Curvature-induced geometric momenta: the origin of waveguide dispersion of surface plasmons on metallic wires

We show that the propagation of surface plasmon polaritons (SPPs) on metallic wires is governed by two solely curvature-induced geometric momenta, leading to a significant modification of the waveguide dispersion, i.e. a change of their phase velocity. By quantifying the azimuthal momentum and superimposing two planar SPPs of opposite helicity, we find an analytic expression for the dispersion of guided SPPs. This expression shows excellent agreement with numerical simulations and allows explaining fundamental SPP properties such as waveguide dispersion.