Excitation of Wannier-Stark states in a chain of coupled optical resonators with linear gain and nonlinear losses

TL;DR

This paper explores how nonlinear dynamics and tailored dissipation in coupled optical resonators can excite Wannier-Stark states, leading to lasing, Bloch oscillations, and controllable excitation regimes.

Contribution

It introduces a theoretical framework for selectively exciting Wannier-Stark states in dissipative optical resonator chains with nonlinear losses.

Findings

Negative losses can induce lasing in Wannier-Stark states

Multiple frequency regimes including Bloch oscillations are possible

Perturbation theory aligns with numerical simulations

Abstract

In this paper we theoretically study the nonlinear dynamics of Wannier-Stark states in the dissipative system consisting of interacting optical resonators, whose resonant frequencies depend linearly on their number. It is shown that the negative losses in some resonators can switch the system into a lasing regime with Wannier-Stark states serving as working modes. It is shown by extensive numerical simulations that there may be single-frequency stationary regimes as well as multi-frequency regimes. In the latter case Bloch oscillations can appear in the system. The possibility of selective excitation of Wannier-Stark states by the appropriate choice of the dissipation profile is investigated. A simple perturbation theory describing the quasi-linear regimes is developed and compared against the numerical results.