On the Wiener–Hopf Method for Surface Plasmons: Diffraction from Semiinfinite Metamaterial Sheet

Dionisios Margetis; Matthias Maier; Mitchell Luskin

doi:10.1111/sapm.12180

On the Wiener–Hopf Method for Surface Plasmons: Diffraction from Semiinfinite Metamaterial Sheet

Dionisios Margetis, Matthias Maier, Mitchell Luskin

School of Mathematics

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

7 Scopus citations

Abstract

By formally invoking the Wiener–Hopf method, we explicitly solve a one-dimensional, singular integral equation for the excitation of a slowly decaying electromagnetic wave, called surface plasmon-polariton (SPP), of small wavelength on a semiinfinite, flat conducting sheet irradiated by a plane wave in two spatial dimensions. This setting is germane to wave diffraction by edges of large sheets of single-layer graphene. Our analytical approach includes (i) formulation of a functional equation in the Fourier domain; (ii) evaluation of a split function, which is expressed by a contour integral and is a key ingredient of the Wiener–Hopf factorization; and (iii) extraction of the SPP as a simple-pole residue of a Fourier integral. Our analytical solution is in good agreement with a finite-element numerical computation.

Original language	English (US)
Pages (from-to)	599-625
Number of pages	27
Journal	Studies in Applied Mathematics
Volume	139
Issue number	4
DOIs	https://doi.org/10.1111/sapm.12180
State	Published - Nov 2017

Bibliographical note

Funding Information:
The first author (DM) is indebted to Professor Tai Tsun Wu for introducing him to M. G. Krein’s seminal paper [16]. The research of the first author (DM) was supported in part by NSF DMS-1517162. The research of the second and third authors (MM and ML) was supported in part by ARO MURI Award W911NF-14-1-0247. The work of the third author (ML) was also partially supported by a grant from the Simons Foundation (Grant Number 339038).

Funding Information:
The first author (DM) is indebted to Professor Tai Tsun Wu for introducing him to M.?G. Krein's seminal paper. The research of the first author (DM) was supported in part by NSF DMS-1517162. The research of the second and third authors (MM and ML) was supported in part by ARO MURI Award W911NF-14-1-0247. The work of the third author (ML) was also partially supported by a grant from the Simons Foundation (Grant Number 339038).

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© 2017 Wiley Periodicals, Inc., A Wiley Company

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abstract = "By formally invoking the Wiener–Hopf method, we explicitly solve a one-dimensional, singular integral equation for the excitation of a slowly decaying electromagnetic wave, called surface plasmon-polariton (SPP), of small wavelength on a semiinfinite, flat conducting sheet irradiated by a plane wave in two spatial dimensions. This setting is germane to wave diffraction by edges of large sheets of single-layer graphene. Our analytical approach includes (i) formulation of a functional equation in the Fourier domain; (ii) evaluation of a split function, which is expressed by a contour integral and is a key ingredient of the Wiener–Hopf factorization; and (iii) extraction of the SPP as a simple-pole residue of a Fourier integral. Our analytical solution is in good agreement with a finite-element numerical computation.",

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On the Wiener–Hopf Method for Surface Plasmons: Diffraction from Semiinfinite Metamaterial Sheet

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