Ray formulation of waves guided by circular cylindrically stratified dielectrics

Abstract

Curved dielectric layers, either by themselves or as claddings on perfectly conducting substrates, are useful elements for guiding and confining electromagnetic energy. The prototype configuration, explored here, has circular cylindrical symmetry. The fields excited by an arbitrarily located and oriented dipole source are the basic building blocks, from which other source configurations can be synthesized. By recourse to the general theory of spectral representations, various alternative formulations of the solution can be constructed, and, via asymptotic techniques at high frequencies, examined concerning their utility and physical interpretation. In this paper, special emphasis is placed on source and observer locations on the outermost shell boundary; this is the relevant Green's function for application to stripline or printed circuits that are deposited there. A good parametrization of the relevant wave phenomena is achieved by treating the radial ρ portion of the problem in terms of the radial discrete mode spectrum, while retaining a continuum for the azimuthal ф and longitudinal z portions, with the ф domain extended to infinity. By asymptotic reduction the radial mode fields guided inside or on the layers follow helical (ф, z) trajectories originating at the source; as a result of dispersion, these waves have anisotropic speeds depending on the departure angle. Therefore in an equivalent two‐dimensional rectilinear (ф, z) space the local modes can be modeled as ray fields that propagate away from the source in a homogeneous anisotropic medium. The theory is summarized briefly. For the special case of a single layer on a perfectly conducting substrate, excited by an axial electric current element, modal dispersion surfaces (azimuthal versus longitudinal wave number) shown for various layer thicknesses reveal different degrees of anisotropy. Full calculation of the spectral integral, both numerically (for reference solution) and asymptotically, is in progress.