Optimization methods for achieving high diffraction efficiency with perfect electric conducting gratings

Rubén Aylwin, Gerardo Silva-Oelker, Carlos Jerez-Hanckes, Patrick Fay

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

4 Citas (Scopus)


This work presents the implementation, numerical examples, and experimental convergence study of first- and second-order optimization methods applied to one-dimensional periodic gratings. Through boundary integral equations and shape derivatives, the profile of a grating is optimized such that it maximizes the diffraction efficiency for given diffraction modes for transverse electric polarization. We provide a thorough comparison of three different optimization methods: a first-order method (gradient descent); a second-order approach based on a Newton iteration, where the usual Newton step is replaced by taking the absolute value of the eigenvalues given by the spectral decomposition of the Hessian matrix to deal with non-convexity; and theBroyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, a quasi-Newton method. Numerical examples are provided to validate our claims. Moreover, two grating profiles are designed for high efficiency in the Littrow configuration and then compared to a high efficiency commercial grating. Conclusions and recommendations, derived from the numerical experiments, are provided aswell as future research avenues.

Idioma originalInglés
Páginas (desde-hasta)1316-1326
Número de páginas11
PublicaciónJournal of the Optical Society of America B: Optical Physics
EstadoPublicada - 1 ago. 2020
Publicado de forma externa


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