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.
© 2020 Optical Society of America
Full Article | PDF ArticleMore Like This
Jingjing Yu, Qin Tang, Qiyue Li, Hongbo Guo, and Xiaowei He
J. Opt. Soc. Am. A 37(6) 1060-1066 (2020)
Jinze Sha, Andrew Kadis, Fan Yang, Youchao Wang, and Timothy D. Wilkinson
J. Opt. Soc. Am. A 40(4) B25-B32 (2023)
Lifeng Li
J. Opt. Soc. Am. A 41(2) 252-260 (2024)