Exact Solution for the Protected TEM Edge Mode in a PTD-Symmetric Parallel-Plate Waveguide

A parity time-reversal duality symmetric structure constituted by a perfect electric conductor and perfect magnetic conductor (PMC) parallel plate waveguide is analyzed. This waveguide supports unimodal transverse electromagnetic (TEM) edge mode propagation protected against backscattering 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° bends and discontinuities 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.