Darran Edmundson

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction of spatial solitons.

Ring Vortex Solitons in Nonlocal Nonlinear Media

Stable two-dimensional vortex solitons are formed using a nonlocal nonlinear model. Nonlocality stabilizes otherwise unstable vortex beams in the case of single or higher charge fundamental vortices as well as higher order vortex solitons.

Nonlocal incoherent solitons in materials with a logarithmic nonlinearity

We study the propagation of partially coherent beams in spatially nonlocal nonlinear materials with a logarithmic nonlinearity. We describe analytically the beam evolution and find conditions for the formation of nonlocal incoherent solitons.

Bright and dark spatial solitons in a nonlocal Kerr-like medium

We consider the phenomenological model of the nonlocal Kerr-type nonlinear medium. We obtain the nonlinear Schroedinger equation describing propagation of the one-dimensional optical beam in a weakly nonlinear medium. It turns out that this nonlinear equation can be exactly solved for both focusing and defocusing nonlinearity. In this way one can obtain the intensity profile of bright and dark solitons as a function of the nonlocality parameter. An important aspect of any soliton solution is its stability. Using the well known stability criteria developed for 1D solitons, we found that bright as well as dark spatial solitons in weakly nonlocal nonlinear medium are stable. We confirmed this result by numerical simulation of the propagation equation using exact soliton solutions as initial condition. Solitons propagate in stable fashion over a distances of many diffraction lengths. We also studied collisions of these solitons. We found that, for large intersecting angle, the collision is basically elastic. However, for small angle (long interaction) nonlocal solitons collide inelastically, in analogy to solitons of other nonintegrable models. An example of inelastic collision of two identical nonlocal dark solitons is shown.

A unified approach to self-trapped partially coherent beams in logarithmically nonlinear media

The subject of incoherent (or partially coherent) spatial solitons has attracted lots of attention recently [1-12]. The light beam generated by the incoherent light source exhibits some level of randomness of phase between any two points.