We reformulate the existing auxiliary differential equation (ADE) technique in the context of the finite-difference time-domain analysis of Maxwell's equations for the modeling of optical pulse propagation in linear Lorentz and nonlinear Kerr and Raman media. Our formulation is based on the polarization terms and allows simple and consistent implementation of such media together with the anisotropic perfectly matched layer (APML) absorbing boundary condition. The disadvantages of the ADE technique, i.e., requiring additional storage for auxiliary variables, has been overcome by adopting the high-order finite-difference schemes derived from the previously reported wavelet-based formulation. With those techniques, we demonstrate in two-dimensional setting an effective and accurate numerical analysis of the spatio-temporal soliton propagation as a consequence of the physically originated balanced phenomena between the self-focusing effect of nonlinearity and the pulse broadening effects of the temporal dispersion and of the spatial diffraction.     «

We reformulate the existing auxiliary differential equation (ADE) technique in the context of the finite-difference time-domain analysis of Maxwell's equations for the modeling of optical pulse propagation in linear Lorentz and nonlinear Kerr and Raman media. Our formulation is based on the polarization terms and allows simple and consistent implementation of such media together with the anisotropic perfectly matched layer (APML) absorbing boundary condition. The disadvantages of the ADE techniq...     »

Maxwell equations, Maxwell's equations, absorbing boundary condition, finite difference time-domain analysis, polarization, high-speed optical techniques, dispersive media, wavelet transforms, differential equations, optical dispersion, spectral line broadening, optical self-focusing, 2-D Kerr nonlinear dispersive media, anisotropic perfectly matched layer, auxiliary differential equation, finite-difference time-domain analysis, high-order FDTD, high-order finite-difference schemes, light diffraction, linear Lorentz media, nonlinear media, nonlinearity, optical pulse propagation, optical solitons, physically originated balanced phenomena, pulse broadening effects, Raman nonlinear dispersive media, self-focusing effect, spatial diffraction, spatio-temporal soliton propagation, spatiotemporal phenomena, temporal dispersion, wavelet-based formulation     «

Maxwell equations, Maxwell's equations, absorbing boundary condition, finite difference time-domain analysis, polarization, high-speed optical techniques, dispersive media, wavelet transforms, differential equations, optical dispersion, spectral line broadening, optical self-focusing, 2-D Kerr nonlinear dispersive media, anisotropic perfectly matched layer, auxiliary differential equation, finite-difference time-domain analysis, high-order FDTD, high-order finite-difference schemes, light diffra...     »