Negative dispersion, refraction and backward polaritons: impedance approach

Background and Objectives: The dispersion equations of surface plasmon-polaritons are derived for the general case of layered dissipative structures. The waves are classified as gliding with energy flow into structure from vacuum and leakage ones. The dispersion equations and conditions for the existence of slow and fast gliding and leaky waves, as well as forward and backward waves are considered. It is shown that for improper gliding and leakage monochromatic waves (in particular, for the Zenneck wave), the group velocity does not match the rate of energy transfer, especially in the bands of resonances, bandgaps and bands of strong spatial dispersion. We demonstrate the convenience of the impedance approach to the tasks. Results: The general form of the dispersion equation for polaritons in the multilayered structures, including thin 2D films, are obtained. The main results of the paper consist in the derived dispersion equations and their numerical solution, the conditions for the existence of forward and backward polaritons and slow or fast polaritons. The type of polariton is determined by the sign of the reactive part of the input impedance for this type of wave. The positive (inductive) one corresponds to a forward polariton and the negative (capacitive) one - to a backward polariton. The slowdown is determined by the ratio of reactive and active parts of the input impedance. 110 A slow surface plasmon occurs when the input impedance is highly reactive. The presence of spot with a backward wave and negative refraction allows us to implement control of plasmons, in particular, to carry out its focusing. The negative refraction does not necessarily occur in the presence of a backward wave.