Parametric instability of non-Hermitian systems near the exceptional point

Abstract: In contrast to Hermitian systems, eigenstates of non-Hermitian ones are in general nonorthogonal. This feature is most pronounced at exceptional points where several eigenstates are linearly dependent. In this work we show that near this point a new effect takes place. It exhibits in energy increases in the system when its parameters change periodically. This effect resembles parametric resonance in a Hermitian system but there is a fundamental difference. It comes from the unique properties of the exceptional point that leads to parametric instability that occurs almost at any change in a parameter, while in the case of Hermitian systems it is necessary to fulfill resonance conditions. We illustrate this phenomenon by the case of two coupling waveguides with gain and loss. This phenomenon opens a wide range of applications in optics, plasmonics, and optoelectronics, where the loss is an inevitable problem and plays a crucial role.