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We assess the influence of the degree of quantum confinement on the carrier recovery times in semiconductor optical amplifiers (SOAs) through an experimental comparative study of three amplifiers, one InAs-InGaAsP-InP quantum dot (0-D), one InAs-InAlGaAs-InP quantum dash (1-D), and one InGaAsP-In-GaAsP-InP quantum well (2-D), all of which operate near 1.55-mum wavelengths. The short-lived (around 1 ps) and long-lived (up to 2 ns) amplitude and phase dynamics of the three devices are characterized via heterodyne pump-probe measurements. The quantum-dot device is found to have the shortest long-lived gain recovery (~80 ps) as well as gain and phase changes indicative of a smaller linewidth enhancement factor, making it the most promising for high-bit-rate applications. The quantum-dot amplifier is also found to have reduced ultrafast transients, due to a lower carrier density in the dots. The quantum-dot gain saturation characteristics and temporal dynamics also provide insight into the nature of the dot energy-level occupancy and the interactions of the dot states with the wetting layer.