Scattering of Electromagnetic Waves in Saxon-Schiff Theory

We calculate the diffraction of electromagnetic waves by weak scatterers with complex dielectric constant and permeability using the Saxon-Schiff theory of potential scattering. Boundary conditions, polarizations, and the optical theorem are discussed to some extent. Our results for the scattering amplitude contain certain special cases obtained previously by other authors. In an Appendix, we compare the results for the scattering by a homogeneous dielectric sphere with those of the exact Mie theory. It is seen that the Saxon-Schiff theory gives a good qualitative agreement insofar as it reproduces the diffraction maxima and minima, in vast superiority to the Born approximation. In the asymptotic limit $\mathrm{kR}\to \infty$, the radar cross section is shown to agree with the exact result for a not too large index of refraction.