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Progress in Electromagnetics Research Symposium (PIERS 2009 Moscow), Moscow, Russia, 12 - 21 August 2009, pp.31-32
A homogeneous non-dispersive anisotropic crystal, characterized by a symmetric positive definite permittivity tensor and a positive constant permeability, is considered. An analytic method for deriving the time-dependent electric and magnetic fields in this anisotropic crystal is suggested in the paper. This method is based on explicit formulae for electric and magnetic fields which are solutions of initial value problems for Maxwell's equations describing the wave propagation in the anisotropic crystal. The suggested method consists in several steps: Maxwell's equations are written in the second-order form in terms of the Fourier modes with respect to space variables; explicit formulae for the Fourier modes of electric and magnetic fields are derived using the matrix transformations and the technique of ordinary differential equations; finally, the inverse Fourier transform is applied to obtained formulae for the Fourier modes.