lk index F is the superposition integral between the guided mode and the density of the electrons The local saturation power is indicated with Psat(t,z) and the characteristic relaxation time of the electron population with T. Finally, the optical power is indicated with P(t,z) and the optical field with E(t,z). 10.3.1.2 Wavelength Converters and Regenerators Based on Cross-Gain Modulation In amplifiers designed to boost the signal power, the saturation power is maintained not too low by designing the amplifier with a high carrier density in the inversion region and a short active waveguide. If the amplifier is used exploiting gain saturation, this effect is enhanced by design- ing a long amplifier. As a matter of fact, SOAs for this application are often longer than 1 mm. The simpler scheme of WC based on SOA gain saturation is reported in Figure 10.12 [20]. A laser, generally a tunable DBR, is integrated into the same chip with a SOA and the laser emission is injected into the SOA via a coupler. The incoming signal is injected into the SOA too via the other coupler input at a different frequency with respect to the continuous wave generated by the local laser, and generally after amplification through another low-gain SOA, to reinforce the gain saturation effect. If the power of the local laser is suitably chosen, the SOA is at the edge of saturation with- out input signal. When the signal pulse arrives, the SOA gain saturates and the output is canceled. In this way, the signal is reported on the local wavelength inverting ones with zeros. Telecommunication Networks Short SOA for signal amplification Contact Integrated directional coupler InP chip FIGURE 10.12 Scheme of a monolithically integrated Three-section Long SOA for WC based on SOA gain saturation. tunable DBR signal processing Moreover, due to the sharp saturation threshold, if the incoming signal pulses are affected by relevant inter-symbol interference (ISI), this is partially canceled by the device that also has regeneration capabilities. The respon