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

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)1316-1326
Number of pages11
JournalJournal of the Optical Society of America B: Optical Physics
Issue number8
StatePublished - 1 Aug 2020
Externally publishedYes


Dive into the research topics of 'Optimization methods for achieving high diffraction efficiency with perfect electric conducting gratings'. Together they form a unique fingerprint.

Cite this