Abstract

The perfectly matched layer boundary condition for arbitrary anisotropic media is incorporated into the approximate scalar beam propagation method. The procedure is based on a finite-element method for three-dimensional anisotropic optical waveguides with off-diagonal elements in a permittivity tensor. In order to treat a wide-angle beam propagation, the Padé approximant operator is employed. To show the validity and usefulness of this approach,numerical results are presented for Gaussian beam propagation in free space and Gaussian beam excitation on a three-dimensional anisotropic optical waveguide.

© 2001 IEEE

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J. Lightwave Technol. (5)

E. Montanari, S. Selleri, L. Vincetti and M. Zoboli, "Finite-element full-vectorial propagation analysis for three-dimensional z -varying optical waveguides", J. Lightwave Technol., vol. 16, pp. 703-714, Apr. 1998 .

D. Schulz, C. Gingener, M. Bludsuweit and E. Voges, "Mixed finite element beam propagation method", J. Lightwave Technol., vol. 16, pp. 1336-1341, Jul. 1998 .

H.-P. Nolting and R. März, "Results of benchmark tests for different numerical BPM algorithms", J. Lightwave Technol., vol. 13, pp. 216-224, Feb. 1995.

Y. Tsuji, M. Koshiba and N. Takimoto, "Finite element beam propagation method for anisotropic optical waveguides", J. Lightwave Technol., vol. 17, pp. 723-728, Apr. 1999.

M. Koshiba, S. Maruyama and K. Hirayama, "A vector finite element method with the high-order mixed-interpolation type triangular elements for optical waveguiding problems", J. Lightwave Technol., vol. 12, pp. 495-502, Mar. 1994 .

Opt. Lett. (2)

Other (13)

Ü Pekel and R. Mittra, "A finite-element method frequency-domain application of the perfectly matched layer (PML) concept", Microwave Opt. Technol. Lett., vol. 9, pp. 117-122, June 1995.

Z. S. Sacks, D. M. Kingsland, R. Lee and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition", IEEE Trans. Antennas. Propagat., vol. 43, pp. 1460-1463, Dec. 1995.

M. Koshiba, Y. Tsuji and M. Hikari, "Finite element beam propagation method with perfectly matched layer boundary conditions", IEEE Trans. Magnet., vol. 35, pp. 1482-1485, May 1999.

A. Cucinotta, G. Pelosi, S. Selleri, L. Vincetti and M. Zoboli, "Perfectly matched anisotropic layers for optical waveguide analysis through the finite-element beam-propagation method", Microwave Opt. Technol. Lett., vol. 23, pp. 67-69, Oct. 1999.

Y. Tsuji and M. Koshiba, "Finite element beam propagation method with perfectly matched layer boundary conditions for three-dimensional optical waveguides", Int. J. Numer. Modeling: Electronic Networks, Devices and Fields, vol. 13, pp. 115-126, 2000.

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.

Y. Tsuji and M. Koshiba, "Adaptive mesh generation for Full-Vectorial guided-mode and beam-propagation solutions", IEEE J. Selected Topics Quantum Electon. , vol. 6, pp. 163-169, Jan./Feb. 2000.

J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves", J. Comput. Phys., vol. 114, pp. 185-200, Oct. 1994.

M. Koshiba, K. Hayata and M. Suzuki, "Approximate scalar finite-element analysis of anisotropic optical waveguides with off-diagonal elements in a permittivity tensor", IEEE Trans. Microwave Theory Tech., vol. 32, pp. 587-593, June 1984.

M. Koshiba, Optical Waveguide Theory by the Finite Element Method, Tokyo/Dordrecht: KTK Scientific Publishers/Kluwer Academic Publishers, 1992.

J.-F. Lee, D.-K. Sun and Z. J. Cendes, "Full-wave analysis of dielectric waveguides using tangential vector finite elements", IEEE Trans. Microwave Theory Tech., vol. 39, pp. 1262-1271, Aug. 1991.

M. Koshiba and Y. Tsuji, "A wide-angle finite-element beam propagation method", IEEE Photon. Technol. Lett., vol. 8, pp. 1208 -1210, Sept. 1996.

Y. Tsuji, M. Koshiba and T. Shiraishi, "Finite element beam propagation method for three-dimensional optical waveguide structures", J. Lightwave Technol. , vol. 15, pp. 1728-1734, Sept. 1997.

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