Parametric instability of optical non-Hermitian systems near the exceptional point

In contrast to Hermitian systems, the modes of non-Hermitian systems are generally nonorthogonal. As a result, the power of the system signal depends not only on the mode amplitudes but also on the phase shift between them. In this work, we show that it is possible to increase the mode amplitudes without increasing the power of the signal. Moreover, we demonstrate that when the system is at the exceptional point, any infinitesimally small change in the system parameters increases the mode amplitudes. As a result, the system becomes unstable with respect to such perturbation. We show such instability by using the example of two coupled waveguides in which loss prevails over gain and all modes are decaying. This phenomenon enables compensation for losses in dissipative systems and opens a wide range of applications in optics, plasmonics, and optoelectronics, in which loss is an inevitable problem and plays a crucial role.