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 | |
| 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).
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