We experimentally investigate and theoretically describe the amplification of ultrashort optical pulses in a double-stage InGaAs-semiconductor laser amplifier system consisting of a double-pass single-stripe diode laser and a tapered amplifier. The pulses were generated by a mode-locked single-stripe laser in an external-resonator configuration. On amplification in a tapered amplifier, pulses exhibited both spectral broadening and distortion, depending on the tapered amplifier current and the injected optical pulse power. This behavior originates from the dynamic nonlinear carrier induced spatiospectral gain and index changes as well as gain saturation and leads to self-phase modulation. The origin of the observed behavior is revealed by a spatially resolved microscopic theory based on Maxwell–Bloch–Langevin equations that takes into account many-body interactions, energy transfer between carrier and phonon systems, and, in particular, the spatiotemporal interplay of stimulated and amplified spontaneous emission and noise.