The singularity expansion method applied to plane wave scattering from a lossy slab on a conducting half-space

The one dimensional electromagnetic scattering from an idealized, conductor backed lossy slab which can be expressed as an infinite sum of natural modes by applying the singularity expansion method (SEM) is discussed. The slab is homogeneous, isotropic, of uniform thickness, and infinite in extent. A close equivalence to this system is a shorted, lossy transmission section. The complex frequencies for the lossy scatterer are continuous functions of the parameters describing the scatterer. It is shown that only a finite number of the SEM poles can be purely imaginary and that there can be no purely real poles. A numerical implementation of the SEM series was validated by comparison to a digital inverse Fourier transform of the solution to the fields in the frequency domain. Examples of the numerically found SEM poles for different slabs are included.