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

his 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 of ultrashort light pulses. The method merges the semi-analytical solution with a perturbative beam propagation technique, namely the Gaussian Beam Decomposition, which describes the effects of the non linear modulation on the free beam propagation. In particular we have studied the problem of the time- and intensity-dependent transmission of the pulse through slits or apertures placed along the path of the beam simulating a geometry suitable for passive laser mode-locking. Although an efficient pulse shortening action can be obtained in stationary conditions, in non stationary conditions the occurrence of an unavoidable amplitude modulation perturbs the beam propagation and reduces the temporal selectivity of the modulator.