  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.
