COMPUTATIONAL MODELING OF FEMTOSECOND OPTICAL SOLITONS FROM MAXWELL EQUATIONS

A new algorithm has been developed that permits, for the first time, the direct time integration of the full-vector nonlinear Maxwell's equations. This new capability permits the modeling of linear and nonlinear, instantaneous and dispersive effects in the electric polarization in material media. The modeling of the optical carrier is retained in this approach. The fundamental innovation of the present approach is to notice that it is possible to treat the linear and nonlinear convolution integrals, which describe the dispersion, as new dependent variables. Using this observation, a coupled system of nonlinear second-order ordinary differential equations can be derived for the linear and nonlinear convolution integrals, by differentiating them in the time domain. These equations, together with Maxwell's equations form the system that is solved to determine the electromagnetic fields in nonlinear dispersive media. Using this algorithm, results are presented of first-time calculations in one dimension of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier. The nonlinear modeling takes into account such quantum effects as the Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector nonlinear Maxwell's equations for integrated optical structures having complex engineered inhomogeneities.