Abstract

Optical scattering by 3-D inhomogeneities of the permittivity at scale sizes that greatly exceed the wavelength is governed by the parabolic wave equation. The wave-kinetic equivalent is an equation for the 5-D Wigner distribution function (WDF) F(ρ,K,z) where K = (K_x,K_y) is a transverse wave vector, and ρ = (x,y) is the transverse-coordinate vector. In the Liouville approximation, the WDF is conserved along ray paths, and the characteristic equations are those of geometrical optics. The conservation law extends well beyond ray crossings into the diffraction regime. The numerical technique exploits the conservation of the WDF along ray paths but restricts ray tracing to relatively few rays. A novel Gaussian interpolation scheme provides the missing information needed in F(ρ,K,z). The scattered flux is then easily obtained from the sum-of-Gaussian form of the WDF. The technique is illustrated for the relatively simple cases of (1) free-space diffraction of a Gaussian beam, and (2) scattering of a plane wave by a weak Gaussian inhomogeneity.

© 1985 Optical Society of America