In a previous investigation we have studied the excitation of a surface plasmon polariton (SPP) when a volume electromagnetic wave in the form of a beam illuminates a circularly symmetric protuberance or indentation of Gaussian form on an otherwise planar metal surface in contact with vacuum. The fraction of the incident flux that was scattered into a SPP was rather small, of the order of one percent. In this paper, we propose a different form for a circularly symmetric surface defect and show that it is possible to achieve a much higher efficiency for the excitation of a SPP. The surface profile function we employ is of cosinusoidal form along the radial coordinate up to a
radius R0, and vanishes outside this radius. Here R0 is chosen such that the profile function is continuous. By exploiting the circular symmetry of the problem we expand the reduced Rayleigh equation for the p- and s-polarized components of the electromagnetic field above and on a vacuum-metal interface into a set of one-dimensional integral equations that we then solve numerically. The solution of the integral equations in the first Born approximation shows that the scattering amplitude is related to the Bragg vector of the periodic part of the surface. Thus, a specific scattering geometry can be optimized by adjusting the periodicity and consequently the Bragg vector. We report excitation efficiencies that are about 15 times larger than those achieved with a Gaussian profile.
In a recent theoretical study of the scattering of a surface plasmon polariton by a circularly symmetric protuberance or indentation on an otherwise planar metal surface in contact with vacuum, it was found that the angular dependence of the intensity of the volume electromagnetic waves scattered into the vacuum region possesses a maximum in the plane of incidence at a polar scattering angle of approximately 28 degree(s). This suggests that if a p-polarized volume electromagnetic field in the form of a beam of finite width is incident on the same surface defect, the efficiency of exciting a surface plasmon polariton will be greatest for a polar angle of incidence close to 28 degree(s). To test this hypothesis, in this paper we study this problem theoretically. The reduced Rayleigh equations for the amplitudes of the p- and s-polarized components of the scattered field are reduced to a set of one-dimensional integral equations by exploiting the circular symmetry of the surface defect, which is assumed to have a Gaussian form. The efficiency of exciting surface plasmon polaritons in this fashion is calculated as a function of the polar angle of incidence, and is found to be maximal when this angle is close to 28 degree(s).
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