Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings

Cinthya Rivas; Manuel E. Solano; Rodolfo Rodríguez; Peter B. Monk; Akhlesh Lakhtakia

doi:10.1364/JOSAA.34.000068

Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings

Cinthya Rivas, Manuel E. Solano, Rodolfo Rodríguez, Peter B. Monk, Akhlesh Lakhtakia

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We have formulated an asymptotic model for implementation in the finite-element method to calculate diffraction from a planar multilayered structure having a shallow surface-relief grating. The thin grating layer containing the shallow grating is replaced by a planar interface with transmission conditions that differ from the standard continuity conditions, thereby eliminating the necessity of representing the grating layer by a fine mesh. The parameters defining the shallow surface-relief grating are thereby removed from the geometry to the transmission conditions. Adoption of the asymptotic model will considerably reduce the computational cost of optimizing the grating shape because there is no need to re-mesh at every optimization step.

Original language	English (US)
Pages (from-to)	68-79
Number of pages	12
Journal	Journal of the Optical Society of America A: Optics and Image Science, and Vision
Volume	34
Issue number	1
DOIs	https://doi.org/10.1364/JOSAA.34.000068
State	Published - Jan 1 2017

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
Atomic and Molecular Physics, and Optics
Computer Vision and Pattern Recognition

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10.1364/JOSAA.34.000068

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title = "Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings",

abstract = "We have formulated an asymptotic model for implementation in the finite-element method to calculate diffraction from a planar multilayered structure having a shallow surface-relief grating. The thin grating layer containing the shallow grating is replaced by a planar interface with transmission conditions that differ from the standard continuity conditions, thereby eliminating the necessity of representing the grating layer by a fine mesh. The parameters defining the shallow surface-relief grating are thereby removed from the geometry to the transmission conditions. Adoption of the asymptotic model will considerably reduce the computational cost of optimizing the grating shape because there is no need to re-mesh at every optimization step.",

author = "Cinthya Rivas and Solano, {Manuel E.} and Rodolfo Rodr{\'i}guez and Monk, {Peter B.} and Akhlesh Lakhtakia",

note = "Funding Information: Comisi{\'o}n Nacional de Investigaci{\'o}n Cient{\'i}fica y Tecnol{\'o}gica (CONICYT) (Fondecyt-1160320, BASAL PFB-03); National Science Foundation (NSF) (DMS-1619901, DMS-1619904). Publisher Copyright: {\textcopyright} 2016 Optical Society of America.",

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AU - Rivas, Cinthya

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AU - Rodríguez, Rodolfo

AU - Monk, Peter B.

AU - Lakhtakia, Akhlesh

N1 - Funding Information: Comisión Nacional de Investigación Científica y Tecnológica (CONICYT) (Fondecyt-1160320, BASAL PFB-03); National Science Foundation (NSF) (DMS-1619901, DMS-1619904). Publisher Copyright: © 2016 Optical Society of America.

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N2 - We have formulated an asymptotic model for implementation in the finite-element method to calculate diffraction from a planar multilayered structure having a shallow surface-relief grating. The thin grating layer containing the shallow grating is replaced by a planar interface with transmission conditions that differ from the standard continuity conditions, thereby eliminating the necessity of representing the grating layer by a fine mesh. The parameters defining the shallow surface-relief grating are thereby removed from the geometry to the transmission conditions. Adoption of the asymptotic model will considerably reduce the computational cost of optimizing the grating shape because there is no need to re-mesh at every optimization step.

AB - We have formulated an asymptotic model for implementation in the finite-element method to calculate diffraction from a planar multilayered structure having a shallow surface-relief grating. The thin grating layer containing the shallow grating is replaced by a planar interface with transmission conditions that differ from the standard continuity conditions, thereby eliminating the necessity of representing the grating layer by a fine mesh. The parameters defining the shallow surface-relief grating are thereby removed from the geometry to the transmission conditions. Adoption of the asymptotic model will considerably reduce the computational cost of optimizing the grating shape because there is no need to re-mesh at every optimization step.

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Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings

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