The goal of the work outlined in this proposal is to build a more complete understanding of spatially localized structures in quadratically nonlinear parametric gain devices, focusing on the stability and dynamics of these structures in a self-heated medium. The scope of the proposed work includes the development of a numerical model capable of incorporating the multiple temporal and spatial scales necessary to characterize the impact of absorption-induced heating of the parametric gain media, and analysis of more tractable model equations such as the parametrically driven nonlinear Schroedinger equation coupled to the one- or two-dimensional heat equation.
This research is important for several reasons. The most immediate of these lies in its applicability to parametric gain devices, such as optical parametric oscillators, used for conversion of optical fields to frequencies in the far-infrared region. Such devices are very important for spectroscopic applications, including the detection of environmentally harmful agents or chemical weapons, and for military countermeasures, including jamming of infrared-based missile guidance systems. From a more theoretical standpoint, the proposed research draws from several areas that have recently made significant advances in maturity, including multiscale simulation techniques, rigorous collective coordinate reductions, and the dynamics of patterns in dissipative equations.
