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On the Wiener–Hopf Method for Surface Plasmons: Diffraction from Semiinfinite Metamaterial Sheet
Author(s) -
Margetis Dionisios,
Maier Matthias,
Luskin Mitchell
Publication year - 2017
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12180
Subject(s) - diffraction , integral equation , mathematical analysis , methods of contour integration , residue theorem , fourier transform , factorization , mathematics , surface plasmon polariton , computation , physics , surface plasmon , optics , plasmon , initial value problem , algorithm , cauchy problem
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.