QUANTUM-NOISE IN OPTICAL BEAM-PROPAGATION IN DISTRIBUTED-AMPLIFIERS

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.