 tion. A stationary amplifier model is justified only if the relaxation time of the inverted medium is much longer than the typical signal fluctuation that generally can be expressed by means of the inverse of the bit rate R (i.e., the bit duration T). This is not always the situation, and if the bit time is not much smaller than the relax- ation time, a dynamic model has to be adopted since amplification changes the signal shape introducing distortions. In these situations, the amplifier rate equations have to be considered, that in general stochastic equations due to the ASE noise terms. Managing a system of two stochastic rate equations is quite difficult, but can be done [46] and it can be demonstrated that the noise properties of the amplifier are not affected in a relevant way by working in a dynamic regime. Thus, here we will consider some dynamic properties of a two-level amplifier in a noise- less picture [7]. The rate equations write in this approximation (4.75) where J is the pumping rate and the local gain is related to the population inversion through the efficiency by - P0). From Equation 4.75, the population inversion can be eliminated by using the conserva- tion of the number of molecules T=(p1+p0) = and the expression g=r(p1 - P0) of the gain. Moreover, the equation of the field can be separated into an equation for the power (obtained by adding it to the complex conjugate) and a separate equation for the phase. At the end, defining the relative time 0=t - z/v the following system is obtained: (4.76) aP(t,2)=gP(t,z) There is a standard procedure to arrive to a simplified form of these equations that can be solved by numerical algorithms [18]. The first effect to observe is dynamic gain saturation. Let us consider, as a simple exam- ple, a two-level amplifier with the parameters of Table 4.7. In Figure 4.15, the input pulse, the dynamic gain, and the output pulse are shown versus time. The amplifier works in deep saturation, since the input pulse has a peak power of -3 dBm against a macroscopic sa