Diffraction-limited sources around 976 nm are attractive to build sources around 488 nm, or to pump rare-earth-doped materials. Continuous wave efficient lasers have been obtained with single-mode fibres, in which we demonstrate pulsed laser diode amplification with gains higher than 30 dB. Theoretical studies can predict the amplifier performances versus the input signal characteristics and show the pulse width influence on excited state population. We used a classical timespace two-level model that we solved thanks to a Finite-Difference Time-Domain method. These simulations taking into account both time and space evolutions and a parasitic laser effect describe correctly the experimental results.