Exact Solution for the Protected TEM edge mode in a PTD-Symmetric Parallel-Plate Waveguide

TL;DR

This paper derives an exact analytical solution for a protected TEM edge mode in a PTD-symmetric PEC-PMC parallel-plate waveguide, demonstrating robustness against deformations and discontinuities through multiple analytical methods and numerical simulations.

Contribution

It presents the first exact analytical solution for the protected TEM mode in a PTD-symmetric waveguide using conformal mapping, mode-matching, and Fourier-transform methods.

Findings

Mode propagation is robust against bends and discontinuities.

Analytical solutions are validated with numerical simulations.

PMC boundary conditions are effectively implemented.

Abstract

A Parity Time-reversal Dual (PTD) symmetric structure constituted by a Perfectly-Electric-Perfectly magnetic (PEC-PMC) parallel plate waveguide (PPW) is analyzed. This waveguide supports unimodal transverse electromagnetic (TEM) edge mode propagation protected against back-scattering from a certain class of deformations and defects. The TEM solution is found in analytical form by using three different methods, namely conformal mapping, mode-matching, and Fourier-transform methods. It is shown through numerical simulations that the mode propagation is robust with respect to deformations such as 90{\deg} bends and discontinuity such as transition to free-space. Implementation of the PMC boundary conditions via both a bed of nails and a mushroom structure is also successfully investigated.