| With the advent of high-bandwidth optical communications, the need for switching technologies capable of handling this information flow becomes imperative. Optical switches are the natural technology to investigate because they eliminate the optical/electronic conversion and their operation can scale with the data rate, unlike electronics. Additional capabilities can be provided through the development of optical logic gates, which have the further properties of data regeneration, gain, cascadability, and the ability to implement more complex operations than possible with a simple switch.; The goal of this work is to study in-depth an implementation of optical logic gates based on spatial and spatio-temporal solitons. Optical solitons propagate long distances without change and have additional properties that are beneficial for the representation of binary data such as stability to perturbations and existence above a threshold power or energy. The non-diffracting nature of spatial optical solitons lends to their use in a class of angular deflection logic gates in which a weak signal can alter the propagation of a strong pump in order to change the device state from high to low, thereby implementing a controlled inverter which is cascadable to produce logically-complete, multi-input NOR.; A significant portion of this work is devoted to developing a theoretical and numerical framework to describe general, multi-dimensional, nonlinear spatio-temporal wave phenomena. This is accomplished by starting directly from Maxwell's equations and deriving via the multiple-scales perturbation technique a first-order, fully-vectorial, nonlinear wave equation, that is valid beyond the standard slowly-varying amplitude, slowly-varying envelope, and paraxial approximations. In addition to coupling with the orthogonal transverse field, vector coupling with the weak longitudinally-projected field is also treated, along with the cascaded interaction with a weak third-harmonic wave which can produce a desirable saturation effect.; Reduced forms of this wave equation are solved numerically to study the spatial collision and dragging interactions between orthogonally-polarized spatial solitons and spatio-temporal solitary waves. These interactions, which are of the class of three-terminal angular deflection gates, provide complete logic-level restoration, fanout of two or greater with large noise margin, and cascadability. In addition, the spatio-temporal logic gates are expected to have nJ to pJ switching energies using enhanced nonlinear media, and ps switching times through temporal pipelined operation. |
