In this work we present a numerical analysis of the mode coupling between the pump-beam and the laser-beam in a Ti:Sapphire crystal used as a gain medium of a femtosecond laser. Using the Matrix ABCD and propagation gaussian beam models, we obtained an optimal configuration for compensate the astigmatism in the output beam laser. Also we analysed pump-beam propagation and got the settings to fix the astigmatism in the crystal. Furthermore we apply this configuration to a homemade femtosecond laser, accomplishing an overall efficiency of laser to 20% in continuum wave (CW) and 16% in mode looking (ML) operation. The femtosecond laser have 30 nm bandwidth to FWHM at 810 nm corresponding 30fs.
In this work, we analyse the use of a micro-machined deformable membrane mirror (MMDM) to shape femtosecond
pulses. We present the Spectral-Phase-Influence-Matrix constructed by an inversion method. Spectral-Phase-Influence-
Matrix represents a novel and direct method to estimates the Spectral Phase design from a given actuator voltage settings
in a single step. Numerical and experimental results are presented.