Abstract

A time-domain beam propagation method (BPM) based on a finite-element scheme is newly formulated for nonlinear optical propagation analysis. In order to obtain steady-state solutions, a way of continuous-wave (CW) excitation is also described. The validity of this method is verified by numerical examples: self-focusing guiding phenomena and nonlinear gratings. Furthermore, this approach is also applied to characterizing nonlinear photonic crystal circuits. Specifically, a grating structure designed to modify the characteristics of light propagating within a photonic crystal waveguide and a stub-like structure including nonlinear rods are proposed, and the potential for use as optical limiting and switching devices is investigated.

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J. Lightwave Technol. (4)

Opt. Lett. (3)

Other (15)

S. F. Mingaleev and Y. S. Kivshar, "Nonlinear transmission and light localization in photonic-crystal waveguides", J. Opt. Soc. Amer. B, vol. 19, pp. 2241-2249, Sept. 2002.

P. Tran, "Optical limiting and switching of short pulses by use of nonlinear photonic band gap structure with a defect", J. Opt. Soc. Amer. B, vol. 14, pp. 2589-2595, Oct. 1997.

V. Van and S. K. Chaudhuri, "A hybrid implicit-explicit FDTD scheme for nonlinear optical waveguide modeling", IEEE Trans. Microwave Theory Tech., vol. 47, pp. 540-545, May 1999.

M. Soljacik, M. Ibanescu, S. G. Johnson, Y. Fink and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals", Phys. Rev. E, vol. 66 055 601(R), Oct. 2002.

K. Hayata, A. Misawa and M. Koshiba, "Split-step finite-element method applied to nonlinear integrated optics", J. Opt. Soc. Amer. B, vol. 7, pp. 1772-1784, Sept. 1990.

X. J. Meng and N. Okamoto, "Numerical analysis of a MQW-sandwich coupler with strong coupling", IEEE Photon. Technol. Lett., vol. 4, pp. 460-462, Apr. 1993.

H. E. Hernández-Figueroa, F. Di Pasquale, D. R. Ettinger, F. A. Fernández and J. B. Davies, "Controlled spatial bright soliton emission from a nonlinear waveguide", Opt. Lett. , vol. 19, pp. 326-328, Mar. 1994.

H. E. Hernández-Figueroa, "Improved split-step schemes for nonlinear optical propagation", J. Opt. Soc. Amer. B, vol. 11, pp. 798-803, May 1994.

F. Di Pasquale and H. E. Hernández-Figueroa, "Improved all-optical switching in a three-slab nonlinear directional coupler with gain", IEEE J. Quantum Electron., vol. 30, pp. 1254-1258, May 1994.

P.-L. Liu, Q. Zhao and F.-S. Choa, "Slow-wave finite-difference beam propagation method", IEEE Photon. Technol. Lett., vol. 7, pp. 890 -892, Aug. 1995.

G. H. Jin, J. Harari, J. P. Vilcot and D. Decoster, "An improved time-domain beam propagation method for integrated optics components", IEEE Photon. Technol. Lett., vol. 9, pp. 348-350, Mar. 1997.

K. S. Yee, "Numerical solution of intial boundary value problems involving Maxwell's equations", IEEE Trans. Antennas Propag., vol. AP-14, pp. 302-307, May 1966.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides", Phys. Rev. Lett., vol. 77, pp. 3787-3790, Oct. 1996.

F. L. Teixeira and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media", IEEE Microwave Guided Wave Lett., vol. 8, pp. 223-225, June 1998.

M. Koshiba, Y. Tsuji and S. Sasaki, "High-performance absorbing boundary conditions for photonic crystal waveguide simulations", IEEE Microwave Wireless Compon. Lett. , vol. 11, pp. 152-154, Apr. 2001.

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