Solitons and vortices in honeycomb defocusing photonic lattices

TL;DR

This paper investigates the existence, stability, and dynamics of solitons, vortices, and necklaces in a honeycomb photonic lattice with defocusing nonlinearity, revealing stable configurations, bifurcations, and complex behaviors.

Contribution

It provides a theoretical analysis of various localized structures in honeycomb photonic lattices, including their stability and bifurcation behavior, which was not comprehensively studied before.

Findings

Existence of stable dipoles, soliton necklaces, and vortex necklaces.

Bifurcations near the upper edge of the first band lead to asymmetric and exotic solutions.

Unstable structures exhibit breathing oscillations or destruction in simulations.

Abstract

Solitons and necklaces in the first band-gap of a two-dimensional optically induced honeycomb defocusing photonic lattice are theoretically considered. It is shown that dipoles, soliton necklaces, and vortex necklaces exist and may possess regions of stable propagation through a photorefractive crystal. Most of the configurations disappear in bifurcations close to the upper edge of the first band. Solutions associated with such bifurcations are also numerically examined, and it is found that they are often asymmetric and more exotic. The dynamics of the relevant unstable structures are also examined through direct numerical simulations revealing either breathing oscillations or, in some cases, destruction of the original waveform.