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The procedure followed in analyzing electromagnetic scattering by irregular layered structures, in which the heights of the interfaces as well as the medium parameters fluctuate laterally, is such that all the simplifying assumptions introduced in order to make the rigorous solutions to the problems more tractable, are made a posteriori rather than a prior. In this way the same analysis can be used to obtian the high frequency physical optics solutions that can be applied to structures with scales of roughness that are much larger than the wavelength as well as to obtain the low frequency small perturbation type solutions for structures with scales of roughness without introducing a wavelength. Thus this analysis can be applied to multiple scale structures without introducing an artificial scale parameter that dictates the solution to the problem. In addition the same analysis can be used to obtain the far field approximations suitable for structures with scales of roughness comparable and larger than the wavelength, as well as to obtain the near field approximations that are suitable for structures with subwavelength scales. The analysis accounts for evanescent as well as propagating waves, the lateral waves and the guided, surface waves of the irregular structures. To this end, a full wave approach that is based on the complete expansion of the fields as well as the imposition of exact boundary conditions at the rough interfaces is used in the analysis. Since these complete fields expansions do not necessarily converge uniformly at the irregular interface, careful mathematical procedures must be followed. It is shown that using the far field approximations, the solutions for the scattered fields are expressed as integrals over the spatial variables. On the other hand when the near field approximations are used, the scattered fields are expressed as integrals over the wave vector variables. This fulll wave analysis can also be applied to anisotropic media such as chiral materials.
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