Theory of Coherent WDM Systems Using In-Line Semiconductor Optical Amplifiers

A theory of nonlinear signal propagation in multi-span wavelength division multiplexed coherent transmission systems that employ the semiconductor optical amplifier as in-line amplifiers is presented for the first time. The rigorous derivation, based on time-domain first-order perturbationtheory, is developed in detail. The end result is the expressions for the signal-to-noiseratio of the received sampled photocurrent, including contributions from noise, fiber-induced nonlinear distortions, and amplified-induced nonlinear distortions.