RIA: Investigating the Exact Behavior of Helmholtz Equationin a Collinear Degenerate Four-Wave Mixing Arrangement

点击翻译按钮获取中文摘要

The one-dimensional vectorial Helmholtz equation in nonlinear isotropic Kerr media is one of the most fundamental equations in nonlinear optics. By nature, this equation is capable of describing any one- dimensional optical field configuration in X(3) materials. As a result, it plays a central role in a number of very important and potentially useful nonlinear interactions, such as that of collinear degenerate four-wave mixing and that of optical bistability. However so far, the nonlinear Helmholtz equation in such configurations has been treated approximately. At this stage, it is by no means clear that these approximate techniques provide an accurate enough picture (or even the whole picture) associated with this problem. The exact solution of this problem is very important, first as a matter of principle, then as a way to test already existing theories and finally it may lead to new significant results. It is the purpose of this research proposal to investigate the exact behavior of Helmholtz equation in isotropic nonlinear Kerr media in a comprehensive program, that will involve both analytical and computer simulations. Specific goals in this Research Initiation Award are: a) to identify integrable cases of this equation using Hamiltonian techniques and in turn use them to test previously obtained approximate results. b) to discover totally new phenomena, such as spatial chaos in isotropic Kerr media that may have been overlooked by previous approximate procedures. c) to improve our understanding of wave propagation in X(3) media, which will in turn benefit other associated areas of research.