Novel Auxiliary Differential Equation-Multiresolution Time Domain Scheme for Dispersive Nonlinear Photonic Devices

In this paper, a novel multiresolution time-domain (MRTD) technique is presented for the analysis of second order nonlinearities in dispersive materials. The suggested method implements multiresolution analysis in the context of method-of-moments for the solution of Maxwell's equations. Based on Lorentz model of linear susceptibility, auxiliary differential equations (ADE) are successfully included in order to accurately account for the chromatic dispersion of the dielectric material. Finally, a uniaxial perfectly matched layers (UPML) absorber for MRTD is rigorously incorporated. Various numerical examples demonstrate the stability and numerical precision of the suggested nonlinear MRTD method and its improved numerical efficiency over conventional FDTD.