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Green's function for electromagnetic scattering from a random rough surface

### Abstract

The stochastic Green's matrix is calculated for a random rough surface with Gaussian statistics and a magnetic boundary condition. The techniques we use are similar to those developed for the scalar and elastic cases. The coupled surface integral equations which are derived are the Green's function version of the Franz formulas. These integral equations are represented in *k*‐space in a certain gauge and a Feynman‐diagram‐like interpretation is given to each term in the equations. The diagram rules have many formal similarities with the scalar and elastic rules. By using partial summation techniques, the mean and second moment of this Green's function are shown to be solutions to Dyson and Bethe‐Salpeter equations respectively. The Green's function is applied to a scattering problem. Some approximations and simple examples are presented. The lowest order approximations agree with the standard literature results. The main advantage of the diagram method, its systematic presentation of higher order approximations, is stressed.

© 1974 The American Institute of Physics

Received 04 May 1973
Published online 04 November 2003