Modeling, Analysis, and Computation of Diffractive and Nano Optics

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The mathematical modeling techniques and computational methods developed in this project will address key scientific challenges in applied mathematics including three-dimensional electromagnetic wave propagation in periodic chiral or nonlinear structures; global uniqueness and numerical solution of the ill-posed inverse diffraction problems; adaptive techniques for solving linear and nonlinear Maxwell's equations; second harmonic generation in dielectric and metallic nonlinear optical media; and multiscale modeling, analysis, and computation of optical responses of nano structures.The recent enabling technologies of high-performance computing facilities and microlithographic fabrication techniques have led to applications of diffraction from subwavelength structures, establishing diffractive optics and nano optics as two of the most rapidly advancing areas of current research in optical engineering. Possible application include: fast optical switches that are a key element of purely optical computers; plasmonic materials and optical metamaterials, which are leading to really amazing technological innovations, such as "invisibility cloaks" and "superlenses"; near-field or super-resolution optical microscopy that allows to observe objects that a smaller than the light wavelength, etc. The substantial growth of significant applications of diffractive and nano optics has driven the need for novel mathematical models and numerical algorithms. Accurate modeling of electromagnetic fields within these materials presents challenging mathematical questions both in theory and computation. Our computational models and optimal design tools will provide an inexpensive and easily controllable virtual prototype of the structures in the design and fabrication of optical devices. The research results will benefit the optics industry and nano technology.