On the Wiener-Hopf Method for Surface Plasmons: Diffraction from Semiinfinite Metamaterial Sheet
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2017 Wiley Periodicals, Inc., A Wiley Company By formally invoking the WienerHopf 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 WienerHopf 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.