Simulation of femtosecond pulses in the medium with frequency dispersion

An algorithm for solving the wave equation for the TE polarization, which is taking into account the frequency dispersion of the material and using the explicit difference scheme, is proposed. Analysis of the numerical simulation of propagation of femtosecond rectangular pulse in a quartz allowed to find precursors that come to the observation point for 1.4 times faster than the main pulse and the intensity of this precursors is in 700 times smaller than the intensity of the main pulse. The calculated delay time of Sommerfeld and Brillouin precursors differents from the theoretical to 7%.