Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimization methods for achieving high diffraction efficiency with
  perfect electric conducting gratings   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.

4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ