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

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 show that coupled transmission lines (CTLs) at radio frequencies having gain (active devices) and loss (e.g., material, radiation) balance exhibit EPDs. We demonstrate the concept of parity- time (PT)-symmetry in uniform CTLs that involve symmetric gain and loss and how this condition is associated with a second-order EPD. Furthermore, we also demonstrate that PT-symmetry is not a necessary condition for realizing EPDs, and indeed, we show that EPD is also obtained with asymmetric distributions of gain and loss in uniform CTLs. We further propose potential applications of the EPDs in designing leakywave antennas with the capability of beam and directivity control as well as enhanced sensitivity. Operating near such special degeneracy conditions leads to potential performance enhancement in a variety of microwave and optical resonators, antennas, and devices such as distributed oscillators, including lasers, amplifiers, radiating oscillators, pulse compressors, and Q-switching sensors.