Birefringence by a smoothly inhomogeneous locally isotropic medium: Three-dimensional case

The propagation problem for electromagnetic waves in a smoothly inhomogeneous locally isotropic medium, which was considered for a layered case in V. S. Liberman and B. Ya. Zel'dovich, Phys. Rev. E 49, 2389 (1994) is generalized to a three-dimensional situation. Effective ``linear'' birefringence, i.e., coherent transformation of a right circularly polarized wave into the left one with the amplitude {~}({λ}/a) is predicted and calculated. It corresponds to the corrections {δ}n{~}({λ}/a)² to the effective refractive index tensor, where a{}{λ} is the size of smooth inhomogeneity. An important feature is that linear birefringence appears only in the presence of gradients of impedance {ρ}(r)= {}{μ}(r)/{ε}(r) , whereas the gradients of refractive index n(r)= {}{ε}(r){μ}(r) are not necessary in a general three-dimensional case. This is in contrast with a layered medium (one-dimensional case) where the net effect was proportional to the product (d ln{ρ}/dz)(d lnn/dz).