Diffraction in Periodic Structures and Optimal Design of Binary Gratings. Part II: Gradient Formulas for TM Polarization

Abstract

This paper provides the mathematical foundation of analytic formulae for derivatives of TM reflection and transmission coefficients of diffraction gratings with respect to geometric parameters of non-smooth grating profiles and interfaces. This problem arises in optimal design problems for those optical devices studied in Part I. The derivatives can be expressed by contour integrals involving the direct and adjoint solutions of TM diffraction problems.KeywordsPeriodic StructureTransmission CoefficientCorner PointContour IntegralDiffraction ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.