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.
Highlights
Photonic crystals (PCs) are structures formed by periodically-organized materials that may create some frequency ranges, named the photonic band gaps (PBGs), in which the electromagnetic (EM) waves are forbidden to propagate
If the 2D PCs are composed of isotropic materials, the above-mentioned numerical models are perfectly sufficient to perform the analysis of band structures
We have successfully developed a full-vectorial finite element method (FEM) based eigenvalue algorithm for the analysis of band structures of 2D PCs with arbitrary 3D anisotropy for in-plane wave propagations
Summary
Photonic crystals (PCs) are structures formed by periodically-organized materials that may create some frequency ranges, named the photonic band gaps (PBGs), in which the electromagnetic (EM) waves are forbidden to propagate With this peculiar property, PCs are especially characterized by the capability of achieving an extremely high degree of control over the propagation of EM waves. To obtain the complete band structures for 2D PCs from these numerical models, the wave modes are often decoupled into transverse-electric (TE) and transverse-magnetic (TM) modes, and the eigen frequencies of these two sets of modes are separately solved In other words, these numerical models are based on a scalar algorithm in which the scalar equations for the TE and TM modes are manipulated apart to construct the band structures for 2D PCs. If the 2D PCs are composed of isotropic materials, the above-mentioned numerical models are perfectly sufficient to perform the analysis of band structures.
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