Mathematical studies in rigorous grating theory.

Mathematics

Scientific paper

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Gratings: Optical Design, Gratings: Polarization

Scientific paper

The authors consider the diffraction of a time-harmonic wave incident upon a grating (or periodic) structure. They study mathematical issues that arise in the direct modeling, inverse, and optimal design problems. Particular attention is paid to the variational approach and to finite-element methods. For the direct problem various results on existence, uniqueness, and numerical approximations of solutions are presented. Convergence properties of the variational method and sensitivity to TM polarization are examined. Their recent research on inverse diffraction problems and optimal design problems is also discussed.

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