Analytic modal solution to light propagation through layer-by-layer metallic photonic crystals

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Abstract
An analytic modal expansion method combined with a transfer-matrix technique is developed to investigate the reflection, transmission, and absorption spectra of three-dimensional layer-by-layer metallic photonic crystals working in a regime from microwave to infrared wavelengths. The eigenmodes for electromagnetic fields within each layer of the crystal are solved analytically by matching boundary conditions. The eigenmodes are then projected onto a plane wave basis, so that the scattering problem for a multilayer structure can be cast into the framework of transfer-matrix method. In addition, the structural symmetry between different layers of the crystal is fully exploited to connect the transfer matrix for different layers and significantly reduce the computation effort on the light scattering problem. Fast convergence of numerical result has been obtained and excellent agreement of theoretical results with experimental measurements has been achieved, indicating the effectiveness and efficiency of the developed analytical modal expansion method.