NOISE AUGMENTATION AND SIGNAL-TO-NOISE RATIO DEGRADATION IN IN-LINE AMPLIFIER SYSTEMS DUE TO THE NONLINEAR REFRACTIVE-INDEX OF OPTICAL FIBERS

Optical noise enhanced by the nonlinear refractive index of optical fibers is one of the major factors limiting the system performance of in-line amplifier transmission. This paper derives an analytical expression of noise enhancement taking into account group-velocity dispersion of optical fibers. Evolution of the in-phase and quadrature-phase noise field components is expressed by a simple matrix describing the transmission characteristics of optical noise through the basic section composed of an optical amplifier and a transmission fiber. This enables minute investigation of noise evolution in in-line amplifier systems; approximate characteristics can be learned as well. A noise increase proportional to the third power of a number of amplifiers is verified in the normal dispersion regime while an exponentially rising noise peak is found in the anomalous dispersion regime. Based on these results, signal-to-noise ratios at the receiver and allowable transmission distances are discussed in terms of the dispersion parameter and the amplifier number. From the noise evolution point of view, the longest transmission distance is achieved in the normal dispersion regime.