Effects of second-order nonstationary cascaded processes on Gaussian beam propagation

This work proposes an analytical perturbative method describing the effects on the propagation of finite aperture beams due to the self-phase and self -amplitude modulation which result from cascaded second order interaction o f ultrashort light pulses. The method merges the semi-analytical solution w ith a perturbative beam propagation technique, namely the Gaussian Beam Dec omposition, which describes the effects of the non linear modulation on the free beam propagation. In particular we have studied the problem of the ti me- and intensity-dependent transmission of the pulse through slits or aper tures placed along the path of the beam simulating a geometry suitable for passive laser mode-locking. Although an efficient pulse shortening action c an be obtained in stationary conditions, in non stationary conditions the o ccurrence of an unavoidable amplitude modulation perturbs the beam propagat ion and reduces the temporal selectivity of the modulator.