s the amplitude nonlinearity due to gain saturation that is present in all the ampli- fiers, SOAs are also characterized by another type of nonlinearity. The refraction index of the waveguide that constitutes the active zone of the amplifier depends, on one side, on the bulk material characteristics and the waveguide structure, and, on the other, on the density of the excited electrons that is on the injected current. When relevant stimulated emission happens into the amplifier, the density of the elec- trons decreases due to the emission of photons and also the refraction index changes. This means that SOAs show a phase nonlinearity that depends on the optical power into the active region. As in the case of Kerr effect during fiber propagation (see Chapter 4), this nonlinear- ity gives rise to a complex behavior of the field at the amplifier output SO that differ- ent "effects" are introduced in correspondence to particular forms of the field at the amplifier input. Also, in this case, we can speak of Self Phase Modulation (SPM), Cross Phase Modulation (XPM) and Four Wave Mixing (FWM). It is not the scope of this brief presentation to develop a complete model of a SOA in a regime of nonlinear behavior. The interested reader is encouraged to consult the huge technical literature dealing with this subject [17-19]. Next Generation Networking: Enabling Technologies, Architectures, and Performances For the scope of understanding the basic mechanisms giving rise to the possibility of designing WCs and regenerators, a simple model will be enough. We will use the dynami- cal equations of a two-level amplifier, reflecting the wideness of the semiconductor bands by eliminating the frequency dependence of the local gain. Thus, we will write the following equations for our amplifier (see Chapter 4). (10.1) where 8 is the net local gain (that means that it contains the losses also) go is the unsaturated gain n is the refraction index whose complete expression is (10.2) where a is the linewidth enhancement factor no is the bu