Localized modes in $\chi^{(2)}$ media with $\PT$-symmetric localized potential

TL;DR

This paper investigates the existence, stability, and bifurcation properties of localized solitons in $ ext{PT}$-symmetric quadratic nonlinear media, revealing stable families, bifurcation behaviors, and the impact of gain/loss parameters.

Contribution

It presents the first detailed analysis of soliton bifurcations and stability in $ ext{PT}$-symmetric $ ext{chi}^{(2)}$ media with localized potential, including new bifurcation phenomena.

Findings

Stable one and two hump solitons are identified.

Fundamental branch power is limited and decreases with gain/loss strength.

Modes from the second harmonic can exist beyond $ ext{PT}$ symmetry breaking threshold.

Abstract

We study the existence and stability of solitons in the quadratic nonlinear media with spatially localized ${\cal PT}$-symmetric modulation of the linear refractive index. Families of stable one and two hump solitons are found. The properties of nonlinear modes bifurcating from a linear limit of small fundamental harmonic field are investigated. It is shown that the fundamental branch, bifurcating from the linear mode of the fundamental harmonic is limited in power. The power maximum decreases with the strength of the imaginary part of the refractive index. The modes bifurcating from the linear mode of the second harmonic can exist even above ${\cal PT}$ symmetry breaking threshold. We found that the fundamental branch bifurcating from the linear limit can undergo a secondary bifurcation colliding with a branch of two-hump soliton solutions. The stability intervals for different values of the propagation constant and gain/loss gradient are obtained. The examples of dynamics and excitations of solitons obtained by numerical simulations are also given.