endence of the propagation constant from the polarization) and mode coupling (through the off diagonal coefficients). It is to be noted that, since a repre- sents the power attenuation, a/2 appears in the field expression. Equation 4.8 summarizes all the propagation effects characterizing the linear propaga- tion regime in case of limited signal bandwidth. 4.2.4 Fiber Chromatic Dispersion Chromatic dispersion in single-mode fibers is the phenomenon causing the broadening of a light pulse propagating along the fiber that is independent from the pulse polarization. In Equation 4.8, chromatic dispersion is caused by the dependence on the angular fre- quency of the common mode propagation constant B(@). In particular, remembering the small signal bandwidth hypothesis and indicating with W0 the central angular frequency of the signal spectrum, we can write B()p()(()(+ (4.10) The terms of the Taylor series of ((@) have different physical meanings. The term B'(@0)z that is obtained substituting Equation 4.10 in Equation 4.8 represents a group delay, as can be easily shown from the property of the Fourier integral. This is the average delay a pulse experiments traversing the fiber span (as a matter of fact it has also the dimension of a time interval). To evidence this meaning, the time delay T can be written as Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices (4.11) being Ug = 1/() the group velocity. In a first approximation, injecting in the fiber a pulse with bandwidth Aw, the pulse broadening At can be evaluated by the group velocity dispersion (GVD) between the fre- quencies at the spectrum borders. Using Equation 4.10 up to the second order, the follow- ing expression is obtained. (4.12) Alternatively, considering wavelengths instead that angular frequencies (4.13) The parameter D = =2/-() is called the fiber dispersion parameter (measured in ps/nm/km). There are fundamentally two phenomena contributing to the value of the parameter D: material dispersion and waveguide dispersion,