Quasi-confined modes produced by the Lugiato-Lefever model with a localized pump and the pseudo-Raman term

TL;DR

This paper extends the Lugiato-Lefever equation with a pseudo-Raman term and localized pump to analyze quasi-confined modes, combining analytical and numerical methods to demonstrate stable soliton solutions and mode dynamics.

Contribution

It introduces a novel extended Lugiato-Lefever model with pseudo-Raman effects and localized pumping, deriving it from the Zakharov system, and studies the stability and dynamics of quasi-solitons.

Findings

Stable quasi-solitons predicted by the sech approximation.

Numerical simulations confirm analytical stability predictions.

Identification of the attraction basin for the fixed point.

Abstract

We introduce an extended nonlinear Lugiato-Lefever equation (LLE) with the pseudo-stimulated-Raman-scattering (pseudo-SRS) cubic term, linear damping/gain, and spatial inhomogeneous (weakly or strongly localized) pump. The LLE is derived, in the extended adiabatic approximation, from the underlying Zakharov system (ZS), which includes a viscosity term, acting on its low-frequency (LF) component, and the pump supporting the high-frequency (HF) one. Dynamics of quasi-solitons in the model is addressed by means of analytical and numerical methods. The sech-based approximation for the quasi-soliton predicts it as a stable fixed point (FP) of the system of evolution equations for the moments of the system moments (the HF norm, wave momentum, and center-of-mass coordinate). The attraction basin of the FP is identified too. The prediction is corroborated by direct simulations of the full LLE. A quasi-singular mode, supported by the delta-functional pump, is briefly considered too.