Title: 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.