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We have calculated the transient behavior and noise figure of a semiconductor optical amplifier (SOA) with the gain clamped by a vertical cavity laser (VCL). The characteristic behavior of the more conventional gain-clamped SOAs and SOAs with no gain-clamping is also studied and compared with the vertically gain-clamped amplifier. The calculations are based on a numerical stochastic rate equation model including several forward- and backward-propagating channels that are coupled to the vertical laser field through the active medium. The noise model takes into account the input noise, randomly amplified spontaneous emission, and random gain. Numerical simulations have been carried out to study the relaxation oscillations, crosstalk, and noise in a system with a strong input signal switched on and off while observing the output signals, VCL photon density, and carrier density. Results show that the VCL field captures most of the disturbances, in agreement with available experimental data.