Plane-wave scattering-matrix formulation for two interfaces plus a scatterer (uniplanar case)

Kern's plane-wave scattering-matrix formulation is extended to treat the case of two interfaces plus a scatterer imbedded in the second region. This formulation can treat different shapes for the scatterer and only requires two different evaluations depending upon the location of the observer: 1) in the near field, a two-dimensional (2-D) fast Fourier transform (FFT) (one-dimensional (1-D) FFT is treated by an analytical integration), and 2) in the far-field an asymptotic evaluation of the integral. These two regimes are in contrast to the Sommerfeld integral approximations where different approximations are required for various parameter ranges (quasistatic, saddle-point evaluation for the radiation field, saddle point evaluation for the surface field when the saddle point is near a pole, and the lateral wave field evaluated using a uniform asymptotic evaluation for the integrals).