ed in [68] where it is also shown that similar curves agree very well with experimental results. Among the noise term that we have neglected in simplifying the Raman equations, the RIN transfer from the pump to the signal is the most important; thus, a model for this noise source is useful when dealing with the design of systems including Raman amplifiers. In order to study this phenomenon, following [68], it is needed to add to the system (4.84) the equations for the signal and the pumps RIN. These equations can be obtained from the complete model presented in Appendix D by applying to the complete RIN evolu- tion equations the approximations already applied to the pumps and signal propagation equations. The RIN equations can be solved analytically too, due to the knowledge of the signal and pumps evolution, SO that the signal RIN at the output of the amplifier is given by FIGURE 4.40 Raman amplifier noise factor versus net gain for an amplifier using 3 km of DCF fiber. (After Bristiel, B. et al., IEEE Photonics Technol. Lett., 18(8), 980, 2006.) Gain (dB) Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices (4.90) Equation 4.90 is in good agreement with experience, as shown in [68], but for the case in which the noise in the bandwidth near the pump is considered. A last observation that can be important in the Raman lumped amplifiers design is that the effect of temperature can be important in degrading the amplifier noise performances. Just to make an example, an increase of the noise spectrum as great as 5 dB has been mea- sured passing from 77 to 300K at 1460 nm in a 9km single-stage amplifier pumped by a pump of 850 mW at 1455nm. In the same conditions, the peak gain at 1545 nm increases from 12 to 18 dB. All the multistage techniques that are well established in the EDFA design can be adopted to design effective Raman amplifiers. For example, multistage amplifiers can be devices with low-gain stages putting in between isolators that prevent the accumulation of double Rayleigh 