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Laser amplifiers can be used in two ways: as preamplifiers to enhance the sensitivity and improve the noise performance of detectors and, in a pulsed mode of operation, as modulators to boost and stabilize the output of an injection laser oscillator. Most mathematical models of injection lasers are based on time-dependent rate equations that ignore the spatial dependence of the electron and photon densities. The model discussed here is based on numerical solutions of traveling-wave equations. The noise output of the laser amplifier is treated by traveling-wave power equations, but the light signal is described by traveling-wave equations for its amplitude. The parameters responsible for spontaneous and stimulated emission are being related to each other by the requirement that the amplifier achieve optimal noise performance in the absence of internal losses and without gain saturation. The most important results obtained from this computer model of a laser amplifier are as follows. 1) The theory contains a heuristic electron injection efficiency parameter. To agree with experimental observations this parameter must be kept small and its value must decrease with increasing current. 2) Cavity amplifiers saturate more readily than amplifiers without feedback. 3) Because of internal loss mechanisms the amplifier supplies more noise than is required by quantum theory, but its noise performance is still surprisingly good. In particular, the optical signal-to-noise ratio prior to detection is insensitive to gain saturation by strong signals. It remains approximately 4 dB below the theoretical maximum value for weak to moderately strong input signals and drops dramatically only when the amplifier is almost completely saturated.