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Dynamical analysis of a weakly coupled nonlinear dielectric waveguide -- surface-plasmon model as a new type of Josephson Junction

We propose that a weakly-coupled nonlinear dielectric waveguide -- surface-plasmon system can be formulated as a new 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 (BJJ) 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.