pic sections with saturation power Psat* The overall effect is integrated over the length and it is intuitive that the saturation is reached far sooner than in the single isolated section. The same reason causes the overall gain bandwidth to be smaller than the local gain bandwidth. Defining B as the frequency bandwidth at which the gain Go is reduced to half (reduced by 3 dB), we get (4.69) The behavior of the amplifier bandwidth versus the linear gain G0 is plotted in Figure 4.14 for a microscopic bandwidth of 2.5 THz. Considering the amplifier noise performances, Equation 4.63 can be formally solved tak- ing into account also the noise term and using the expression of the noise autocorrelation function, the following expression is obtained for the noise variance (4.70) where is the noise bandwidth that is fixed either from a filter at the amplifier output or from the normalized integral of the amplified spontaneous emission (ASE) spectrum. In practical communication systems, it is frequently important to evaluate the signal to noise ratio after the detection of the optical signal through a photodiode. For this reason, often optical amplifiers are characterized from a noise point of view through the so-called noise factor NF, defined as the ratio between the signal to noise ratio of the detected input signal (SN0) and the signal to noise ratio of the same signal after amplifi- cation (SN). Since in practical systems the signal incoming into the receiver is always with a very god approximation in a coherent state [44], in the absence of amplification, SN0 is determined FIGURE 4.14 Gain bandwidth of an ideal two-level amplifier ver- sus the linear gain Go for a microscopic bandwidth of 2.5 THz. Macroscopic gain (dB) Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices by the quantum noise related to a coherent state (i.e., the variance of the photon number in a coherent state). This quantity can be thus expressed as SNo = 21r coo B. (4.71) where Be is the electrical signal bandwidth 