Strong asymmetry for surface modes in nonlinear lattices with long-range coupling

TL;DR

This paper investigates how long-range interactions in nonlinear lattices influence the formation and properties of surface localized modes, revealing asymmetries between focusing and defocusing cases and identifying power thresholds for mode excitation.

Contribution

It demonstrates that long-range coupling causes significant asymmetries in surface mode topology and power thresholds, a phenomenon previously underexplored in nonlinear lattice systems.

Findings

Long-range interactions induce asymmetry between focusing and defocusing cases.

Upper power thresholds exist for exciting staggered modes in defocusing lattices.

Power thresholds for surface mode excitation vary with long-range coupling strength.

Abstract

We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially-decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the focusing and defocusing cases for the topology of the surface modes and also for the minimum power needed to generate them. In particular, for the defocusing case, there is an upper power threshold for exciting staggered modes, which depends strongly on the long-range coupling strength. The power threshold for dynamical excitation of surface modes increase (decrease) with the strength of long-range coupling for the focusing (defocusing) cases. These effects seem to be generic for discrete lattices with long-range interactions.