Abstract

Novel boundary conditions based on Padé approximations for the frequency domain two-dimensional/finite element (2-D/FE) simulation of planar optical junctions of arbitrary geometry and number of accessing waveguides are presented and described in detail. This efficient formulation is straightforwardly implemented within the 2-D/FE framework and also can easily be used in finite difference schemes. Three examples show the applicability and reliability of the present method: a waveguide step discontinuity, waveguide transverse displacement and T-shaped beam splitter.

© 2004 IEEE

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J. Lightwave Technol. (5)

Other (9)

U. Pëkel and R. Mittra, "A finite-element-method frequency-domain application of the perfectly matched layer (PML) concept", Microwave Opt. Technol. Lett., vol. 9, no. 3, pp. 117-122, 1995.

G. R. Hadley, "Wide-angle beam propagation using Padé approximation operator", Opt. Lett., vol. 17, no. 20, pp. 1426 -1428, 1992.

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

Y. Y. Lu, "A complex coefficient rational approximation of 1 + x", Appl. Numerical Mathematics, vol. 27, pp. 141-154, 1998.

H. El-Refaei, I. Betty and D. Yevick, "The application of complex Padé approximations to reflection at optical waveguide facets", IEEE Photon. Technol. Lett., vol. 12, 2000.

Y. Tsuji and M. Koshiba, "Finite element method using port truncation by perfectly matched layer boundary condition for optical waveguide discontinuity problems", J. Lightwave Technol., vol. 20, Mar. 2002.

M. I. Davanco, C. E. Rubio-Mercedes and H. E. Hernández-Figueroa, "Novel boundary condition for the finite-element solution of arbitrary planar junction", IEEE Photon. Technol. Lett., vol. 13, pp. 46-47, 2001 .

C. E. Rubio-Mercedes, "Frequency domain finite element analysis of photonic structures", Ph.D. dissertation, UNICAMP, Campinas-SP, Brazil, 2002. .

J. Jin, The Finite Element in Electromagnetics, New York: Wiley, 1993.

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