Directional coupler using gap plasmon waveguides

Here, we demonstrate that efficient nano-optical couplers can be developed using closely spaced gap plasmon waveguides in the form of two parallel nano-sized rectangular slots in a thin metal film or membrane. Using the rigorous numerical finite-difference and finite element algorithms, we investigate the physical mechanisms of coupling between two neighboring gap plasmon waveguides and determine typical coupling lengths for different structural parameters of the coupler. Special attention is focused onto the analysis of the effect of such major coupler parameters, such as thickness of the metal film/membrane, slot width, and separation between the plasmonic waveguides. Detailed physical interpretation of the obtained unusual dependencies of the coupling length on slot width and film thickness is presented based upon the energy consideration. The obtained results will be important for the optimization and experimental development of plasmonic sub-wavelength compact directional couplers and other nano-optical devices for integrated nanophotonics.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.