A Simple Analysis for Obtaining Cutoff Wavenumbers of an Eccentric Circular Metallic Waveguide in Bipolar Coordinate System

This paper describes a simple analysis of the guided waves in an eccentric circular waveguide based on the bipolar coordinate system (BCS). The separation of the variable technique is used for the solution. The structure under study is an infinite perfect electric conductor (PEC) cylinder in the z-direction, which encloses eccentrically another infinite PEC cylinder. The modal analysis has been conducted using an analytical method, solving the TE and TM modes by the aid of electromagnetic formulation. Despite previous studies which mostly rely on numerical techniques or otherwise considering the dominant TEM mode, in this paper, the analytical solution is proposed for the electromagnetic fields which consequently lead to the characterization of the cutoff wavenumbers of higher order modes and explicit solution to electric and magnetic fields in BCS. The solution of the Helmholtz equation in BCS using the technique of separation of variables exhibits as a one of the contributions of this paper, and the validity range of the answer is discussed. The values of the cutoff wavenumbers for the first few modes are calculated and compared with the benchmark results. The precise correspondence of the obtained values with the proposed method with those of the previous studies and computer simulations, along with the high speed and simplicity in implementation, introduces the present method as an appropriate option for analyzing eccentric circular cylindrical structures.