Target scattering calculations with the parabolic equation method

Abstract

The parabolic equation technique is used to solve the Helmholtz equation in the presence of scatterers of arbitrary shape, in two and three dimensions. The scattered field is computed directly, using non-homogeneous boundary conditions on the scattering object to represent the incident field. Effectively this decouples the PE paraxial direction from the direction of incidence. For convex objects the whole range of scattering angles can be covered with a small number of narrow-angle calculations. Finite-difference implementations involve tridiagonal matrices in two dimensions and more general sparse matrices in three dimensions. The resulting codes can be used to solve scattering problems for objects ranging in size from a few wavelengths to hundreds of wavelengths. The method has been tested against analytical solutions for soft and rigid circular cylinders in 2D and soft and rigid spheres in 3D, showing good agreement at all scattering angles.