Quantum noise in a solitonlike repeater system

It is shown that in the limit when the amplifier spacing in an all-optical amplifier–repeater system is much smaller than a soliton period, an equivalent nonlinear Schrödinger equation can be developed. It contains noise sources that account for the noise introduced by the attenuation and the amplifiers. The limit on soliton propagation caused by amplifier noise, as formulated by Gordon and Haus [ Opt. Lett.11, 665 ( 1986)], becomes rigorous for this system.