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We report time-resolved measurements of the linewidth enhancement factors (-factors) , and , associated with the adiabatic carrier recovery, carrier heating, and two-photon absorption dynamical processes, respectively, in semiconductor optical amplifiers (SOAs) with different degrees of dimensionality-one InAs/InGaAsP/InP quantum dot (0-D), one InAs/InAlGaAs/InP quantum dash (1-D), and a matching InGaAsP/InGaAsP/InP quantum well (2-D)-all operating near 1.55- wavelengths. We find the lowest values in the QD SOA, 2-10, compared to 8-16 in the QW, and values of and that are also lower than in the QW. In the QD SOA, the -factors exhibit little wavelength dependence over the gain bandwidth, promising for wide-bandwidth all-optical applications. We also find significant differences in the -factors of lasers with the same structure, due to the differences between gain changes that are induced optically or through the electrical bias. For the lasers we find the QW structure instead has the lower -factor, having implications for directly modulated laser applications.