High-Order FDTD and Auxiliary Differential Equation Formulation of Optical Pulse Propagation in 2-D Kerr and Raman Nonlinear Dispersive Media

Abstract

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.

Split-Field Finite-Difference Time-Domain Scheme for Kerr-Type Nonlinear Periodic Media

“…As can seen from the figure, a temporal soliton and also a smaller-magnitude precursor-pulse, that is identified as transient thirdharmonic energy, are formed. These results reproduce those presented in the literature [4][5][6].…”

“…Firstly, we show simulations of temporal solitons, and compare them with results presented in the literature [4][5][6]23]. Secondly, we analyze both DC and AC Kerr effects by means of the reflectance analysis of different stack of layers with nonlinear characteristics.…”

“…For example, different parts of an optical pulse are unequally affected by the Kerr-effect. One of the consequences of this is the optical soliton [2,[4][5][6], that arises from the balancing between the dispersion and the Kerr effect. Other implications of the effect include all-optical ultrafast applications, such as waveguides that combine linear media with nonlinear media [7] or all-optical switching devices utilizing nonlinear material [8].…”

Computationally-efficient FDTD modeling of supercontinuum generation in photonic crystal fibers

“…Dispersive properties of the fiber will be supplemented in the S1D-FDTD model with a third-order nonlinear polarization model derived on the basis of the Born-Oppenheimer approximation (Fujii et al 2004;Hellwarth 1977):…”

“…One of prospective candidates is the finite-difference time-domain (FDTD) method as a versatile numerical tool naturally adapted to broadband EM analysis (Taflove and Hagness 2005). Although several valuable papers focused on FDTD modelling of third-order nonlinear effects, that stay behind SC generation, have been published (Fujii et al 2004;Lubin et al 2011), large computational effort and memory requirements involved in the full-wave EM analysis of centimeter-long PCFs make the method inapplicable (Hu et al 2008). For that reason, a novel approach that takes the advantage of the accuracy of the FDTD method, while substantially alleviating its prohibitive computational requirements, is proposed in this paper.…”