Theory of Exceptional Points of Degeneracy in Uniform Coupled-Waveguides and Balance of Gain and Loss

TL;DR

This paper develops a transmission line theory for exceptional points of degeneracy (EPD) in coupled waveguides, exploring their relation to PT-symmetry and gain-loss balance, with implications for enhancing microwave and optical devices.

Contribution

It introduces a novel transmission line framework for EPD in coupled waveguides, demonstrating EPD formation without strict PT-symmetry, and discusses potential device performance improvements.

Findings

EPD can occur in uniform coupled waveguides with balanced gain and loss.

PT-symmetry is not a necessary condition for EPD in these structures.

Operating near EPD enhances performance of microwave and optical devices.

Abstract

We present a transmission line theory of exceptional points of degeneracy (EPD) in coupled-mode guiding structures, i.e., a theory that illustrates the characteristics of coupled electromagnetic modes under a special dispersion degeneracy condition, yet unexplored in the contest of gain and loss. We demonstrate the concept of Parity-Time ($\cal{PT}$)-symmetry in coupled uniform waveguides with balanced and symmetric gain and loss and how this condition is associated with a second order EPD. We show that by introducing gain into naturally lossy structures provides for the conditions whereby exceptional points of non-Hermitian degeneracies can be manifested, such as in $\cal{PT}$- symmetric structures. Furthermore, we also demonstrate that $\cal{PT}$- symmetry, despite being the method often suggested for obtaining non-Hermitian degeneracies at optical frequencies, is not a necessary condition and indeed we show that EPD can be obtained with broken topological symmetry in uniform TLs. Operating near such special degeneracy conditions leads to potential performance enhancement in a variety of microwave and optical resonators, and devices such as distributed oscillators, including lasers, amplifiers, radiating arrays, pulse compressors, and Qswitching sensors.