Pinned modes in lossy lattices with local gain and nonlinearity

TL;DR

This paper models a lossy lattice system with a localized gain and nonlinearity, analyzing the existence and stability of pinned modes, revealing conditions for stability and bistability influenced by gain, loss, and nonlinearity.

Contribution

It introduces an analytical framework for localized modes in a lossy lattice with a hot spot, exploring their stability influenced by gain and nonlinear effects.

Findings

Stable modes can be achieved through the interaction of cubic gain and self-defocusing nonlinearity.

Bistability arises from the interplay of cubic loss and self-defocusing.

Stability regions depend on the parameters of linear gain and cubic gain/loss.

Abstract

We introduce a discrete linear lossy system with an embedded "hot spot" (HS), i.e., a site carrying linear gain and complex cubic nonlinearity. The system can be used to model an array of optical or plasmonic waveguides, where selective excitation of particular cores is possible. Localized modes pinned to the HS are constructed in an implicit analytical form, and their stability is investigated numerically. Stability regions for the modes are obtained in the parameter space of the linear gain and cubic gain/loss. An essential result is that the interaction of the unsaturated cubic gain and self-defocusing nonlinearity can produce stable modes, although they may be destabilized by finite amplitude perturbations. On the other hand, the interplay of the cubic loss and self-defocusing gives rise to a bistability.