## Numerical investigation of a self-induced transparency soliton in a nonlinear photonic bandgap structure doped uniformly with two-level atoms

JOSA B, Vol. 20, Issue 9, pp. 1866-1874 (2003)

http://dx.doi.org/10.1364/JOSAB.20.001866

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### 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

**OCIS Codes**

(190.0190) Nonlinear optics : Nonlinear optics

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.4400) Nonlinear optics : Nonlinear optics, materials

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

**Citation**

Boren Luo, Hong-Yih Tseng, and Sien Chi, "Numerical investigation of a self-induced transparency soliton in a nonlinear photonic bandgap structure doped uniformly with two-level atoms," J. Opt. Soc. Am. B **20**, 1866-1874 (2003)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-20-9-1866

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### References

- S. L. McCall and E. L. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
- J. H. Eberly, “Optical pulse and pulse-train propagation in a resonant medium,” Phys. Rev. Lett. 22, 760–762 (1969).
- M. D. Crisp, “Distortionless propagation of light through an optical medium,” Phys. Rev. Lett. 22, 820–823 (1969).
- L. Matulic and J. H. Eberly, “Analytic study of pulse chirping in self-induced transparency,” Phys. Rev. A 6, 822–836 (1972).
- M. Nakazawa, E. Yamada, and H. Kubota, “Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton,” Phys. Rev. Lett. 66, 2625–2628 (1991).
- T. Y. Wang and S. Chi, “Self-induced transparency in a dispersive and nonlinear Kerr host medium,” Opt. Lett. 16, 1575–1577 (1991).
- 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).
- 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).
- E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
- S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
- B. I. Mantsyzov, “Gap 2 pi pulse with an inhomogeneously broadened line and an oscillating solitary wave,” Phys. Rev. A 51, 4939–4943 (1995).
- B. I. Mantsyzov, “Laue soliton in a resonantly absorbing photonic crystal,” Opt. Commun. 189, 275–280 (2001).
- B. I. Mantsyzov and R. A. Sil’nikov, “Oscillating gap 2 pi pulse in resonantly absorbing lattice,” JETP Lett. 74, 456–459 (2001).
- A. E. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
- 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).
- M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
- 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).
- 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).
- C. M. de Sterke, K. R. Jackson, and B. D. Robert, “Nonlinear coupled-mode equations on a finite interval: a numerical procedure,” J. Opt. Soc. Am. B 8, 403–412 (1991).
- C. M. de Sterke and J. E. Sipe, “Map solitons,” Prog. Opt. 33, 203–259 (1994).
- B. J. Eggleton, R. E. Slusher, and C. M. de Sterke, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
- 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).
- 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).
- C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E 59, 1267–1269 (1999).
- S. Chi, B. Luo, and H.-Y. Tseng, “Ultrashort Bragg soliton in a fiber Bragg grating,” Opt. Commun. 206, 115–121 (2002).
- G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).
- 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).
- 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).
- 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).
- 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).

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