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

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.