We study the optical properties of strongly photo-excited GaAs/AlxGa1-xAs Quantum Wells in the one-dimensional optical amplifier geometry. One part of our work deals with gain measurements using the "variable stripe length method". We are proposing two new fitting procedures to adjust gain spectra from the amplified luminescence (AL) measured as a function of stripe length L. These procedures allow us to reduce the number of fitting parameters, and to verify whether a quasi thermal equilibrium among the carriers of the electron-hole plasma is established. Our samples, optically pumped using intensities up to 100 kw/cm2, show optical gain coefficients (g) between 10 and 30 cm-1 per well, at our low bath temperatures ranging between 2 K and 140 K. The losses of AL, caused by crystal imperfections, are difficult to determine. Another part of our work deals with saturation effects of optical amplification. For this, we measured the spatial dependence of the amplified luminous density travelling in the direction of the stripe and of the spontaneous emission in perpendicular direction to it. These profiles are symmetrical with respect to the center of the stripe, as there are two counter-propagating waves in our guide. We solved numerically the one-dimensional amplifier equation, assuming stationary conditions and a quasi thermal distribution of the carriers, and accounting for the optical losses in the wave guiding structure. The solutions have two regimes: the first one, which we call linear or unsatured, is applicable in the case of short stripe lengths L and/or low gain coefficients for which the carrier density is constant in direction of the amplifier; the second one describes saturation effects. For g·L > 5, the AL intensity decreases at certain photon energies. This saturation of the optical amplification appears initially on the high energy part of AL spectra. We find that these saturation effects are due to: (1) carrier depopulation through stimulated recombination of the electron-hole pairs, and (2) the losses of light. The experimental profiles agree semi-quantitatively with our numerical calculations. Observing the spontaneous emission spectra, we find no evidence of non-thermal carrier distribution. The light losses prevent the AL from reaching very strong intensities and thus the stimulated recombination rate remains always lower than the intra subband thermalization rate.