The Berreman matrix method is used to analyze the polarization and propagation of electromagnetic waves and beams in anisotropic metamaterials. The metamaterial, comprising a multilayer structure of alternating metal and dielectric layers, is modeled as an effective anisotropic medium. The Maxwell’s equations for electromagnetic propagation are then represented as a set of coupled differential equations using the Berreman matrix. These coupled equations are then solved analytically and cross checked numerically using MATLAB® for plane wave propagation. The analysis can be extended to Gaussian beam propagation through such anisotropic metamaterials using the angular plane wave spectral approach.
Rudra Gnawali and Partha Banerjee, "Berreman approach to electromagnetic wave and beam propagation in anisotropic metamaterials," Proc. SPIE 9918, Metamaterials, Metadevices, and Metasystems 2016, 99181Y (Presented at SPIE Nanoscience + Engineering: September 01, 2016; Published: 16 September 2016); https://doi.org/10.1117/12.2239199.
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