Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling

TL;DR

This paper investigates a 2D nonlinear Schrödinger lattice modeling waveguide arrays, revealing poor mobility of localized modes despite zero energy difference, and demonstrating flexible power flow control with potential applications in optical devices.

Contribution

It introduces a detailed analysis of nonlinear coupling effects on waveguide array dynamics, including stability, mobility, and power control, with novel insights into complex mode structures and tunable currents.

Findings

Poor mobility of localized excitations despite zero Peierls-Nabarro barrier.

Flexible power flow control with amplitude-dependent directionality.

Existence of complex modes like breathers and vortices with stability regimes.

Abstract

A two-dimensional nonlinear Schrodinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy difference (Peierls-Nabarro barrier) of fundamental stationary modes the mobility of localized excitations is very poor. This is attributed to a large separation in parameter space of the bifurcation points of the involved stationary modes. At these points the stability of the fundamental modes is changed and an asymmetric intermediate solution appears that connects the points. The control of the power flow across the array when excited with plane waves is also addressed and shown to exhibit great flexibility that may lead to applications for power-coupling devices. In certain parameter regimes, the direction of a stable propagating plane-wave current is shown to be continuously tunable by amplitude variation (with fixed phase gradient). More exotic effects of the nonlinear coupling terms like compact discrete breathers and vortices, and stationary complex modes with non-trivial phase relations are also briefly discussed. Regimes of dynamical linear stability are found for all these types of solutions.