Abstract

The spectral element method (SEM) is used to calculate band structures of two-dimensional photonic crystals (PCs) consisting of dispersive anisotropic materials. As in the conventional finite element method, for a dispersive PC, the resulting eigenvalue problem in the SEM is nonlinear and the eigenvalues are in general complex frequencies. We develop an efficient way of incorporating the dispersion in the system matrices. The band structures of a PC with a square lattice of dispersive cylindrical rods are first analyzed. The imaginary part of the complex frequency is the time-domain decay rate of the eigenmode, which is very useful for tracing a band from discrete numerical data. Modification of the band structure of TE mode by an external static magnetic field in the out-of-plane direction is explored for this square lattice. A plasmon resonance mode is found near the plasmon frequency when the magnetic field is nonzero. The band structure of a PC with a triangular lattice is also calculated with the SEM. Other types of lattices can also be treated readily by the SEM.

© 2009 Optical Society of America

Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency

Ma Luo and Qing Huo Liu
J. Opt. Soc. Am. A 27(8) 1878-1884 (2010)

Modeling two-dimensional anisotropic photonic crystals by Dirichlet-to-Neumann maps

Huan Xie and Ya Yan Lu
J. Opt. Soc. Am. A 26(7) 1606-1614 (2009)

Finite element method analysis of band gap and transmission of two-dimensional metallic photonic crystals at terahertz frequencies

Elif Degirmenci and Pascal Landais
Appl. Opt. 52(30) 7367-7375 (2013)

Investigation of band structures for 2D non-diagonal anisotropic photonic crystals using a finite element method based eigenvalue algorithm

Sen-ming Hsu, Ming-mung Chen, and Hung-chun Chang
Opt. Express 15(9) 5416-5430 (2007)

Enhancement of second-harmonic generation in an air-bridge photonic crystal slab: simulation by spectral element method

Ma Luo and Qing Huo Liu
J. Opt. Soc. Am. B 28(12) 2879-2887 (2011)