Collaborative Research: Patterns, Stability, and Thermal Effects in Parametric Gain Devices

这项工作的目标是建立对空间局域结构的更完整的理解，这些结构通常是非线性的参数增益器件，重点是这些结构在自热介质中的稳定性和动力学。这项工作的范围包括发展一个能够包含描述参数增益介质的吸收诱导加热的影响所需的多时间和空间尺度的数值模型，以及分析更容易处理的模型方程，例如参数驱动的非线性薛定谔方程与一维或二维热方程的耦合。其中最重要的一点在于它对参数增益器件的适用性，例如用于将光场转换为远红外区频率的光学参量振荡器。这类设备对于光谱应用，包括环境有害物质或化学武器的探测，以及军事对抗，包括对红外基导弹制导系统的干扰，都是非常重要的。从更理论的角度来看，拟议的研究借鉴了最近取得重大进展的几个领域，包括多尺度模拟技术、严格的集体坐标简化和耗散方程中图案的动力学。

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.