n = 1/[exp[hAw/kT]-1], where k is the Boltzmann con- stant. Starting from the expression of the thermal phonon number, the phonon- induced optical noise parameter can be expressed as Fjh = - Nphon for scattering in the opposite direction with respect to the incident light (anti-Stokes) and as Fjh = 1 + Nphon = for scattering in the direction of the incident light (Stokes). Also this Appendix D: Fiber Optical Amplifiers: Analytical Modeling term has to appear only in the equation for the ASE evolution, that is, in the equa- tion for j=0, = from which the presence of Sj,0 in its expression. Khj is a polarization factor; in the typical telecommunication case in which the pumps are depolarized to achieve uniform gain on all the input polarizations, Khj = 2/3. Ahj is the Raman fiber effective area defined as a function of the interacting modes transversal shape as (D.8) The Raman gain coefficient can be calculated even starting from prime principles, but often Equations D.7 are solved by inserting a measured value of this coefficient. In any case, it is important to remember that Raman scattering is a polarization-dependent phenomenon. Equations D.7 are written neglecting the field polarizations (otherwise they would be doubled in number). To take into account the polarization effect phenomenologically, a polarization coefficient is introduced that has to be set to 2/3 if, as often in practice, the pump is depolarized and the polarization of the incoming signal field is random. As far as the ASE term is concerned, in Equations D.7, the population inversion is set to perfect inversion, as always with Raman amplifiers. The model provided by Equations D.7 contains all the most important phenomena that impact on design and performances of a Raman amplifier. References 1. Kozak, M.M., Caspary, R., and Unrau, U. B., Computer aided EDFA design, simulation and opti- mization, International Conference on Transparent Optical Networks-ICTON 2001, pp. 202-205. s.l.: IEEE, Cracow, Poland, 2001. 2. Schmidtke, H. J. et al., EDFA mod