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.
Highlights
Frequency splitting phenomena at exceptional points of degeneracy (EPDs) is adopted to serve in sensing applications [1,2]
II we provide the general theory and formulation for EPDs to exist in linear time-periodic systems
For the sake of simplicity, the following analysis and examples are focusing on second order EPDs that emerge in linear time-periodic (LTP) systems, the transition matrix Φ has dimensions
Summary
Frequency splitting phenomena at exceptional points of degeneracy (EPDs) is adopted to serve in sensing applications [1,2]. We demonstrate the occurrence of EPDs directly induced by temporal periodic variation of a system. In this paper we show that EPDs are induced in a single resonator directly by periodic time-variation of the system itself, without the need of elements that exhibit time-invariant gain. In an LTP system the EPD is obtained by tuning the period of the time modulation which is a standard practice in many engineering applications, in contrast to PT symmetric systems where the requirements on gain and loss elements may be difficult to achieve in practice. We show that even a single passive resonator (without gain or loss elements such as transistors or negative resistors) exhibit EPDs once time periodic modulation is introduced. We show how a simple resonator with time modulation can perform as an extremely sensitive sensor
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
