Exceptional Points of Degeneracy Induced by Linear Time-Periodic Variation

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 element 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. Finally, we propose a potential application of EPDs in designing highly-accurate sensors. EPDs in time-periodic systems may serve towards enhancing various applications like sensors, amplifiers and modulators.