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Exact and Asymptotic Dispersion Relations for Homogenization of Stratified Media with Two Phases

Using exact dispersion relations for electromagnetic wave propagation in layered, periodic media, consisting of two phases, we derive explicit asymptotic solutions for small wavenumbers. These solutions are compared to the numerical solutions of the exact dispersion relations, and applications to homogenization problems are discussed. The results can be used as test cases for homogenization techniques intended for finite scale homogenization, that is, where the wavelength is not assumed infinitely large compared to the microscale.