Abstract

A finite-element method (FEM) is newly formulated for the modal analysis of nonlinear periodic optical waveguides. In order to treat periodicity in the propagation direction, periodic boundary conditions are imposed on the envelope of electromagnetic fields. The validity of this method is verified by way of numerical examples of a PC waveguide composed of nonlinear dielectric pillars placed on square array in the cladding region. Furthermore, the present method is applied to various nonlinear photonic crystal waveguide structures for exploring appropriate structures to enhance the nonlinearity and their nonlinear modal properties are presented, including coupled-resonator optical waveguides.

© 2005 IEEE

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Opt. Express (3)

Opt. Lett. (4)

Other (12)

M. F. Yanik, S. Fan and M. Soljacic, "High-contrast all-optical bistable switching in photonic crystal microcavities", Appl. Phys. Lett., vol. 83, pp. 2739-2741, Oct. 2003.

T. Fujisawa and M. Koshiba, "Time-domain beam propagation method for nonlinear optical propagation analysis and its application to photonic crystal circuits", J. Lightw. Technol.,

J. D. Joannopoulos, P. R. Villeneuve and S. Fan, "Photonic crystals: putting a new twist on light", Nature, vol. 386, pp. 143-149, Mar. 1997.

M. Koshiba, "Wavelength division multipexing and demultiplexing with photonic crystal waveguide couplers", J. Lightw. Technol., vol. 19, pp. 1970-1975, Dec. 2001.

M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity", J. Opt. Soc. Amer. B, vol. 19, pp. 2052-2059, Sep. 2002.

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, Sep. 2002.

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

Y. Tsuji and M. Koshiba, "Finite element method using port truncation by perfectly matched layer boundary conditions for optical waveguide discontinuity problems", J. Lightw. Technol., vol. 20, pp. 463-468, Mar. 2002.

W. J. Kim and J. D. O'Brien, "Optimization of a two-dimensional photonic-crystal waveguide branch by simulated annealing and the finite-element method", J. Opt. Soc. Amer. B, vol. 21, pp. 289-295, Feb. 2004.

S. G. Johnson, P. R. Villeneuve, S. Fan and J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs", Phys. Rev. B, vol. 62, pp. 8212-8222, Sep. 2000.

A. Martinez, J. Garcia, G. Sanchez and J. Marti, "Planar photonic crystal structure with inherently single-mode waveguides", J. Opt. Soc. Amer. A, vol. 20, pp. 2131-2136, Nov. 2003.

K. Al-hemyari, A. Villeneuve, J. U. Kang, J. S. Aitchison, C. N. Ironside and G. I. Stegeman, "Ultrafast all-optical switching in GaAlAs directional couplers at 1.55 � m without multiphoton absorption", Appl. Phys. Lett., vol. 63, pp. 3562-3564, Dec. 1993.

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