Trapping wave fields in an expulsive potential by means of linear coupling

TL;DR

This paper demonstrates the existence and stability of confined wave states in coupled 1D and 2D systems with harmonic and anti-harmonic potentials, relevant for optical and BEC applications.

Contribution

It introduces exact and numerical solutions for confined states in linearly-coupled systems with mixed potentials, including vortex states and bound states in continuum.

Findings

Exact solutions for ground and dipole modes in 1D

Exact solutions for ground and vortex states in 2D

Stability of states under nonlinear interactions

Abstract

We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly-coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component, and an expulsive anti-HO potential acting upon the other. The systems ca be implemented in optical and BEC dual-core waveguides. In the 1D linear system, codimension-one solutions are found in an exact form for the ground state (GS) and dipole mode (the first excited state). Generic solutions are produced by means of the variational approximation, and are found in a numerical form. Exact codimension-one solutions and generic numerical ones are also obtained for the GS and vortex states in the 2D system (the exact solutions are found for all values of the vorticity). Both the trapped and anti-trapped components of the bound states may be dominant ones, in terms of the norm. The localized modes may be categorized as bound states in continuum, as they coexist with delocalized ones. The 1D states, as well as the GS in 2D, are weakly affected and remain stable if the self-attractive or repulsive nonlinearity is added to the system. The self-attraction makes the vortex states unstable against splitting, while they remain stable under the action of the self-repulsion.