# Characterization of Chromatic Dispersion and
## 4 Measuring Technique and Results
The lack of accuracy when \(\Delta\lambda\) is too large can be observed in Figure 5, in which the results obtained by using Equation (4) for the 50 m Toray fiber are compared with the dispersion values corresponding to larger intervals of \(\Delta\lambda\) (from 10 to 120 nm). The discrepancies are plotted as relative errors. In such intervals, the derivative (\(dt_{\text{g}}/d\lambda\)) that is necessary to calculate \(D(\lambda)\) was estimated by using the two edges of the wavelength interval considered. As can be observed, the relative error is lower than 1% only when the wavelength interval is smaller than 40 nm. In other words, for any light source centered at any wavelength, the dispersion given by Equation (4) is accurate as long as the spectral width is not broader than 40 nm, taking the criterion of the 1%. Figure 3: (**a,c,e**): Streak images of the output pulses measured from Toray fibers whose lengths are 25, 50, and 75 m, respectively. (**b,d,f**): corresponding instants of maximum pulse intensity together with the fittings to Equation (3). The insets show the resulting constants and the corresponding coefficients of determination of the fittings. We also analyzed three PMMA fiber samples manufactured by a second manufacturer, i.e., Mitsubishi (see Table 1 for further details). The lengths of these fibers were, again, 25, 50, and 75 m. In this respect, the process was carried out under the same conditions and exactly in the same way as described above, and the obtained results for the material dispersion are shown in Figure 4b and Table 2. The new measurements using a different brand confirm again that the dispersion coefficients are independent of the fiber length. Moreover, for each fiber length, the results obtained with both brands of fiber (Toray and Mitsubishi) are almost identical, the maximum difference detected being 3%. Once the coefficients \(A\) and \(B\) of Equation (3) have been obtained, they can be introduced into Equation (2) in order to calculate the values of the refractive indices of the measured POFs. The results obtained by doing so for all the OPF samples are shown in Figure 6. Again, the results are independent of the employed fiber length. Notice that the zoomed vertical scale in the figure causes the discrepancies to seem greater. However, the maximum relative errors are of only 0.13% and 0.2% for the Toray and the Mitsubishi fibers, respectively. Similarly, the results obtained for both manufacturers are alike again, the maximum difference between them being of 0.3% in the measured range of wavelengths. Figure 4: Material-dispersion coefficients obtained for POFs made by Toray (**a**) and by Mitsubishi (**b**). Three different lengths of fiber were employed for each manufacturer: 25 m (green lines), 50 m (blue lines), and 75 m (red lines). Figure 5: Relative error (%) obtained in the material dispersion coefficients as a function of the wavelength interval \(\Delta\lambda\) for the 50 m Toray fiber. All these results allow us to conclude that the most important issue affecting the refractive index and the chromatic dispersion is the fiber material. In order to corroborate this, we made some Raman measurements. In this respect, most of the Raman bands shown in Figure 7 coincide with those available in the literature [23; 24]. At first glance, we can see in Figure 7a that the Raman bands of the fiber cores do not depend on the fiber manufacturer. We can also see that the same happens with the bands of the claddings, because the materials employed are the same in both cases. Consequently, it is reasonable to have obtained that both the refractive indices and the coefficients of chromatic dispersion in our POFs are almost independent of the manufacturer. Note, in Figure 7a, the slightly higher values obtained for the Mitsubishi fiber as compared to those of the Toray fiber. This effect can be a consequence of a more intense fluorescence emission in this fiber, which does not have any influence on its refractive index or its chromatic dispersion.