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

Abstract

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 \ensuremath{\sim}(\ensuremath{\lambda}/a) is predicted and calculated. It corresponds to the corrections \ensuremath{\delta}n\ensuremath{\sim}(\ensuremath{\lambda}/a${)}^{2}$ to the effective refractive index tensor, where a\ensuremath{\gg}\ensuremath{\lambda} is the size of smooth inhomogeneity. An important feature is that linear birefringence appears only in the presence of gradients of impedance \ensuremath{\rho}(r)= \ensuremath{\surd}\ensuremath{\mu}(r)/\ensuremath{\varepsilon}(r) , whereas the gradients of refractive index n(r)= \ensuremath{\surd}\ensuremath{\varepsilon}(r)\ensuremath{\mu}(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\ensuremath{\rho}/dz)(d lnn/dz).