Noise characteristics of nonlinear semiconductor optical amplifiers in the Gaussian limit

This paper addresses noise properties of nonlinear semiconductor optical amplifiers. From a basic point of view, noise properties of nonlinear optical amplifiers are sufficiently different from those of linear amplifiers to warrant detailed modeling which has not been formulated previously. From a practical point of view, nonlinear semiconductor optical amplifiers are important for future all-optical signal-processing applications which may involve the operation of these devices in a saturated regime. Nonlinear amplifiers are also common in systems operating near 1300 nm and in integrated booster amplifiers. Under nonlinear operating conditions, amplifier noise contains a narrow-band contribution that comes about due to the nonlinear coupling of noise and gain. The more conventional broadband spontaneous noise also changes as the inversion factor becomes power-dependent and varies along the amplifier axis. We analyze noise in nonlinear amplifiers in the Gaussian limit (meaning, for fields consisting of large photon numbers) for CW or NRZ modulated signals and separately for short pulses. We consider the case of a single input as well as configurations of multi-input signals interacting via four-wave mixing. Using a specific detection system for the calculations of electronic signal-to-noise ratios, we demonstrate a reduction in the narrow-band electronic noise due to saturation in the single input case. We also demonstrate a vast advantage of using short pulses in four-wave-mixing applications.