On the Wiener-Hopf method for surface plasmons: Diffraction from semi-infinite metamaterial sheet
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 semi-infinite, 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.
Cite
@article{arxiv.1701.02784,
title = {On the Wiener-Hopf method for surface plasmons: Diffraction from semi-infinite metamaterial sheet},
author = {Dionisios Margetis and Matthias Maier and Mitchell Luskin},
journal= {arXiv preprint arXiv:1701.02784},
year = {2017}
}