Analysis of Eccentric Coaxial Waveguides Filled with Lossy Anisotropic Media via Finite Difference

TL;DR

This paper develops a finite difference method to model electromagnetic wave propagation in eccentric coaxial waveguides with lossy anisotropic media, offering improved computational efficiency and adaptability for complex media applications.

Contribution

It introduces a novel FDM approach with conformal transformation and a normalized Helmholtz equation to decouple modes, enhancing modeling of complex media in waveguides.

Findings

Validated against multiple numerical methods with superior computational speed

Effective in modeling lossy anisotropic media and complex media applications

Can be extended to metamaterials, optical fibers, and geophysical sensors

Abstract

This study presents a finite difference method (FDM) to model the electromagnetic field propagation in eccentric coaxial waveguides filled with lossy uniaxially anisotropic media. The formulation utilizes conformal transformation to map the eccentric circular waveguide into an equivalent concentric one. In the concentric problem, we introduce a novel normalized Helmholtz equation to decouple TM and TE modes, and we solve this non-homogeneous partial differential equation using the finite difference in cylindrical coordinates. The proposed approach was validated against perturbation-based, spectral element-based, and finite-integration-based numerical solutions. The preliminary results show that our solution is superior in computational time. Furthermore, our FDM formulation can be extended with minimal adaptations to model complex media problems, such as metamaterial devices, optical fibers, and geophysical exploration sensors.