).

1993 (2)

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass-fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2333 (1993).
[CrossRef]

S. Chi, T. Y. Wang, and S. Wen, “Theory of self-induced transparency in a Kerr host medium beyond the slowly-varying-envelope approximation,” Phys. Rev. A 47, 3371–3379 (1993).
[CrossRef] [PubMed]

1992 (2)

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

1991 (3)

1987 (2)

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]

1972 (1)

L. Matulic and J. H. Eberly, “Analytic study of pulse chirping in self-induced transparency,” Phys. Rev. A 6, 822–836 (1972).
[CrossRef]

1969 (2)

J. H. Eberly, “Optical pulse and pulse-train propagation in a resonant medium,” Phys. Rev. Lett. 22, 760–762 (1969).
[CrossRef]

M. D. Crisp, “Distortionless propagation of light through an optical medium,” Phys. Rev. Lett. 22, 820–823 (1969).
[CrossRef]

1967 (1)

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

Aitchison, J. S.

Aközbek, N.

N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
[CrossRef]

Asobe, M.

M. Asobe, T. Ohara, I. Yokohama, and T. Kaino, “Fabrication of Bragg grating in chalcogenide glass fiber using the transverse holographic method,” Electron. Lett. 32, 1611–1613 (1996).
[CrossRef]

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass-fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2333 (1993).
[CrossRef]

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

Blaauboer, M.

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

Broderick, N. G. R.

Chi, S.

S. Chi, B. Luo, and H.-Y. Tseng, “Ultrashort Bragg soliton in a fiber Bragg grating,” Opt. Commun. 206, 115–121 (2002).
[CrossRef]

S. Chi, T. Y. Wang, and S. Wen, “Theory of self-induced transparency in a Kerr host medium beyond the slowly-varying-envelope approximation,” Phys. Rev. A 47, 3371–3379 (1993).
[CrossRef] [PubMed]

T. Y. Wang and S. Chi, “Self-induced transparency in a dispersive and nonlinear Kerr host medium,” Opt. Lett. 16, 1575–1577 (1991).
[CrossRef] [PubMed]

Crisp, M. D.

M. D. Crisp, “Distortionless propagation of light through an optical medium,” Phys. Rev. Lett. 22, 820–823 (1969).
[CrossRef]

De La Rue, R. M.

de Sterke, C. M.

Eberly, J. H.

L. Matulic and J. H. Eberly, “Analytic study of pulse chirping in self-induced transparency,” Phys. Rev. A 6, 822–836 (1972).
[CrossRef]

J. H. Eberly, “Optical pulse and pulse-train propagation in a resonant medium,” Phys. Rev. Lett. 22, 760–762 (1969).
[CrossRef]

Eggleton, B. J.

C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E 59, 1267–1269 (1999).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Bragg solitons in the nonlinear Schrödinger limit: experiment and theory,” J. Opt. Soc. Am. B 16, 587–599 (1999).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
[CrossRef]

B. J. Eggleton, R. E. Slusher, and C. M. de Sterke, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Hahn, E. L.

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

Jackson, K. R.

John, S.

N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
[CrossRef]

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

Kaino, T.

M. Asobe, T. Ohara, I. Yokohama, and T. Kaino, “Fabrication of Bragg grating in chalcogenide glass fiber using the transverse holographic method,” Electron. Lett. 32, 1611–1613 (1996).
[CrossRef]

Kanamori, T.

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass-fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2333 (1993).
[CrossRef]

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

Kimura, Y.

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

Kozhekin, A. E.

G. Kurizki, A. E. Kozhekin, T. Opatrný, and B. A. Malomed, “Optical solitons in periodic media with resonant and off-resonant nonlinearities,” Prog. Opt. 42, 93–146 (2000).
[CrossRef]

A. E. Kozhekin, G. Kurizki, and B. A. Malomed, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

A. E. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

Krauss, T. F.

Kubodera, K.

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass-fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2333 (1993).
[CrossRef]

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

Kubota, H.

M. Nakazawa, E. Yamada, and H. Kubota, “Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton,” Phys. Rev. Lett. 66, 2625–2628 (1991).
[CrossRef] [PubMed]

Kurizki, G.

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

G. Kurizki, A. E. Kozhekin, T. Opatrný, and B. A. Malomed, “Optical solitons in periodic media with resonant and off-resonant nonlinearities,” Prog. Opt. 42, 93–146 (2000).
[CrossRef]

A. E. Kozhekin, G. Kurizki, and B. A. Malomed, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

A. E. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

Kurokawa, K.

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

Luo, B.

S. Chi, B. Luo, and H.-Y. Tseng, “Ultrashort Bragg soliton in a fiber Bragg grating,” Opt. Commun. 206, 115–121 (2002).
[CrossRef]

Malomed, B. A.

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

G. Kurizki, A. E. Kozhekin, T. Opatrný, and B. A. Malomed, “Optical solitons in periodic media with resonant and off-resonant nonlinearities,” Prog. Opt. 42, 93–146 (2000).
[CrossRef]

A. E. Kozhekin, G. Kurizki, and B. A. Malomed, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

Mantsyzov, B. I.

B. I. Mantsyzov and R. A. Sil’nikov, “Oscillating gap 2 pi pulse in resonantly absorbing lattice,” JETP Lett. 74, 456–459 (2001).
[CrossRef]

B. I. Mantsyzov, “Laue soliton in a resonantly absorbing photonic crystal,” Opt. Commun. 189, 275–280 (2001).
[CrossRef]

B. I. Mantsyzov, “Gap 2 pi pulse with an inhomogeneously broadened line and an oscillating solitary wave,” Phys. Rev. A 51, 4939–4943 (1995).
[CrossRef] [PubMed]

Matulic, L.

L. Matulic and J. H. Eberly, “Analytic study of pulse chirping in self-induced transparency,” Phys. Rev. A 6, 822–836 (1972).
[CrossRef]

McCall, S. L.

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

Millar, P.

Nakazawa, M.

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

M. Nakazawa, E. Yamada, and H. Kubota, “Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton,” Phys. Rev. Lett. 66, 2625–2628 (1991).
[CrossRef] [PubMed]

Ohara, T.

M. Asobe, T. Ohara, I. Yokohama, and T. Kaino, “Fabrication of Bragg grating in chalcogenide glass fiber using the transverse holographic method,” Electron. Lett. 32, 1611–1613 (1996).
[CrossRef]

Opatrný, T.

G. Kurizki, A. E. Kozhekin, T. Opatrný, and B. A. Malomed, “Optical solitons in periodic media with resonant and off-resonant nonlinearities,” Prog. Opt. 42, 93–146 (2000).
[CrossRef]

Richardson, D. J.

Robert, B. D.

Sil’nikov, R. A.

B. I. Mantsyzov and R. A. Sil’nikov, “Oscillating gap 2 pi pulse in resonantly absorbing lattice,” JETP Lett. 74, 456–459 (2001).
[CrossRef]

Sipe, J. E.

C. M. de Sterke and J. E. Sipe, “Map solitons,” Prog. Opt. 33, 203–259 (1994).

Slusher, R. E.

Suzuki, K.

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

Tseng, H.-Y.

S. Chi, B. Luo, and H.-Y. Tseng, “Ultrashort Bragg soliton in a fiber Bragg grating,” Opt. Commun. 206, 115–121 (2002).
[CrossRef]

Wang, T. Y.

S. Chi, T. Y. Wang, and S. Wen, “Theory of self-induced transparency in a Kerr host medium beyond the slowly-varying-envelope approximation,” Phys. Rev. A 47, 3371–3379 (1993).
[CrossRef] [PubMed]

T. Y. Wang and S. Chi, “Self-induced transparency in a dispersive and nonlinear Kerr host medium,” Opt. Lett. 16, 1575–1577 (1991).
[CrossRef] [PubMed]

Wen, S.

S. Chi, T. Y. Wang, and S. Wen, “Theory of self-induced transparency in a Kerr host medium beyond the slowly-varying-envelope approximation,” Phys. Rev. A 47, 3371–3379 (1993).
[CrossRef] [PubMed]

Yablonovitch, E.

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

Yamada, E.

M. Nakazawa, E. Yamada, and H. Kubota, “Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton,” Phys. Rev. Lett. 66, 2625–2628 (1991).
[CrossRef] [PubMed]

Yokohama, I.

M. Asobe, T. Ohara, I. Yokohama, and T. Kaino, “Fabrication of Bragg grating in chalcogenide glass fiber using the transverse holographic method,” Electron. Lett. 32, 1611–1613 (1996).
[CrossRef]

Electron. Lett. (1)

M. Asobe, T. Ohara, I. Yokohama, and T. Kaino, “Fabrication of Bragg grating in chalcogenide glass fiber using the transverse holographic method,” Electron. Lett. 32, 1611–1613 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Asobe, T. Kanamori, and K. Kubodera, “Applications of highly nonlinear chalcogenide glass-fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29, 2325–2333 (1993).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4, 362–365 (1992).
[CrossRef]

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

JETP Lett. (1)

B. I. Mantsyzov and R. A. Sil’nikov, “Oscillating gap 2 pi pulse in resonantly absorbing lattice,” JETP Lett. 74, 456–459 (2001).
[CrossRef]

Opt. Commun. (2)

B. I. Mantsyzov, “Laue soliton in a resonantly absorbing photonic crystal,” Opt. Commun. 189, 275–280 (2001).
[CrossRef]

S. Chi, B. Luo, and H.-Y. Tseng, “Ultrashort Bragg soliton in a fiber Bragg grating,” Opt. Commun. 206, 115–121 (2002).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (4)

B. I. Mantsyzov, “Gap 2 pi pulse with an inhomogeneously broadened line and an oscillating solitary wave,” Phys. Rev. A 51, 4939–4943 (1995).
[CrossRef] [PubMed]

S. Chi, T. Y. Wang, and S. Wen, “Theory of self-induced transparency in a Kerr host medium beyond the slowly-varying-envelope approximation,” Phys. Rev. A 47, 3371–3379 (1993).
[CrossRef] [PubMed]

M. Nakazawa, Y. Kimura, K. Kurokawa, and K. Suzuki, “Self-induced-transparency solitons in an erbium-doped fiber waveguide,” Phys. Rev. A 45, R23–R26 (1992).
[CrossRef] [PubMed]

L. Matulic and J. H. Eberly, “Analytic study of pulse chirping in self-induced transparency,” Phys. Rev. A 6, 822–836 (1972).
[CrossRef]

Phys. Rev. E (3)

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
[CrossRef]

C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E 59, 1267–1269 (1999).
[CrossRef]

Phys. Rev. Lett. (9)

B. J. Eggleton, R. E. Slusher, and C. M. de Sterke, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

J. H. Eberly, “Optical pulse and pulse-train propagation in a resonant medium,” Phys. Rev. Lett. 22, 760–762 (1969).
[CrossRef]

M. D. Crisp, “Distortionless propagation of light through an optical medium,” Phys. Rev. Lett. 22, 820–823 (1969).
[CrossRef]

M. Nakazawa, E. Yamada, and H. Kubota, “Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton,” Phys. Rev. Lett. 66, 2625–2628 (1991).
[CrossRef] [PubMed]

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. E. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

A. E. Kozhekin, G. Kurizki, and B. A. Malomed, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

Prog. Opt. (2)

C. M. de Sterke and J. E. Sipe, “Map solitons,” Prog. Opt. 33, 203–259 (1994).

G. Kurizki, A. E. Kozhekin, T. Opatrný, and B. A. Malomed, “Optical solitons in periodic media with resonant and off-resonant nonlinearities,” Prog. Opt. 42, 93–146 (2000).
[CrossRef]

Other (1)

G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).

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Figures (7)

Fig. 1
Fig. 1

Incident power is 0.8, which was normalized by the incident power for a SIT 2π pulse in the PBG. (a) Pulse evolution of a pulse that propagates through a resonant nonlinear PBG structure. (b) Contour plot of the pulse power. (c) Atomic population difference (W0) during pulse propagation. (d) Contour plot of the atomic population difference (W0).

Fig. 2
Fig. 2

Incident power is 0.9, which was normalized by the incident power for a SIT 2π pulse in the PBG. (a) Pulse evolution of a pulse that propagates through a resonant nonlinear PBG structure. (b) Contour plot of the pulse power. (c) Atomic population difference (W0) during pulse propagation. (d) Contour plot of the atomic population difference (W0).

Fig. 3
Fig. 3

Incident power is 1, which was normalized by the incident power for a SIT 2π pulse in the PBG. (a) Pulse evolution of a 2π pulse that propagates through a resonant nonlinear PBG structure. (b) Contour plot of the 2π pulse power. (c) Atomic population difference (W0) during 2π pulse propagation. (d) Contour plot of the atomic population difference (W0). (e) Atomic population difference (W2) during 2π pulse propagation. (f ) Contour plot of the atomic population difference (W2).

Fig. 4
Fig. 4

Incident power is 1, which was normalized by the incident power for a SIT 2π pulse in the PBG. (a) Pulse evolution of a 2π pulse that propagates through a resonant nonlinear PBG structure. (b) Contour plot of the 2π pulse power. (c) Atomic population difference (W0) during 2π pulse propagation. (d) Contour plot of the atomic population difference (W0). (e) Atomic population difference (W2) during 2π pulse propagation. (f) Contour plot of the atomic population difference (W2). (g) Atomic population difference (W4) during 2π pulse propagation. (h) Contour plot of the atomic population difference (W4). Characteristics of SIT-gap soliton simulated by Bloch NLCMEs with a third-order electric field and polarization and a fourth-order population difference.

Fig. 5
Fig. 5

(a) Pulse width and (b) corresponding peak intensity required for the SIT-gap solitons as a function of carrier detuning δβ0 on exact atomic resonance. Tolerance of the coexistence state is represented by error bars.

Fig. 6
Fig. 6

Group velocity of the SIT-gap soliton as a function of carrier detuning δβ0.

Fig. 7
Fig. 7

Pulse width of a SIT-gap soliton as a function of the doping concentration of erbium atoms at δβ0=500 m-1.

Equations (23)

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2E(z, t)x2-n(z)2c2 2E(z, t)t2
-4πc2 2PNLt2-4πc2 2PRt2=0,
PNL(z, t)=χ(3)|E(z, t)|2E(z, t),
PR(z, t)t=-iΔωPR(z, t)+i μ W(z, t)E(z, t),
W(z, t)t=-i μ2 [E(z, t)PR*(z, t)-E*(z, t)PR(z, t)],
E(z, t)=12 {[E+(1)(z, t)exp(iβgz)+E+(3)×(z, t)exp(i3βgz)]exp(-iωBt)+[E-(1)(z, t)exp(-iβgz)+E-(3)×(z, t)exp(-i3βgz)]exp(-iωBt)}+c.c.,
PR(z, t)=12 {[P+(1)(z, t)exp(iβgz)+P+(3)×(z, t)exp(i3βgz)]exp(-iωBt)+[P-(1)(z, t)exp(-iβgz)+P-(3)×(z, t)exp(-i3βgz)]exp(-iωBt)}+c.c.,
W=W0+W2exp(i2βgz)+W2*exp(-i2βgz)+W4exp(i4βgz)+W4*exp(-i4βgz),
±i E±(1)z+iβ1E±(1)t+δβ0E±(1)+Γ[|E±(1)|2+2|E±(1)|2]E±(1)+Γ[3|E+(3)|2+|E-(3)|2]E±(1)+κE±(1)+κE±(3)+μ0ωB22β0 P±(1)=0,
±i E±(3)z+i β13E±(3)t+23 δβ0E±(3)-43 β0E±(3)+Γ3 [2|E+(1)|2+2|E-1(1)|2]E±(3)+Γ3 [2|E+(3)|2+|E-(3)|2]E±(3)+κ3 E±(1)+μ0ωB26β0 P±(3)=0.
η(κ/3)2(κ/3)2+(2δβ0/3-4β0/3)2
t P+(1)=-iΔωP+(1)+i μ [W0E+(1)+W2E-(1)+W2*E+(3)+W4E-(3)],
t P-(1)=-iΔωP-(1)+i μ [W0E-(1)+W2E-(3)+W2*E+(1)+W4*E+(3)],
t P+(3)=-iΔωP+(3)+i μ [W0E+(3)+W2E+(1)+W4E-(1)],
t P-(3)=-iΔωP-(3)+i μ [W0E-(3)+W2*E-(1)+W4*E+(1)],
t W0=-i μ2 [-E-(1)*P-(1)+E-(1)P-(1)*-E+(1)*P+(1)+E+(1)P+(1)*-E-(3)*P-(3)+E-(3)P-(3)*-E+(3)*P+(3)+E+(3)P+(3)*],
t W2=-i μ2 [-E-(3)*P-(1)+E+(1)P-(1)*-E-(1)*P+(1)+E+(3)P+(1)*+E-(1)P-(3)*-E+(1)*P+(3)],
t W4=-i μ2 [E+(3)P-(1)*-E-(3)*P+(1)+E+(1)P-(3)*-E-(1)*P+(3)].
±i E±(1)z+iβ1E±(1)t+δβ0E±(1)+κE±(1)+Γ[|E±(1)|2+2|E±(1)|2]E±(1)+μ0ωB22β0 P±(1)=0,
t P+(1)=-iΔωP+(1)+i μ [E+(1)W0+E-(1)W2],
t P(1)=-iΔωP(1)+i μ [E-(1)W0+E+(1)W2*],
t W0=-i μ2 [E+(1)P+(1)*+E-(1)P-(1)*-E+(1)*P+(1)-E-(1)*P-(1)],
t W2=-i μ2 [E+(1)P-(1)*-E-(1)*P+(1)],

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