Law of noise accumulation in a chain of amplified sections
Optical communications: introduction and performance assessment

Amplified Spontaneous Emission (ASE) noise, produced by optical amplifiers, is one of the most fundamental phenomena of concern to designers of optical transmission systems. If they want to guarantee a predefined error rate, they must ensure that the signal-to-noise ratio remains above a certain limit value. In this section, we calculate the evolution of the signal-to-noise ratio in a transmission line made up of multiple fiber sections separated by optical amplifiers.

First, we'll assume that the amplifiers are localized, i.e. that the amplification phenomenon occurs over a negligible distance compared with the propagation distance, as in erbium-doped fiber amplifiers. The amplified spontaneous emission noise power P _ASE produced by the amplifier is given by the equations