Electromagnetic dynamical characteristics of a surface plasmon-polariton

We consider an electromagnetic field near the interface between two media with arbitrary real frequency-dependent permittivities and permeabilities, under conditions supporting the surface plasmon-polariton (SPP) propagation. The dispersion of the electric and magnetic properties is taken into account based on the recent approach for description of the spin and momentum of electromagnetic field in complex media [Phys. Rev. Lett. 119, 073901 (2017); New J. Phys., 19, 123014 (2017)]. It involves the Minkowski momentum decomposition into spin and orbital parts with the dispersion-modified permittivities and permeabilities. Explicit expressions are derived for spatial densities of the energy, energy flow, spin and orbital momenta and angular momenta of the transverse-magnetic (TM) SPP field. The expressions are free from non-physical singularities; the only singular contribution describes a strictly localized surface part of the spin momentum that can be associated with the magnetization current in the conductive component of the SPP-supporting structure. On this ground, a phenomenological theory of the SPP-induced magnetization (predicted earlier based on the simplified microscopic approach) is outlined. Possible modifications and generalizations, including the transverse-electric (TE) SPP waves, are discussed.