Computational Electromagnetic Methods in Nonlinear Optics and Microwave Material Processing

DMS-9803568 Cheryl V. Hile TECHNICAL DESCRIPTION --------------------- The research in this project focuses on the development of efficient computational electromagnetic methods that will be utilized to gain a fundamental understanding of (1) ultrashort pulse propagation in nonlinear optical fibers and devices and (2) microwave material processing systems. The first project focuses on understanding the behavior of ultrashort pulse propagation in nonlinear optics fibers and devices by (1) developing computational solutions of Maxwell's equations and (2) determining the extent to which asymptotic envelope approximations can be used to describe these pulses. Specifically, we develop computational solutions of Maxwell's equations to understand the behavior of one-dimensional pulse propagation near the zero dispersion wavelength in dispersion-shifted optical fibers and to understand the behavior of two-dimensional pulse propagation of ultrashort spatial solitons. In parallel with this, we derive corresponding envelope equations and determine the extent to which these more simplified equations can be used to model ultrashort pulse propagation near the zero dispersion wavelength and two-dimensional pulse propagation of ultrashort spatial solitons. The second project focuses on the development of efficient hybrid numerical methods to model microwave material processing in single- and multi-mode cavity heating systems. We will begin by developing an efficient hybrid numerical method to model the electromagnetic interaction of a low-loss ceramic in a high-Q single-mode waveguide applicator. Finally, we will extend these ideas to create a hybrid numerical method for modeling high-Q multi-mode cavity heating systems. NON-TECHNICAL DESCRIPTION ------------------------- The research in this project focuses on the development of efficient computational electromagnetic methods that will be utilized to gain a fundamental understanding of (1) ultrashort pulse propagation in nonlinear optical fibers and devices and (2) microwave material processing systems. Understanding these complex phenomena and processes is essential for the development of new optical technologies and the industrial production of high quality materials and products. The first aspect of this project focuses on understanding the behavior of ultrashort pulse propagation in nonlinear optics fibers and devices by (1) developing computational solutions of Maxwell's equations and (2) determining the extent to which asymptotic envelope approximations can be used to describe these pulses. The second aspect of this project focuses on the development of efficient hybrid numerical methods to model microwave material processing in single- and multi-mode cavity heating systems. These numerical methods will provide detailed knowledge of the interaction between the waveguide applicator, the electromagnetics fields and the ceramic in these microwave heating systems. Detailed knowledge of this interaction will lead to a more complete characterization of the heating process and thereby help to prevent nonuniform heating and lead to future optimizations of the heating process.