Plasmon-polaritons on a surface with fluctuating impedance: Scattering, localization, stability

Abstract

Scattering of TM-polarized surface plasmon-polariton waves (PPW) by a finite segment of the metal–vacuum interface with randomly fluctuating surface impedance is examined. Solution of the integral equation relating the scattered field with the field of the incident PPW, valid for arbitrary scattering intensity and arbitrary dissipative characteristics of the conductive medium, is analyzed. As a measure of the PPW scattering, the Hilbert norm of the integral scattering operator is used. The strength of the scattering is shown to be determined not only by the parameters of the fluctuating impedance (dispersion, correlation radius and the length of the inhomogeneity region) but also by the conductivity of the metal. If the scattering operator norm is small, the PPW is mainly scattered into the vacuum, thus losing its energy through the excitation of quasi-isotropic bulk Norton waves above the conducting surface. The scattered field intensity is expressed in terms of the random impedance pair-correlation function. Its dependence on the incident and scattered wavenumbers shows that in the case of random-impedance-induced scattering of PPW it is possible to observe the effect analogous to Wood's anomalies on gratings. Under strong scattering, when the norm of the scattering operator becomes large compared to unity, the radiation into free space is strongly suppressed, and, in the limit, the incoming PPW is almost perfectly back-reflected from the inhomogeneous part of the interface. Therefore, within the model of a dissipation-free conducting medium, the surface polariton is unstable against arbitrary small fluctuations of the medium polarizability. Transition from scattering to back-reflection under strong fluctuations of the impedance is interpreted in terms of the Anderson localization.