Optimization methods for achieving high diffraction efficiency with perfect electric conducting gratings.
J Opt Soc Am A Opt Image Sci Vis
; 37(8): 1316-1326, 2020 Aug 01.
Article
en En
| MEDLINE
| ID: mdl-32749266
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.
Texto completo:
1
Colección:
01-internacional
Banco de datos:
MEDLINE
Idioma:
En
Revista:
J Opt Soc Am A Opt Image Sci Vis
Asunto de la revista:
OFTALMOLOGIA
Año:
2020
Tipo del documento:
Article