[EL Faylali, 2(5): May, 2013] ISSN: 2277-9655 http: // www.ijesrt.com (C) International Journal of Engineering Sciences & Research Technology [1308-1312] IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY Modeling of Optical Pulse Propagation in Nonlinear Dispersive Media using JE-TLM Method H. El Faylali *1 , M. Iben Yaich 2 and M. Khaladi 3 *1,2,3 Electronic & Microwaves Group Faculty of Sciences, Abdelmalek Essaadi University P. O. Box: 2121, Tetuan 93000 Morocco wh_elfaylali@yahoo.fr Abstract In this paper, we propose a simulation model of electromagnetic wave’s propagation in two- level atomic system. This model exploits the dependence of the polarization current density and the voltage electric in the context of the Transmission Line Matrix method with the Symmetrical Condensed Node (SCN -TLM) and novel voltage sources. By solving Maxwell's and the polarization current density equations, the proposed model, named JE-TLM, allows the simulation of the time variation of electric field and the population difference between the two energy levels of an atomic system. The scattering matrix characterizing the SCN with the new voltage sources is provided and the numerical results are compared with those of the literature or with the theoretical ones. Keywords: Nonlinear media, JE-TLM method. Introduction The numerical treatment in the time domain of the propagation of an electromagnetic (EM) wave in a material medium involves frequently the use of differential methods. In the Finite difference-Time domain (FDTD) and Transmission Line Matrix (TLM) methods, it consists to resolve jointly the Maxwell's equations and the macroscopic polarization or the polarization current density equations. The approach based on the auxiliary differential equation (ADE-FDTD) was used to characterize absorption and gain, respectively in two and four energy level atomic systems [1]. It was also used to study EM wave interaction with four-level two-electron atomic systems [2] and multi-level multi-electron atomic systems [3], taking to account the Pauli Exclusion Principle and the dynamic pumping. The TLM method with the Symmetrical Condensed Nodes (SCN) proposed by P. B. Johns [4] has successfully simulated the behaviour of EM waves in linear and nonlinear media [5]-[6]. In this paper, we propose a novel algorithm based on the SCN-TLM method with new voltage sources. By resolving the polarization current density equation, our model allows the simulation of the effects of the media on the propagated EM wave. The time evolution of population difference between the two energy levels of an atomic system is presented. Furthermore, the scattering matrix characterizing the SCN with the new voltage sources is provided and the simulation's results are compared to those of the literature or obtained by theoretical solutions. Electromagnetic Wave Propagation in Dispersive Nonlinear Media The polarization current density () Jt in a nonlinear media is linked to the electric field () Et by the equation: 2 2 21 21 21 2 () () () () () dJt dJ t dE t Jt k N t dt dt dt ω ω + ∆ + = ∆ (1) Where 3 0 2 21 21 6 a c k πε ω τ = , 0 ε is the permittivity of free space and 12 ω is the resonant frequency of the medium. It is related to the atomic energy levels 1 E and 2 E 1 2 ( ) E E < via the relationship 2 1 21 - E E ω = h , h is the Planck constant. 12 ∆ω is the total energy damping factor describing the spectral width of the transition taking into account the energy loss through non radiative effects (pumping and relaxation effects). 12 ∆N is the instantaneous difference of population describing the