Optical theorems for electromagnetic scattering by inhomogeneities in layered dielectric media

The optical theorem, which relates the forward scattering amplitude to the total cross section of a scatterer in free-space, is extended to problems of scattering of an incident transverse electric plane wave or guided mode by inhomogeneities in lossless, waveguiding, dielectric interfaces or layers. The cases of a compact irregularity on either the interface between two unbounded dielectric media or in the waveguiding layer of a dielectric-slab waveguide are considered. Simple formulas that connect the scattered amplitudes of the different types of waves excited by the incident energy are derived. They can be used as an independent check of numerical codes when benchmark solutions are not available or are hard to obtain. In addition, a relationship between the scattered amplitudes and the spectral power of each excited wave is derived using the method of stationary phase