Electromagnetic wave propagation in inhomogeneous multilayered structures of arbitrary thickness-Full wave solutions

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Abstract
In this paper, we derive full wave solutions to the problem of electromagnetic wave propagation in inhomogeneous multilayered structures of arbitrarily varying thickness. To this end, we employ generalized transforms that provide an appropriate basis for the complete expansion of the transverse components of the electromagnetic fields. The continuous parts of the wavenumber spectrum are the radiation and the lateral wave terms while the discrete part is identified as the finite set of trapped waveguide modes (surface waves). When the bounding media are characterized by perfect electric or magnetic walls (μ/ε → 0 or ε/μ → 0, respectively) or surface impedances, the fields are expressed exclusively in terms of an infinite set of waveguide modes. These solutions are not restricted by the approximate surface impedance concept and the sources and observation point may be located in any of the nonuniform layers of the structure. Exact boundary conditions are imposed and the solutions satisfy the reciprocity relationships. Thus, the solutions are applicable to artificial layered structures as well as natural structures such as the inhomogeneous ionosphere and the earth's crust. These solutions can also be used to determine the scattering from objects of finite cross section in free space or embedded in the earth's crust.