Field Transforms for Multilayered Cylindrical and Spherical Structures of Finite Conductivity

Abstract

Problems of propagation around multilayered cylindrical or spherical structures possessing highly conducting cores have been analyzed in terms of discrete sets of modes. However, when propagation through the core of the structure is significant and of particular interest, the discrete set of modes is not suitable for the complete expansion of the electromagnetic fields.To provide a suitable basis for the expansion of the electromagnetic field in nonuniform multilayered, cylindrical or spheroidal, dielectric structures we derive expressions for the electric and magnetic field transforms consisting of both a discrete and a continuous spectrum of waves. The relationship between these transforms, the Kontorowich–Lebedev transform, and the discrete Watson transform is discussed. When the radius of curvature of the structure is infinite these transforms merge with generalized Fourier type transforms.The transforms can be used to investigate electromagnetic propagation through irregularly shaped dielectric wave guides, and through irregularly shaped spheroids. It can also be used to solve the problem of propagation in the interior (concave side) of irregularly shaped conducting cylinders or spheroids.