Theory of noise in optical transmission systems repeated by two-mode phase-sensitive optical parametric amplifiers

We analyze the noise characteristics of an optical transmission system repeated by two-mode phase-sensitive optical parametric amplifiers. In such a system, the non-degenerated signal and idler waves co-propagate through the link, interacting with each other in the optical parametric amplifiers. For the first time, we derive a closed-form expression for the accumulated noise using the quantum-mechanical Langevin-equation approach. The derived noise formula allows calculating the noise figure of the optical-amplifier chain under the influence of the internal loss of the amplifiers and the transmission loss of the link, thereby theoretically demonstrating its low-noise characteristics.