Noise in resonant optical amplifiers of general resonator configuration

The population-statistical description of a linear optical amplifier, extended to include both a resonant optical cavity and explicit input and output photon fluxes, is shown to yield three useful noise relationships. Despite the treatment´s plainly particulate character, it provides an expression for the variance of the time-integrated output-photon-detection process in which terms associated with interferometrically generated beat noise are prominent. For systems whose photodetector electrical bandwidth B is much smaller than the amplifier´s optical bandwidth Δv, as is almost invariably the case for semiconductor amplifiers in lightwave-communication systems, the time-integrated photocurrent variance can be written in a simple, physically intuitive form. Two quotients are of central importance: (Δν/B) and the ratio (<n_S>/<n_ASE>) of mean amplified-signal power to mean amplified-spontaneous-emission power. In the usual case of interest for optical amplifiers in communication systems where <n_S>≫<n _ASE>, the signal-to-noise ratio of the integrated photocurrent, on which the error probability in an on-off-keyed system depends, is ≈1/2(Δv/B) ({n_S }/{n_ASE})