AN ALTERNATIVE MODEL FOR WAVE PROPAGATION IN ANISOTROPIC IMPEDANCE-MATCHED METAMATERIALS

The propagation of light in an anisotropic impedance-matched metamaterial is studied in the frame of geometrical optics. We prove that directions of fields D, B and v (ray velocity) are a triad of conjugate directions with respect to the inverse relative dielectric permittivity tensor and constitutes a local basis, whose reciprocal one is formed by directions of E, H fields and wave-vector k. Consequently, both dual bases are intrinsically related to the physical properties of medium. We have identified these bases with direct and reciprocal bases of a curvilinear coordinates system, showing that physics defines geometry. This identification provides a powerful tool to solve two kinds of problems (direct and inverse ones) that currently arise: In direct problems, medium properties are given and it suffices to know ε = μ tensor at every point, to obtain the wave structure. In inverse problems, medium properties must be found for the rays to propagate along prescribed trajectories. The procedure is applied to an illustrating example.