Perturbative Analysis of Anisotropic Coaxial Waveguides With Small Eccentricities via Conformal Transformation Optics

This article describes two novel perturbation solutions for the electromagnetic analysis of eccentric coaxial waveguides. Different techniques have been used for solving this type of problem in the past. Most of them rely on solving a complicated transcendental equation obtained from the Graf’s addition theorem or on brute-force numerical methods such as finite differences and finite elements. The proposed approach, instead, employs transformation optics to map the original problem into a problem consisting of a concentric coaxial waveguide filled with an anisotropic and inhomogeneous medium. The corresponding (transformed) wave equation is then solved via a regular perturbation series. This method allows to compute field and wavenumber corrections of the transverse magnetic (TM) and transverse electric (TE) modes for coaxial waveguides with small eccentricities. In addition, another solution is obtained by using the cavity-material perturbation approach for providing the cutoff wavenumbers of TM and TE fields. The proposed perturbation solutions are validated against full-wave finite-element and finite-volume results in several examples.