ELECTROMAGNETIC SCATTERING BY STRATIFIED NANOSTRUCTURES WITH SMALL AND LARGE SCALE PERIODIC AND RANDOM MEDIA AND INTERFACE FLUCTUATION: A FULL WAVE APPROACH

摘要

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 priori. In this way the same analysis can be used to obtain 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 that are comparable to the wavelength. Thus this analysis can be applied to structures with multiple scales of roughness 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 of roughness. By imposing reciprocity it can be shown that near field measurements can be implied from far field measurements, provided that objects in the vicinity of the interfaces excite the near fields. Thus the analysis should account 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 are used in the analysis. Since these complete fields expansions do not necessarily converge uniformly at the irregular interfaces, careful mathematical procedures must be followed such that any interchange in the order of summation and differentiation of the complete field expansions is strictly avoided. Thus for example 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 full wave analysis can also be applied to anisotropic media such as chiral materials.