Observation of Exceptional Points in Parity-Time Symmetric Coupled Impedance Sheets

Two identical impedance sheets separated by a subwavelength distance form a coupled waveguide system. If the impedance sheets also employ balanced gain and loss forming a parity-time (PT) symmetric system, an exceptional point can be observed. Exceptional points are points in the parameter space of the coupled mode system (balanced loss/gain factor) where both the eigenmodes and the eigenvalues coalesce forming an overall lossless degenerate mode. The dispersion relation is derived in two ways: (1) by considering the mathematical form of propagating modes and applying the PT-symmetric impedance boundary conditions, and (2) by transmission line modeling and the transverse resonance condition. Identical results are obtained using the two approaches. To validate the obtained results, modal analysis in COMSOL Multiphysics is used. The modal electric field profiles and complex wavenumbers are plotted against the loss/gain factor. It is shown that at the exceptional point, both the eigenmodes and the eigenvalues coalesce.