Transfer function for electromagnetic propagation through anisotropic metamaterials

Abstract

The Berreman matrix method has been previously used to model electromagnetic plane wave propagation through a hyperbolic metamaterial, and to determine transmission and reflection coefficients as a function of wavelength and varying angles of incidence. The Berreman matrix approach is now used to derive the propagation transfer function matrix in such materials. The eigenvalues of the Berreman matrix, which determine the transfer function, depend on the anisotropy. Beam propagation in such anisotropic materials are simulated using the transfer functions of all components of the electric (and magnetic) fields. Implications of this on negative refraction and the self-lensing of beams are explored.