Electromagnetic wave propagation in inhomogeneous multilayered structures of arbitrarily varying thickness-Generalized field transforms

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Abstract
To provide a suitable basis for the expansion of electromagnetic fields in multilayered structures of arbitrarily varying thickness we derive, in this paper, the appropriate transform pairs for the transverse electric and magnetic field components. Applying the technique utilized earlier for two semi‐infinite media, we first derive the transform pairs for the three‐medium problem. Building on these expressions for the transform pairs, we systematically extend our results for structures with an arbitrary number of layers. The generalized transforms derived consist 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. Exact boundary conditions are employed rather than surface impedance boundary conditions. In the analysis, the sources and the observation point may be located in any of the structure's layers. Thus for instance, the derived field expressions are suitable for the study of antennas embedded in the earth's crust or submerged underwater.