Full-wave vector Maxwell equation modeling of the self-focusing of ultrashort optical pulses in a nonlinear Kerr medium exhibiting a finite response time

The extension of the conventional finite-difference time-domain solution of the full vector Maxwell equations to modeling femtosecond optical-pulse propagation in a nonlinear Kerr medium that exhibits a finite response time is presented. Numerical results are given for nonlinear self-focusing in two space dimensions and time; the technique can be generalized to three space dimensions with adequate computer resources. Comparisons with previously reported and anticipated results are made. Several novel phenomena that are not observed with scalar models of self-focusing and that can be attributed only to the complete solution of the vector Maxwell equations are discussed.