 of the interferometer and then the overall disper- sion characteristic, the phase contribution (@) of the response in Equation 9.2 has to be calculated and derived with respect to the angular frequency. FIGURE 9.3 Block scheme of an interferometric TODC: DE1 and DE2 represents two different dispersion elements. Telecommunication Networks The result depends again on the factor A(w) = (Akw2 + ATW) that appears under a cosine function. It is possible to select Ak and At SO that in a determined optical bandwidth, the approxi- mation is verified: A(w) = (Akw2 + Atw) = 0. Assuming to be in this condition, the differential delay expression of the interferometer can be quite simplified, up to arriving at the following expression (9.4) Equation 9.4 has the form expected by a TODC, since it linear in W and depends on an adjustable parameter, which is a. Just to make an example, let us consider a fiber interferometer where the dispersion is achieved by fiber brag gratings. The device parameters are summarized in Table 9.1. From the table it results that the condition of A(w) = 0 is attained introducing a length difference of about 1.1 um among the gratings at a wavelength of 1.55 um. The behavior of cos[A(w)] is represented in Figure 9.4 versus the wavelength deviation with respect to 1.55 um. TABLE 9.1 Physical Parameters of the Fiber Components Used in the Example of Wideband Tunable Dispersion Compensator do (um) a (um) Aw (cy/s) -3.7 X 1013 WO (cy/s) (null dispersion) 2.3 X 1014 w (cy/s) 1.9 X 1014 Grating 1 Grating 2 L (mm) 80.0000 79.94 T (ps) 266.66 266.48 Dispersion (ps2/mm) Cos [A(w)] FIGURE 9.4 Bandwidth of the response of an interferometric TODC. Wavelength deviation (nm) Next Generation Transmission Systems Differential delay (ps) a 0.1 a=0.5 =0.994 FIGURE 9.5 Differential delay versus the wavelength for an interferometric TODC and for different values of the Wavelength deviation (nm) setting parameter a. The TODC in this example has a bandwidth of about 40 nm around the reference wavelength (corresponding to 1