Dielektrik dalga kılavuz-yüzey plazmonu Josephson ekleminin doğrusal olmayan dinamik özellikleri

In this thesis, we formulate and investigate the dynamical properties of a coupledoptic-plasmonic system based on classical treatment, which consists of an optical solitonin a nonlinear dielectric waveguide and a surface-plasmon along a metal surface.Particular to this system, the coupling parameter depends on the soliton amplitude,and thus becomes an inherent dynamical parameter rather than being a couplingƒconstant‚. This is an essential property that differentiates this two-level system fromothers. We formulate the dynamics of the system by the fractional population imbalance,and the relative phase between the soliton and surface-plasmon modes. Thefractional population imbalance is a measure of how the total electric field intensity(or the number of photons) is divided between the soliton and surface plasmonmodes. Remarkably, this formulation reveals a surprising analogy to the dynamicsof Bosonic Josephson junction (BJJ) of weakly coupled Bose-Einstein condensates ofatomic physics at very low temperatures. In the BJJ, the atoms (bosons) populatea two level system formed by a double-well optical trap. The wells are separatedby a thin barrier (junction) which allows tunneling between the two levels. There,however, the coupling between the levels depends on the barrier, which is constantor tunable externally. A further analogy is established with a classical mechanicalsystem known as the momentum shortened pendulum. The main model parametersconsists of the surface-plasmon propagation constant, the nonlinearity of the dielectricmedium, and the distance between the soliton and the metal surface. We employ thelinear stability analysis method to exploit the dynamical features in the phase-spacefor certain regimes of these model parameters. Fixed points are determined and theeigenvalues of the respective Jacobian matrix are calculated. Phase space trajectoriesare determined and compared to that of the BJJ system.The dissipation effects areinvestigated by introducing a phase-velocity damping term (which correspondsto a damping to the angular velocity of the pendulum in the mechanical analogue).Finally, we investigated damped-driven system to observe Shapiro-resonances in thestroboscopic phase portrait, under weak damping. The effect of the values of the distancebetween surface plasmon and optical soliton on Shapiro resonances is discussed.In addition to this, the Shapiro resonances are investigated by increasing the value ofthe damping in the system.