The plasmon–polariton scattering by random-impedance surface defects: The interplay between localization and outflow

Abstract

We study the scattering of TM-polarized surface plasmon-polariton (SPP) by the finite section of flat metal–vacuum interface with a random impedance. We analyze the solution to the integral equation that connect the scattered field and the incident plasmon–polariton, and is valid for any strength of the scattering and dissipative characteristics of the conducting half-space. We show that the norm of the intermode scattering operator as a measure of scattering strength is not only determined by the parameters of the random impedance (the variance, correlation radius, the length of the heterogeneous section of the interface), but also crucially depends on the metal conductivity. For a small norm of the integral operator, the incident surface plasmon polariton radiates effectively into vacuum, resulting in excitation of quasi-isotropic Norton-type waves above the conducting surface. The intensity of the leaking field is expressed in terms of the pair correlation function of the impedance, whose dependence on wave numbers of incident and scattered waves demonstrates the possibility to observe a phenomenon similar to Wood’s anomalies of wave scattering by periodic gratings. Under strong scattering regime, the radiation into the upper half-space is highly suppressed and the SPP wave is mainly backscattered from the heterogeneous surface segment. For the lossless conducting half-space, the surface plasmon–polariton becomes unstable for arbitrarily small fluctuations of the conductor polarizability. The mirroring should also take place at small norm of the scattering operator, yet in this case it is related to Anderson’s localization of the SPP within the disordered section.