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Computation of the Electromagnetic Modes in Two-Dimensional Photonic Crystals: A Technique to Improve the Convergence Rate of the Plane Wave Method

Silveirinha, M. G. ; Fernandes, C. A.

Electromagnetics Vol. 26, Nº 2, pp. 175 - 187, February, 2006.

ISSN (print): 1532-527X
ISSN (online): 0272-6343

Scimago Journal Ranking: 0,41 (in 2006)

Digital Object Identifier: 10.1080/02726340500486492

In this article, a regularization technique that allows the computing of the electromagnetic Floquet solutions in two-dimensional photonic crystals using a modified plane wave approach with very good convergence rate is described. The idea is to map the original electromagnetic fields into a space of smooth functions. This work is a generalization of a method previously proposed by the authors for metallic crystals, and the formulation presented here allows the characterizing of two-phase dielectric crystals. The numerical results show that the efficiency of our method is dramatically superior to that of the standard plane wave method.