Dissipative quadratic solitons supported by a localized gain

TL;DR

This paper introduces models for stable dissipative quadratic solitons in optical media with localized gain, demonstrating their existence, stability, and complex behaviors like symmetry breaking through numerical and analytical methods.

Contribution

It presents new models for dissipative quadratic solitons with localized gain and analyzes their existence, stability, and bifurcation properties.

Findings

Existence of stable dissipative $ ext{chi}^{(2)}$ solitons pinned to a hot spot.

Analytical boundary for soliton existence based on linear guided modes.

Observation of spontaneous symmetry breaking and bistability in solitons.

Abstract

We propose two models for the creation of stable dissipative solitons in optical media with the $\chi^{(2)}$ (quadratic) nonlinearity. To compensate spatially uniform loss in both the fundamental-frequency (FF) and second-harmonic (SH) components of the system, a strongly localized "hot spot", carrying the linear gain, is added, acting either on the FF component, or on the SH one. In both systems, we use numerical methods to find families of dissipative $\chi^{(2)}$ solitons pinned to the "hot spot". The shape of the existence and stability domains may be rather complex. An existence boundary for the solitons, which corresponds to the guided mode in the linearized version of the systems, is obtained in an analytical form. The solitons demonstrate noteworthy features, such as spontaneous symmetry breaking (of spatially symmetric solitons) and bistability.