Ultra short nonlinear optical pulse propagation

The nonlinear Schrödinger equation (NLS) describes approximately the dynamics of optical pulse envelopes in the limit of many oscillations in the carrier wave. In ultra short optical pulses of order 10 femtoseconds, the number of oscillations is so few that the validity of the NLS equation is highly questionable. In this case it is necessary to study the original vector Maxwell equations including nonlinearity and polarization dynamics.
So far investigations have shown that extending the NLS equation using higher order dispersion and nonlinearities and comparing to Maxwells equations describes well even ultra short pulses within the slowly varying envelope approximation. However, in a number of cases also the extended NLS equation cannot be used. As the magnitude of the dispersion and nonlinearity depends on the wave number/frequency, waves with different wave numbers obey different NLS equations. Accordingly, interaction among ultra short pulses of different wave numbers can only be treated using the original Maxwell's equations.
Blow up observed in quintic NLS equations may be arrested when investigated in the framework of these original equations. Interference phenomena and propagation in optical crystals of ultra short pulses is better modelled by employing the Maxwell's equations. The purpose of this project is to go beyond the limit of the NLS equation and its extensions in studies of ultra short nonlinear optical pulses by invoking the first principle vector Maxwells equations coupled nonlinearily to the Lorenz equations for the polarization dynamics.