Dynamical analysis of a weakly coupled nonlinear dielectric waveguide: Surface-plasmon model as another type of Josephson junction

We propose that a weakly coupled nonlinear dielectric waveguide surface-plasmon system can be formulated as another type of Josephson junction. Such a system can be realized along a metal-dielectric interface where the dielectric medium hosts a nonlinear waveguide (e.g., fiber) for soliton propagation. We demonstrate that the system is in close analogy to the bosonic Josephson junction of atomic condensates at very low temperatures, yet exhibits different dynamical features. In particular, the inherently dynamic coupling parameter between soliton and surface plasmon generates self-trapped oscillatory states at nonzero fractional populations with zero and π time-averaged phase difference. The salient features of the dynamics are presented in the phase space.