Depolarization of electromagnetic waves excited by distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness. Generalized field transforms

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Abstract
A suitable basis for the full wave expansion of electromagnetic fields in inhomogeneous multilayered structures of arbitrarily varying thickness is presented in this paper. To this end, we formulate appropriate sets of transform pairs for the transverse electric and magnetic fields. Since arbitrary distribution of electric and magnetic sources are considered, the complete expansion must be composed of both vertically and horizontally polarized waves. Each set of generalized transforms, for the vertically and horizontally polarized waves, consists of two infinite integrals (continuous spectrum) which correspond to the radiation and the lateral wave terms as well as a finite number of terms (discrete spectrum) which correspond to the surface waves. For a general three‐dimensional distribution of sources in any of the structure's layers, the transverse electric and magnetic fields are in general two component vector functions. Thus, the transform pairs involve vector rather than scalar functions. Exact boundary conditions are employed in the analysis rather than approximate surface impedance boundary conditions. When the boundary media of the structure are regarded as perfect electric or magnetic walls, or are characterized by surface impedances, the fields are expressed exclusively in terms of infinite sets of waveguide modes.