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arXiv · 1701.02784

On the Wiener-Hopf method for surface plasmons: Diffraction from semi-infinite metamaterial sheet

Dionisios Margetis·Matthias Maier·Mitchell Luskin
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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 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.

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Dionisios Margetis, Matthias Maier, Mitchell Luskin. 2017-01-10. On the Wiener-Hopf method for surface plasmons: Diffraction from semi-infinite metamaterial sheet. https://arxiv.org/abs/1701.02784

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