l Amplifiers: Analytical Modeling unilateral optical bandwidth is used, which is half the value of B. For a diffused discussion on this convention, see Section 5.8.5. The factor F is called inversion factor and it is given by Individual (D.5) The four terms at the denominator of Equation D.4 represents the contribution of four dif- ferent noise terms to the SN: 1. The first term is the quantum noise associated with the output signal wave, which is assumed to be in a quantum coherent state. 2. The second term is the quantum noise associated with the spontaneous emission wave at the amplifier output. 3 The third term is the noise due to the beat between spontaneous emission and signal wave. 4. The fourth term is the self-beating of the spontaneous emission wave. In all the practical conditions, the term due to the beat between spontaneous emission and signal is largely prevalent SO that the other noise terms can be neglected. In this condition, if G >> 1, (D.4) reduces to (D.6) where NF = 2F is the amplifier noise factor B = B/2 is the optical unilateral bandwidth Sn = 2hw is the unilateral noise power spectral density D.3 Raman-Lumped Fiber Amplifiers Let us image to have k signals at frequencies w;(j=1...2k) whose instantaneous power (i.e., the power flux in a certain instant and in a certain fiber section) is indicated as Pi(t,z). These signals propagate both forward (for j odd, that is, J = 1, 3, 5, ...) and backward (for j even) having the signals Pi(t, z) and Pi+1(t, z) the same angular frequency Wi (j = 1, 3, k - 1). The index S, is also tagged to each signal, with Si = +1 depending upon the propaga- tion direction (+ toward greater values of z, which is in the useful signal direction). These signals will be pumps, in general part of them forward and part of them backward, and useful signals (that, in general, we assume all forward). We will assume also that all the pumps are indicated with j = 1, kpr while signal with j=kp+1, k. All signals cause reflections that propagate through the fiber in the opposite 