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

Abstract

We study the existence and stability of solitons in the quadratic nonlinear media with spatially localized $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$ 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.

References in corpus (4)

• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Solitons in PT-symmetric nonlinear lattices
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x

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