9501099 Bao The goal of this proposal is to develop analytic techniques and computational methods for solving inverse and optimal design problems in diffractive optics and wave propagation. The main topics of the proposed work are as follows: stability analysis for inverse scattering problems in diffractive optics, optimal surface design problems, direct modeling of scattering and diffraction in complicated nonlinear optical materials, study of surface enhanced nonlinear optical effects, and regularity analysis of inverse problems in several dimensional wave propagation. Diffractive optics is an emerging technology with many applications. The practical applications of diffractive optics technology have driven the need for both rigorous mathematical models and numerical algorithms to describe the diffraction of complicated grating structures, to compute the electromagnetic vector fields and to predict the performance of any given structure, and to carry out optimal design of new structures. The theory and algorithms help, for example, with the design and fabrication of new and efficient gratings and optical lenses. The work concerning inverse problems in wave propagation can be used to deduce the interior mechanical properties of the earth from the measured boundary data generated by an energy source. This problem arises naturally from reflection seismology, oil and gas exploration, ground-penetrating radar, and many other physical problems.
