We examine the propagation of surface plasmon-polariton terahertz waves along the interface between two media: metal or metamaterial with a negative index and an optically active medium or a nonlinear dielectric. It is shown that in both cases wave profile is not exponential. On the interface of optically active media surface waves are combination of TE and TM localized modes. Diffraction and dispersion of terahertz beams and pulses is studied
Dynamical properties of a coupled nonlinear dielectric waveguide - surface-plasmon system as another type of Josephson junction