Metastable two-component solitons near an exceptional point

Abstract

We consider a two-dimensional nonlinear waveguide with distributed gain and losses. The optical potential describing the system consists of an unperturbed complex potential depending only on one transverse coordinate, i.e., corresponding to a planar waveguide, and a small non-separable perturbation depending on both transverse coordinates. It is assumed that the spectrum of the unperturbed planar waveguide features an exceptional point (EP), while the perturbation drives the system into the unbroken phase. Slightly below the EP, the waveguide sustains two-component envelope solitons. We derive one-dimensional equations for the slowly varying envelopes of the components and show their stable propagation. When both traverse directions are taken into account within the framework of the original model, the obtained two-component bright solitons become metastable and persist over remarkably long propagation distances.

9 pages, 5 figures; several typos corrected; final version

References in corpus (7)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Nonlinear Schrödinger equation for a PT symmetric delta-functions double well
• Phase transition through the splitting of self-dual spectral singularity in optical potentials
• New classes of non-parity-time-symmetric optical potentials with all-real spectra and exceptional-point-free phase transition
• PT-symmetric Double Well Potentials Revisited: Bifurcations, Stability and Dynamics
• Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons

Cited by in corpus (5)

• Features, paradoxes and amendments of perturbative non-Hermitian quantum mechanics
• Phase transitions in quasi-Hermitian quantum models at exceptional points of order four
• Emergence and localization of exceptional points in an exactly solvable toy model
• Triple exceptional point with unitary paths of unfolding in a three-site fermionic Swanson-like model
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics