Nonlinear optical catastrophe and dark spatial solitons

This thesis covers different spatial nonlinear optical effects that occur in self-defocusing media. The first effect is the power-dependent evolution of an elliptical Gaussian beam, e.g., the development of peripheral vortex quadrupoles at low powers and a nonlinear cusp diffraction catastrophe at high powers. Up to three quadrupoles were observed, each appearing after equal increments of beam power. Our analysis of this discovery shows that the incremental power is related to the net phase change needed to support a quadrupole. At higher incident power we found a complex interference pattern in the center of the beam that was attributed to the nonlinear cusp catastrophe. By varying the thickness of the liquid column we traced the development of the catastrophe back to an annular ellipse in the middle of the nonlinear cell. Results of this study may be applied to the analysis of patterns appearing when a high-power astigmatic beam is transmitted through a gas or liquid.; The second effect concerns the propagation of a single optical vortex in Kerr and thermal defocusing nonlinear optical media. We numerically investigated the abrupt contraction of a vortex whose core size was initially larger than the soliton size. The contraction is accompanied by a bright ring around the vortex core which supports the reduced vortex size over distances exceeding the characteristic nonlinear distance. In thermal medium, the contraction depends on time due to the diffusion of heat into the vortex core. The contraction of the vortex core may be an advantageous feature for optical modulators or transistors, where the vortex beam induces a dynamic waveguide for a signal-carrying beam.; Lastly, we experimentally investigated the power-dependent arrangement of a periodic array of one-dimensional dark solitons. The initial field of the soliton array was produced with the aid of computer-generated holography. A unit cell of the array contained a pair of solitons propagating in opposite transverse directions. The speed of each soliton depends on power and thus the solitons are made to collide by increasing the value of power. We observed collisions of up to three pairs of counterpropagating solitons. This experiment prototypes an all-optical switch based on dark solitons.