Exceptional Points of Degeneracy Induced by Linear Time-Periodic Variation Hamidreza

TL;DR

This paper develops a general theory for exceptional points of degeneracy (EPD) in time-periodic systems, showing they can occur without loss or gain and have applications in sensors and photonics.

Contribution

It introduces a novel theoretical framework for EPDs in lossless and gain/loss systems, including single resonators with time-periodic components.

Findings

EPDs can occur in lossless/gainless systems with real resonance frequencies.

A single LC resonator can exhibit EPDs due to time-periodic variation.

Time-varying EPDs enable highly-sensitive sensors.

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.