Quantum effects on optical beam propagation in a gain medium having di
stributed loss are analyzed using an amplifier-attenuator array model.
For the amplifier-attenuator set, the Wigner function of the output f
ield is related to that of the input field by a convolution law. Using
this, we derive the Fokker-Planck equation for the beam propagation i
n the distributed amplifier with loss, and the added quantum noise is
analyzed by solving this equation. When the amplification just compens
ates the attenuation, the mean amplitude of the signal does not change
but the mean energy increases due to the added noise. Even in this ca
se, the photon number variance can be reduced when a proper phase-sens
itive reservoir is incorporated.