EVENT DETAILS AND ABSTRACT

Title: Understanding control strategies for resonant waves interactions using geometric techniques
Speaker: Professor Gregory Luther
Speaker Info: Northwestern U.
Brief Description:
Special Note:
Abstract:

Resonant wave interactions provide a generic mechanism for instabilities by transferring energy among waves. In optical systems these instabilities have been harnessed for a broad range of technologies. They have been used to make tunable sources of laser light, all-optical switches, and soliton amplifiers. Essential difficulties for these technologies are the lack of materials with large nonlinear response and the need for careful alignment of crystalline materials. Considered from a dynamical systems perspective, the central issue in the design of these devices is to control a collection of resonantly coupled waves.

In this talk the Hamiltonian structure of resonant wave interactions will be described with an emphasis on using symmetry reduction to understand their dynamics on reduced phase spaces. Control techniques are devised in this setting to improve the effective nonlinear response of optical materials and to reduce the requirements for alignment. The quasi-phase-matching technique will be examined explicitly.