Extraordinary optical transmission through periodic Drude-like graphene sheets using FDTD algorithms and its unconditionally stable approximate Crank–Nicolson implementation

Based upon the approximate Crank–Nicolson (CN) finite-difference time-domain method implementation, the unconditionally stable algorithm is proposed to investigate the wave propagation and transmission through extremely thin graphene layers. More precisely, by incorporating the CN Douglas–Gunn algorithm, the piecewise linear recursive convolution method and the auxiliary differential equation method, the analytical model is proposed for Drude-like graphene model. To obtain the solution of the governing equations, the perfectly matched layer and the periodic boundary condition are applied to the graphene structure with two dimensional nano-materials. Numerical examples are carried out for further investigation. During the simulation, the influences of the parameters such as the grating slit and its thickness on the wave transmission are investigated and discussed. The result shows that not only the graphene grating has high transmission performance but also the proposed methods have considerable performance and accuracy.

Modified Auxiliary Differential Equation Method and Exact Solutions Generalized Schrödinger

This paper describes a method on which modify auxiliary differential equation method by using this method for solving nonlinear partial differential equations and with aid of Maple Software ,we get the exact solution of the generalized schrödinger, including hyperbolic function solutions, trigonometric solution.

The Multiple Exact Solutions for the Variable Coefficient KdV Equation

The auxiliary differential equation method has recently been proposed ,It is introduced to construct more new exact solutions for the variable coefficient KdV equations. As a result , hyperbolic function solutions, trigonometric function solutions, and elliptic function solutions rational function solutions with parameters are obtained.

Simulation of Phonon-Polariton Generation and Propagation in Ferroelectric LiNbO3 Crystals

ABSTRACTWe simulate propagation of phonon-polaritons (admixtures of polar lattice vibrations and electromagnetic waves) in ferroelectric LiNbO3 with a model that consists of a spatially periodic array of harmonic oscillators coupled to THz electromagnetic waves through an electric dipole moment. We show that when this model is combined with the auxiliary differential equation method of finite difference time domain (FDTD) simulations, the salient features of phonon-polaritons may be illustrated. Further, we introduce second order nonlinear coupling to an optical field to demonstrate phonon-polariton generation by impulsive stimulated Raman scattering (ISRS). The phonon-polariton dispersion relation in bulk ferroelectric LiNbO3 is determined from simulation.