The inverted population model of a linear optical amplifier is extended to incorporate explicit input and output photon fluxes. The input field is assumed to be incoherently coupled to the internal field of the amplifier, thus permitting a population statistical description of the complete system, including photon detection. Steady-state behavior and intensity amplification are simultaneously realizable. The integrated statistics of the photoelectron count at the detector are obtained and employed to evaluate a suitably defined signal-to-noise ratio for the system. The conditions under which signal enhancement can occur are derived and discussed for the case in which the input field photocount is Poisson distributed.
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Shepherd et al. (1987) studied this question.
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