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The phase dynamics that occur in bulk InGaAsP-InP semiconductor optical amplifiers (SOAs) in response to picosecond pulse excitations at 10 and 40 GHz are studied experimentally and numerically for various amplifier lengths. The time dependencies of the phase changes and of the absolute gain of the amplifier are measured simultaneously. The total phase shifts induced by 1.5-ps pulses at 10 GHz are higher than π in SOAs with active region lengths between 0.5 and 2 mm and exceed 2π in a 1.5-mm-long amplifier. Phase shifts above π are measured at 40 GHz in 1.5- and 2-mm-long SOAs. The dependence of the total phase shift on the amplifier bias current and length and on pump pulse energy is investigated. Numerical simulations based on a comprehensive time-domain SOA model allow us to confirm the experimental results for a wide range of amplifier parameters. In particular, SOAs with lengths up to 5 mm have been modeled, and the calculations suggest that the maximum phase shifts occur in amplifiers of approximately 2-mm length. The phase dynamics measurements are illustrated at the example of an optical time division multiplexing add-drop multiplexer, based on a SLALOM switch, gated by 10- or 40-GHz control pulses. We find that simultaneous good dropping and clearing is possible if the length and the operating conditions of the SOA in the switch are chosen such as to induce a full π phase shift.