Nonlinear Beam Propagation in a Class of Complex Non-PT -Symmetric Potentials

TL;DR

This paper investigates nonlinear beam propagation in complex potentials that are close to, but not exactly, PT-symmetric, revealing that optimized beam profiles remain stable over propagation despite the lack of exact stationary solutions.

Contribution

It introduces a method to analyze nonlinear beam dynamics in non-PT-symmetric complex potentials and demonstrates stability of optimized profiles in such settings.

Findings

Optimized beam profiles exhibit stability during propagation in certain parameter regimes.

Departure from PT-symmetry prevents exact stationary solutions but does not significantly alter beam dynamics.

Weak growth or decay observed but profiles remain largely unchanged over distance.

Abstract

The subject of PT-symmetry and its areas of application have been blossoming over the past decade. Here, we consider a nonlinear Schr\"odinger model with a complex potential that can be tuned controllably away from being PT-symmetric, as it might be the case in realistic applications. We utilize two parameters: the first one breaks PT-symmetry but retains a proportionality between the imaginary and the derivative of the real part of the potential; the second one, detunes from this latter proportionality. It is shown that the departure of the potential from the PT -symmetric form does not allow for the numerical identification of exact stationary solutions. Nevertheless, it is of crucial importance to consider the dynamical evolution of initial beam profiles. In that light, we define a suitable notion of optimization and find that even for non PT-symmetric cases, the beam dynamics, both in 1D and 2D -although prone to weak growth or decay- suggests that the optimized profiles do not change significantly under propagation for specific parameter regimes.