Tracking down localized modes in PT-symmetric Hamiltonians under the influence of a competing nonlinearity

TL;DR

This paper investigates localized modes in PT-symmetric optical systems with nonlinearities, analyzing their stability and bifurcation behavior through a systematic study of a nonlinear Schrödinger model with novel potentials.

Contribution

It introduces two new families of PT-symmetric potentials in nonlinear Schrödinger systems and analyzes the stability and bifurcation of localized modes within this framework.

Findings

Localized eigenmodes are generated for the new potentials.

Linear stability analysis reveals bifurcation points where eigenvalues transition.

Transition to imaginary eigenvalues indicates a change in mode stability.

Abstract

The relevance of parity and time reversal (PT)-symmetric structures in optical systems is known for sometime with the correspondence existing between the Schrodinger equation and the paraxial equation of diffraction where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrodinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation charaterized by the parameter of perturbative growth rate passing through zero where a transition to imaginary eigenvalues occurs.