The spontaneous and stimulated emissions of strongly excited GaAs/(Ga,Al)As quantum wells are investigated in the one-dimensional optical amplifier geometry, using the variable-stripe-length method. The optical amplification and its saturation are studied by monitoring the spectra of spontaneous and amplified luminescence as a function of the position on the stripe. The deduced experimental spatial dependences of carrier and luminous densities are found to agree in a semiquantitative way with the numerical solutions of the amplifier equation, obtained by assuming steady state and thermal carrier distributions. Saturation of optical amplification is caused by two effects: (1) carrier depopulation through stimulated recombination of electron-hole pairs, and (2) loss of light caused by scattering at sample defects and by imperfect wave guiding.