Patterns, Stability, and Thermal Effects in Parametric Gain Devices

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The goal of the work outlined in this proposal is to build a morecomplete understanding of spatially localized structures inquadratically nonlinear parametric gain devices, focusing on thestability and dynamics of these structures in a self-heatedmedium. The scope of the proposed work includes the developmentof a numerical model capable of incorporating the multipletemporal and spatial scales necessary to characterize the impactof absorption-induced heating of the parametric gain media, andanalysis of more tractable model equations such as theparametrically driven nonlinear Schroedinger equation coupled tothe one- or two-dimensional heat equation.This research is important for several reasons. The mostimmediate of these lies in its applicability to parametric gaindevices, such as optical parametric oscillators, used forconversion of optical fields to frequencies in the far-infraredregion. Such devices are very important for spectroscopicapplications, including the detection of environmentally harmfulagents or chemical weapons, and for military countermeasures,including jamming of infrared-based missile guidance systems.From a more theoretical standpoint, the proposed research drawsfrom several areas that have recently made significant advances inmaturity, including multiscale simulation techniques, rigorouscollective coordinate reductions, and the dynamics of patterns indissipative equations.