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

We study the scattering of surface TM-polarized plasmon-polariton waves (PPWs) by the finite red region of plane metal-vacuum boundary with randomly inhomogeneous impedance. We analyze the solution of the integral equation connecting the scattered field with the field of the oncoming PPWs, that is valid for any strength of the scattering and dissipative properties of the conducting half-space. As a measure of scattering strength, the Hilbert norm of the intermode scattering operator is used. It is shown that the intensity of the scattering is not only determined by the parameters of the random impedance (the variance, correlation radius, the length of the heterogenious region), but it also crucially depends on the metal substrate conductivity. For a small norm of the integral operator, the incident surface plasmon polariton (SPP) radiates effectively into vacuum, loosing the part of its energy for 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, the dependence of which 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 lattices. With strong scattering, when the norm of the scattering operator becomes large as compared to unity, the radiation into the volume is highly suppressed and the PPW is basically mirrored from the heterogeneous surface area in backward direction. In the model of dissipationless conducting halfspace, the surface plasmon-polariton becomes unstable for arbitrarily small fluctuations of the conductor polarizability. The mirroring also takes 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 region.