Uzamsal etkileşim içinde bulunan soliton ve yüzey plazmonlarının oluşturduğu tek ve çift Josephson eklemlerinin geçiş dinamiği

This thesis work investigates the crossing dynamics of photons between spatially coupled co-propagating soliton and surface-plasmon, which constitute a type of photonic Josephson junction. By introducing modulations to the spatial coupling, the crossing dynamics exhibit features similar as well as different to that of nonlinear Landau-Zener or Rosen-Zener type transitions. The dependence of the coupling to the soliton amplitude provides an inherent dynamic which may manifest distinct features in the transition characteristics. The dynamics of the system which is formulated as a Josephson junction is investigated by introducing fractional population imbalance and the relative phase variables. A full population conversion between optical soliton and surface plasmon is achieved. The governing equations of the system represents a set of nonlinear Schrödinger equations, and the eigenvalue analysis of these equations sheds light on the behaviour of the fixed points of the system, herewith the stability analysis will be investigated. Under a spatial periodic modulation, this type of Josephson junction may exhibit driven resonance states similar to Shapiro resonances. The stability of these resonances will be investigated in the presence of an external periodic field. The double Josephson junction is formed by coupling the soliton spatially to two surface-plasmons which reside on either side of the soliton propagation axis, respectively. This three-state system may provide rich dynamics with features like collapse-revival and plasmon-plasmon coupling via a frozen soliton state. By introducing spatial modulations, further dynamical effects will be explored. Heuristic designs are analyzed for sensor applications by investigating realistic materials and associated parameters.