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

本提案中概述的工作目标是建立对二次非线性参数增益器件的空间局部化结构的更完整的理解，重点关注这些结构在自热介质中的稳定性和动力学。提出的工作范围包括开发一个能够结合多时间和空间尺度的数值模型，以表征参数增益介质的吸收引起的加热的影响，并分析更易于处理的模型方程，如参数驱动的非线性薛定谔方程耦合到一维或二维热方程。这项研究之所以重要，有几个原因。其中最直接的是它对参数增益器件的适用性，例如光学参数振荡器，用于将光场转换为远红外区域的频率。这种装置对于光谱应用非常重要，包括对环境有害的试剂或化学武器的探测，以及军事对抗，包括干扰基于红外的导弹制导系统。从更理论的角度来看，所提出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、严格的集体坐标约简和耗散方程的模式动力学。

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.