Parametric instability of non-Hermitian systems near the exceptional point

摘要

In contrast to Hermitian systems, eigenstates of non-Hermitian ones are ingeneral nonorthogonal. This feature is most pronounced at exceptional pointswhere several eigenstates are linearly dependent. In this work we show thatnear this point a new effect takes place. It exhibits in energy increases inthe system when its parameters change periodically. This effect resemblesparametric resonance in a Hermitian system but there is a fundamentaldifference. It comes from the unique properties of the exceptional point thatleads to parametric instability that occurs almost at any change in aparameter, while in the case of Hermitian systems it is necessary to fulfillresonance conditions. We illustrate this phenomenon by the case of two couplingwaveguides with gain and loss. This phenomenon opens a wide range ofapplications in optics, plasmonics, and optoelectronics, where the loss is aninevitable problem and plays a crucial role.