A theoretical analysis of slow and fast light effects in semiconductor optical amplifiers based on coherent population oscillations and including the influence of optical filtering is presented. Optical filtering is shown to enable a significant increase of the controllable phase shift experienced by an intensity modulated signal traversing the waveguide. The theoretical model accounts for recent experimental results and is used to analyze and interpret the dependence on material and device parameters. Furthermore analytical approximations are derived using a perturbation approach and are used to gain a better physical understanding of the underlying phenomena.
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