@article{b86540492f8442b19c9f063cf54a8f80,
title = "Quantifying the Impact of Random Surface Perturbations on Reflective Gratings",
abstract = "We present a novel deterministic method capable of calculating statistical moments of transverse electric polarized fields scattered by perfect electric conductor gratings with small surface random perturbations. Based on a first-order shape Taylor expansion, the resulting electric field integral equations are solved via the method of moments with constant hierarchical basis or Haar wavelets. This allows for a sparse tensor approximation, significantly reducing the number of required unknowns and yielding a higher rate of convergence than a dense approximation. Moreover, the proposed approach converges faster than Monte Carlo simulations with significantly less computational effort. Validation of the proposed approach is performed for several cases, and realistic simulations applied to the calculation and prediction of grating efficiency reveal the applicability of the method.",
keywords = "Gratings, moment methods, random media, surfaces, uncertainty, wavelets",
author = "Gerardo Silva-Oelker and Ruben Aylwin and Carlos Jerez-Hanckes and Patrick Fay",
note = "Funding Information: Manuscript received May 2, 2017; revised October 4, 2017; accepted November 27, 2017. Date of publication December 7, 2017; date of current version February 1, 2018. This work was supported in part by the Comisi{\'o}n Nacional de Investigaci{\'o}n Cient{\'i}fica y Tecnol{\'o}gica under Grant CONICYT-PCHA/Doctorado Nacional/2013-21130829, in part by the Fondo Nacional de Desarrollo Cient{\'i}fico y Tecnol{\'o}gico under Grant Regular 1171491, in part by the Conicyt Programa de Investigaci{\'o}n Asociativa under Grant ACT 1417, in part by the CORFO 2030 Seed Fund under Grant ND-PUC 201505, and in part by the VRA Programa de Intercambio Acad{\'e}mico Universidad Cat{\'o}lica—Notre Dame 2015. (Corresponding author: Carlos Jerez-Hanckes.) G. Silva-Oelker is with the Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556 USA, and also with the Electrical Engineering Department, School of Engineering, Pontificia Universidad Cat{\'o}lica de Chile, Santiago 7820436, Chile. Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",
year = "2018",
month = feb,
doi = "10.1109/TAP.2017.2780902",
language = "English",
volume = "66",
pages = "838--847",
journal = "IEEE Transactions on Antennas and Propagation",
issn = "0018-926X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "2",
}