Phase space propagation of waves in nonhomogeneous media: corrections beyond the optical geometry limit

We investigate the corrections to the optical geometry approximation for waves traveling in non homogeneous media. We model the wave propagation in dispersive and non dispersive materials in terms of the phase space Wigner-Weyl formalism. The ray tracing optical geometry limit is introduced by numerical tests. We solve the exact Wigner propagation equation for 1D non dispersive materials. We discuss the connection of the Wigner-Weyl description of waves with the particle-wave duality phenomenon in quantum mechanics.