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

Dionisios Margetis, Matthias Maier, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

8 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 languageEnglish (US)
Pages (from-to)599-625
Number of pages27
JournalStudies in Applied Mathematics
Volume139
Issue number4
DOIs
StatePublished - 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).

Publisher Copyright:
© 2017 Wiley Periodicals, Inc., A Wiley Company

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