Direct and Inverse Modeling of Diffractive Optics and Near-Field Optics

Michigan State University, East Lansing MI

Investigators

Abstract

This project investigates mathematical issues and develops computational methods for solving important classes of direct and inverse problems in optical diffraction from subwavelength structures. The work is motivated by industrial applications, including scattering and diffraction by linear and nonlinear biperiodic structures (crossed gratings), inverse and optimal design problems in diffractive optics, and near-field optics in periodic and general structures. The research examines three-dimensional electromagnetic wave propagation in periodic structures, ill-posedness for inverse problems, adaptive techniques for solving linear and nonlinear Maxwell equations, and modeling of near-field imaging. New computational methods and mathematical modeling techniques will be developed to solve the underlying direct and inverse problems for near-field optics. New techniques will be developed to deal with the associated linear and nonlinear Maxwell equations for scattering in complex media and structures. We will develop robust solution methods for the associated optimal design, inverse, and imaging problems, to provide guidance for the creation of novel optical devices. <br><br> Micro diffractive optics and near-field optics are fundamental and vigorously growing technologies with diverse applications, including optical computing, communications, laser technology, near-field optical microscopy, imaging of biological samples, and nanotechnology. Because of the small structural features, light propagation in micro-optical structures is generally dominated by diffraction. Accurate modeling of electromagnetic fields within these materials presents challenging and significant mathematical and computational questions. The computational models and optimal design tools developed by this project will provide inexpensive and easily controllable "virtual prototypes" of the structures and media involved in the design of novel optical devices. The research results will be of immediate benefit to the optics industry.