TY - JOUR

T1 - Optimization methods for achieving high diffraction efficiency with perfect electric conducting gratings

AU - Aylwin, Rubén

AU - Silva-Oelker, Gerardo

AU - Jerez-Hanckes, Carlos

AU - Fay, Patrick

N1 - Publisher Copyright:
© 2020 Optical Society of America.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85089162554&partnerID=8YFLogxK

U2 - 10.1364/JOSAA.394204

DO - 10.1364/JOSAA.394204

M3 - Article

C2 - 32749266

AN - SCOPUS:85089162554

SN - 0740-3224

VL - 37

SP - 1316

EP - 1326

JO - Journal of the Optical Society of America B: Optical Physics

JF - Journal of the Optical Society of America B: Optical Physics

IS - 8

ER -