Scattering Amplitude of Surface Plasmon Polariton Excited by a Finite Grating

Unusual optical properties of laser-ablated metal surfaces arise from the excitation of local plasmon resonances in nano- and microstructures produced by laser-processing and from the mutual interaction of those structures through surface plasmon polariton (SPP) waves. This interaction provides a synergistic effect, which can make the optical properties of the composite nanostructure drastically different from the properties of its elements. At the same time, the prediction and analysis of these properties are hampered by the complexity of the analytical solution to the problem of SPP excitation by surface objects of arbitrary configuration. Such a problem can be reduced to a simpler one if one considers the geometry of a structured surface as a superposition of harmonic Fourier components. Therefore, the analytical solution to the problem of surface plasmon polariton excitation through the scattering of light by a sinusoidally perturbed plasmonic metal/vacuum boundary becomes very important. In this work, we show that this problem can be solved using a well-known method for calculating guided-mode amplitudes in the presence of current sources, which is used widely in the waveguide theory. The calculations are carried out for the simplest 2D cases of (1) a sinusoidal current of finite length and (2) a finite-length sinusoidal corrugation on a plasmonic metal surface illuminated by a normally incident plane wave. The analytical solution is compared with the results of numerical simulations. It is shown that, in the first case, the analytical and numerical solutions agree almost perfectly. In the second case, the analytical solution correctly predicts the optimum height of the corrugation xopt, providing the maximum SPP excitation efficiency. At the same time, the analytical and numerical values of the SPP amplitude agree very well when the corrugation height x turns out to be x≪xopt or x≫xopt (at least up to 3xopt); at x=xopt, the mismatch of those does not exceed 25%. The limitations of the analytical model leading to such a mismatch are discussed. We believe that the presented approach is useful for modeling various phenomena associated with SPP excitation.