 loss a(z). Comparing Equations D.1, with the standard coupled equations for a generic system, the following equations are found: g(z)=2(2) (D.2) a(z) = 2(z) Starting from Equations D.2 and imposing the stationary approximation, the pump and signal equations can be solved obtaining the following expression of the macroscopic amplifier gain: (D.3) This is the equation that we have used to evaluate the behavior of the gain versus length of the active fiber or versus the injected signal power. As far as the noise is concerned, the first step to determine the amplifier noise factor is to solve the noise equation, which is an easy task due to the fact that signal and pump behaviors are already known. From the noise equation we immediately derive that the noise flux depends on both the signal and the pump fluxes due to the gain saturation of the amplifier. In amplifiers used for optical communications, this is a slow phenomenon with respect to the bit rate and in the standard situation of constant average signal power also, the noise flux is constant. In order to take into account correctly the noise performances of the amplifier, the quan- tum noise should be taken into account. In a semiclassical picture, this term can be incor- porated into the amplifier equations considering the fluxes the average value of a random variable. Since multiplying the flux by the mode area and dividing it by W the density of photons in the mode is obtained, the statistical distribution of the fluxes is readily evalu- ated starting from the Poisson characteristics of the photon number. From this observation, the output SNout can be evaluated obtaining (D.4) where Ps,0 is the power in the signal bandwidth in the absence of spontaneous emission (i.e., the signal power) Ps is all the power flux in the signal bandwidth P is the input signal The signal angular frequency is indicated with Ws and the optical bilateral bandwidth is indicated with B. It is to be noted that in all the chapters devoted to system design, the Appendix D: Fiber Optica