Dispersion of surface plasmons in structures with a conducting film

The dispersion equations, the group velocity, the slowdown, and the conditions for forward and backward slow and fast plasmons propagating along thin metal films, as well as along graphene sheets, including those located on a dielectric layer and in a dielectric medium, are investigated. Nondissipative and dissipative surface plasmons are considered. Backward nondissipative symmetric plasmons do not occur in a dissipative silver film. It is shown that the anomalous negative dispersion of a dissipative plasmon does not necessarily mean that this plasmon is backward. For a backward dissipative plasmon, the input impedance of the structure from the side of vacuum should be capacitive, while the plasmon itself should be incoming. Symmetric and nonsymmetric structures with these properties are considered.