Optimization methods for achieving high diffraction efficiency with perfect electric conducting gratings
Abstract
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 the Broyden-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 as well as future research avenues.
Cite
@article{arxiv.2004.02029,
title = {Optimization methods for achieving high diffraction efficiency with perfect electric conducting gratings},
author = {Rubén Aylwin and Gerardo Silva-Oelker and Carlos Jerez-Hanckes and Patrick Fay},
journal= {arXiv preprint arXiv:2004.02029},
year = {2020}
}
Comments
\c{opyright} [2020 Optical Society of America]. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited. https://www.osapublishing.org/josaa/abstract.cfm?uri=josaa-37-8-1316