st time with a specific derivation, can be derived from the general pulse broadening equation presented in Appendix C. The expression of the characteristic lengths related to the different phenomena is an important source of intuitive information on the system. Due to their role in Equation 6.24 and many other equations related to nonlinear propa- gation in single-mode fibers, they represent the fiber length needed to have a relevant contribution of the considered phenomenon. Thus, longer the characteristic length, the weaker the phenomenon. The average detected field expression can be rewritten as (6.26) where Pout is the detected power, taking into account all the attenuation effects T is the average propagation delay Q collects in a single constant all the constant phase terms is a slowly varying random unitary polarization vector Mout is a normalized Gaussian pulse whose width Tout is given by T1 + AT, where At is the PMD random delay (compare Equation 4.31) Equation 6.26 allows us to determine the performance of RZ transmission. 6.2.3.4 Realistic Receiver Noise Model We have seen that the field emitted by a laser is with an excellent approximation in a coherent quantum state [11]. Narrow band modulation does not change this situation since the coherence time of the modulated field remains very long with respect to the time T needed for a complete revolution of the field phase (@T = 2). Thus, the number of photons arriving on the photodiode has a poison statistics and generates the so-called shot noise or quantum noise. If shot noise is considered, three noise terms appear in the expression of the current: squared shot noise, beat between shot noise and signal, and thermal noise. 6.2.3.4.1 Shot Noise Terms The shot noise is a signal-dependent noise affecting mainly the transmission of a "one." Neglecting the squared shot noise, since it is a second-order term in the noise, and con- sidering that probability p that an incident photon generates an electron is related to the photodiode responsivity Rp by the for