direction of the signal itself; thus the backward signal has to also be considered if it is not injected into the fiber (which means that the corresponding boundary condition is zero). Appendix D: Fiber Optical Amplifiers: Analytical Modeling We can suppose that the relative intensity noise affects both pumps and signals and is constituted by a set of random band limited processes: we will call the instantaneous power flux of such processes Ni(t, z) (j = 1, k) with the same convection adopted for the signal instantaneous power. Moreover, spontaneous emission noise, caused by amplifica- tion of the spontaneous photons emitted due to the interaction with the fundamental state of the field, has to also be inserted in the equations. In order to model the ASE evolution, we introduce No(t, z), which represents ASE instantaneous power in a fiber section. Once all the waves, pumps, signals, and noise propagating through the fiber are deter- mined, we can apply as usual the rotating wave and the slowly varying approximation to pass from the wave equation to a set of coupled evolution equations that can be written as follows: (D.7) (h=1,..,k)(j=0,...k) In Equations D.7, symbols represent the following physical parameters: ghj represents the Raman gain and is equal to g(wh - wj) if Wh > Wji otherwise 8hj = The term hw/2 in the noise equation represents the continuous noise generation due to the spontaneous emission along the amplifier length [4]. This term obvi- ously has to appear only in the equation for the ASE evolution, that is, in the equa- tion for j = 0. In (D.7), the term Sjo, which is 1 only if j = 1; else it is zero is present just to write in the general expression the terms appearing in the ASE equation only. Vi represents the backward Rayleigh scattering coefficient, which is the loss due to Rayleigh scattering only. Fjh is the phonon-induced optical noise parameter that is related to the phonon den- sity due to temperature [1]. The phonons number at a certain energy hAw is given by the Bose distribution, Npho