Four main bodies of work are presented. The first is a summary of two dimensional type II parametric solitons. Exact stationary solutions were obtained by direct Newton-Raphson style relaxation for radially symmetric forms, and by conjugate gradient methods for full two dimensional forms. Signal and idler energy balanced and imbalanced solitons were observed, as also were radially asymmetric, or elliptical, solitons. Type II parametric band gap solitons were also considered. Details of the application of the two relaxation methods stated above are also presented.
Secondly, an all-optical AND logic gate utilising type II parametric soliton formation in a planar waveguide is demonstrated by numerical simulation. Switching performance as a function of input logic simultaneity and internal geometry is investigated, with a highly digital response in the transmitted pulse energy observed. This was found to be due to bi-stability in the soliton formation process. The performance of this concept when utilising frequency degenerate type I interaction was also briefly investigated, and was found to be highly sensitive to the relative phasing between the input pulses. Finally, the incorporation of photonic crystal technology into this concept was also considered. This entailed the use of a detuned longitudinal parametric Bragg grating to increase the interaction of the optical pulses and also cause enhanced dispersion effects. Unfortunately, this caused the interaction to become more sensitive to timing errors in the input pulses and bi-stable switching was no longer observed.
Thirdly, a device for performing all-optical digital signal regeneration utilising type II parametric interaction within a one dimensional waveguide was investigated. Significantly, it was found to perform full 4-R (re-amplifying, re-timing, re-shaping, and re-tuning) signal regeneration. Being based on a femtosecond time scale interaction, bandwidths of order 10—lOOTHz are achievable with this technology. A provisional patent for this device has been obtained, and the full patent is currently pending. As above, the incorporation of photonic crystal technology into this concept was also considered. Qualitatively similar performance was obtained.
Finally, a summary of the design and development of the open source software package, xmds, is presented, xmds is a code generator. It processes an input script written in a tailored subset of xml, and subsequently writes and compiles a C code listing dedicated to solving the problem described. Highly efficient code is obtained as a result, while retaining a flexible approach that is capable of solving a wide range of problems - from simple ODEs up to complex multi-mode multi-dimensional nonlinear stochastic PDEs.