Title: Matrix representation of the double-curl operator for simulating three dimensional photonic crystals
Authors: Huang, Tsung-Ming
Hsieh, Han-En
Lin, Wen-Wei
Wang, Weichung
Department of Applied Mathematics
Keywords: Photonic crystals;Face centered cubic lattice;The Maxwell equations;Yee's scheme;Double-curl operator;Matrix representation
Issue Date: 1-Jul-2013
Abstract: Three dimensional photonic crystals can be modeled by the Maxwell equations as a generalized eigenvalue problem (GEVP). Simulations based on the numerical solutions of the GEVP are used to reveal physical properties and boost innovative applications of photonic crystals. However, to solve these GEVP remains a computational challenge in both timing and accuracy. The GEVP corresponding to the photonic crystals with face centered cubic (FCC) lattice is one of the challenging eigenvalue problems. From a viewpoint of matrix computation, we demonstrate how such obstacles can be overcome. Our main contribution is an explicit matrix representation of the double-curl operator associated with the photonic crystal with FCC lattice. This particular matrix represents the degenerate coefficient matrix of the discrete GEVP obtained by Yee's scheme. The explicit matrix leads to an eigendecomposition of the degenerate coefficient matrix and then a fast eigenvalue solver. Promising numerical results in terms of timing and accuracy are reported for solving the discrete GEVP arising in three dimensional photonic crystals with various geometric parameters. (C) 2012 Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.mcm.2012.11.008
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2012.11.008
Volume: 58
Issue: 1-2
Begin Page: 379
End Page: 392
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