Vortex solitons at the boundaries of photonic lattices

Dragana Jović,Cornelia Denz,Milivoj Belić

doi:10.1364/oe.19.026232

Abstract

Using numerical analysis we demonstrate the existence of vortex solitons at the edge and in the corners of two-dimensional triangular photonic lattice. We develop a concise picture of their behavior in both single-propagating and counterpropagating beam geometries. In the single-beam geometry, we observe stable surface vortex solitons for long propagation distances only in the form of discrete six-lobe solutions at the edge of the photonic lattice. Other observed solutions, in the form of ring vortex and discrete solitons with two or three lobes, oscillate during propagation in a way indicating the exchange of power between neighboring lobes. For higher beam powers we observe dynamical instabilities of surface vortex solitons and study orbital angular momentum transfer of such vortex states. In the two-beam counterpropagating geometry, all kinds of vortex solutions are stable for propagation distances of the order of typical experimental crystal lengths.

Highlights

Self-trapped nonlinear surface states propagating along the interface of two different media have attracted recently a great deal of interest in different optical systems [1, 2]
Investigating the stability of such vortex solitons, for the single-beam geometry, we find that only the six-lobe edge solutions with small asymmetry are stable during propagation, and can exist for long propagation distances
We have studied surface vortex solitons in truncated 2D photorefractive photonic lattices and revealed the existence of novel types of discrete vortex surface solitons, localized in the lattice corners or at the edges

Summary

Introduction

Self-trapped nonlinear surface states (surface solitons) propagating along the interface of two different media have attracted recently a great deal of interest in different optical systems [1, 2]. Special attention has been devoted to the nonlinear surface vortex solitons Such solitons are supported at the interface of two different optical lattices imprinted in Kerr-type focusing nonlinear media [13] and are demonstrated experimentally at the surface of an optically induced 2D photonic lattice [14]. Recent experimental results [14] predict the existence of stable vortex solitons at the edge of 2D square photonic lattice in the form of four-site vortex solitons, in the single-propagating beam geometry. We demonstrate that in the single-beam geometry, the lattice surface produces a strong stabilizing effect only on the discrete vortex solitons in the form of the six-lobe solutions, enabling them to stably propagate for long distances.

Model and basic equations

Vortex surface states

Soliton instabilities

Conclusion