Exceptional Points of Degeneracy Induced by Linear Time-Periodic Variation

Abstract

We present a general theory of exceptional points of degeneracy (EPD) in periodically time-variant systems that do not necessarily require the presence of loss or gain, and we show that even a single resonator with a time-periodic component may develop EPDs. An EPD is a special point in a system parameter space at which two or more eigenmodes coalesce in both their eigenvalues and eigenvectors into a single degenerate eigenmode. We demonstrate the conditions for EPDs to exist in time-periodic systems that are either lossless/gainless or with loss and/or gain and we show that a system with zero time-average loss/gain exhibits EPDs with purely real resonance frequencies, yet the resonator energy grows algebraically in time. We show the occurrence of EPDs in a single LC resonator while the introduced concept is general for any time-periodic system. These findings have significant importance in various electromagnetic/photonic systems and pave the way of applications in areas of sensors, amplifiers and modulators. A potential application of this time varying EPD is highlighted as a highly-sensitive sensor. system matrices as 1 j j J j T e    M Φ , where j

Spacetime modulation in floating thin elastic plates

“…By inserting the Fourier expansion of the water elevation field in Eq. (2), we get ∀n ∈ Z, For instance, the picture of k-bandgap can be seen from another perspective, i.e., that of exceptional points of degeneracy (EPs) [55][56][57]. The edges of the bandgap correspond also to EPs as these are induced by space, time, and/or spacetime-modulation.…”

Temporally modulated metamaterial based on a multilayer graphene structure

“…Stability analysis is one of the essential things when dealing with temporally modulated systems since it examines whether a dynamically modulated material can support finite fields [49]. One of the common approaches is based on the eigenvalue problem analysis [50], playing a crucial role in exceptional point evaluation [51]. Here, we adapt an approach based on the time-transitioning state matrix, which was demonstrated recently by Koutserimpas and Fleury for a generalized medium under temporal modulation [46].…”

Demonstration of Exceptional Points of Degeneracy in Gyrator-Based Circuit for High-Sensitivity Applications

“…An EPD is a point in the parameter space of a system for which the eigenvalues and the eigenvectors of the relevant matrix coalesce. The EPD concept has been investigated in lossless, spatially [1], [2], [3], [4], or temporally [5], [6] periodic structures, and in coupled-resonator systems with loss and/or gain under parity-time symmetry [7], [8], [9]. Since the characterizing feature of an exceptional point is the full degeneracy of at least two eigenmodes, as mentioned in [10], the significance of referring to it as a "degeneracy" is here emphasized, hence including the D in EPD.…”

“…Alexander Figotin is with the Department of Mathematics, University of California, Irvine, CA 92697 USA, e-mail: afigotin@uci.edu. [12], optical gyroscopes [13], [14], bending curvature sensors [15], and at radio frequency [16], [5], [17].…”