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

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 ($\mathcal{P}\mathcal{T}$)-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 $\mathcal{P}\mathcal{T}$- symmetric structures. Furthermore, we also demonstrate that $\mathcal{P}\mathcal{T}$- 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.

13 pages, 10 figures

References in corpus (6)

• The physics of exceptional points
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Coherent Perfect Absorbers: Time-reversed Lasers
• Visualization of Branch Points in PT-Symmetric Waveguides
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Solitons in PT-symmetric nonlinear lattices

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