Ultrafast Dark Spatial Solitary Wave Propagation Phenomena

Dark spatial solitons are particular solutions to the two-dimensional nonlinear Schrodinger equation for a defocusing nonlinearity. The dark solitons are localized intensity minima existing on a bright optical background that propagate without changing shape. Spatial solitons have been extensively investigated recently because the potential use of these phenomena for optical switching and optical communication applications. Pairs of dark spatial solitons have previously been observed in Na vapor and various thermally nonlinear liquids. Bright spatial solitons have been observed in CS_2 and glass waveguides. Here, we present work showing the first observation of dark spatial solitons in semiconductors and on picosecond timescales. The semiconductor material chosen to perform these experiments is ZnSe. ZnSe is selected because it is known to have an instantaneous defocusing bound electronic component of the nonlinear refractive index at lambda = 532 nm. Also presented will be experimental observations of dark soliton collisions and interactions. The experimental results presented here are consistent with theoretical predictions of various propagation parameters for dark spatial solitons. In the absence of symmetry along the transverse profile of the medium, a new type of solution can emerge: solitons localized at inhomogeneities. Stationary dark surface waves are such solitons. We will derive the solution to the stationary fundamental dark surface wave propagating at an interface between two dissimilar defocusing Kerr media and then find the space of dependent and independent parameters for which the surface wave can exist. This is done by obtaining solutions for the guided wave in terms of the eigenmodes of the two respective media and then matching boundary conditions at the interface in order to obtain the propagation parameters governing the total solution. Next, we will investigate the stability of the dark surface waves in an effort to identify the parameter regime of the fundamental dark surface waves for which stable propagation may be obtained, and also provide an intuitive understanding of the stability criteria in the context of a coupled mode theory argument. The stability will be investigated by numerically launching the appropriate wave, using the split-step algorithm, and following its evolution.