Full-Vectorial Finite Element Method Based Eigenvalue Algorithm for the Analysis of 2D Photonic Crystals with Arbitrary 3D Anisotropy
Resource
Optics Express 15 (24): 15797-15811
Journal
OSA Optics Express
Journal Volume
15
Journal Issue
24
Pages
15797–15811
Date Issued
2007-11
Author(s)
Abstract
A full-vectorial finite element method based eigenvalue algorithm is developed to analyze the band structures of two-dimensional (2D) photonic crystals (PCs) with arbitray 3D anisotropy for in-planewave propagations, in which the simple transverse-electric (TE) or transverse-magnetic (TM) modes may not be clearly defined. By taking all the field components into consideration simultaneously without decoupling of the wave modes in 2D PCs into TE and TM modes, a full-vectorial matrix eigenvalue equation, with the square of the wavenumber as the eigenvalue, is derived. We examine the convergence behaviors of this algorithm and analyze 2D PCs with arbitrary anisotropy using this algorithm to demonstrate its correctness and usefulness by explaining the numerical results theoretically.
Type
journal article
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