# Characterization of Chromatic Dispersion and
## 4 Measuring Technique and Results
It is worth mentioning that the maximum error when using a 50 cm fiber as a reference was only 1%, in the case of the 50 m sample. The fiber length employed for Figure 2 was 50 m, but the measurements were also repeated for other fiber lengths. The results for 25, 50, and 75 m are shown in Figure 3 for a train of pulses launched into each fiber (all the pulses of the train superimposed in the same figure by taking into account the absolute time delays obtained as described above). Notice that the first pulses that reach the fiber output end are those centered at longer wavelengths, at which the refractive index is lower [16]. The fiber dispersion is also noticeable in this figure, since the temporal width of the measured pulses widens as the fiber length is increased. On the other hand, it can be noticed that the pulses are affected by the PMMA attenuation, but not in the same way for all the pulses. The influence of this attenuation may be observed in the blurriness of the pulses of shorter wavelengths, i.e., of higher attenuation, as expected, this blurriness being more obvious as the fiber length is increased. The instants of maximum pulse intensity in Figure 3a,c,e are shown in the corresponding figures on the right-hand side. The least-squares fittings of these points to Equation (3) give us the expressions for the spectral time delays for each fiber length. The resulting constants for Equation (3) and the corresponding coefficients of determination of the fittings (\(R^{2}\)) are summarized in Table 2. These constants are employed in Equation (4) to achieve the material dispersion coefficients \(D(\lambda)\) of the fibers. The results are shown in Figure 4a. It can be noticed that the value of \(D(\lambda)\) slightly depends on the fiber length. Specifically, the maximum relative discrepancy from one fiber length to another is around 3% at the wavelength interval considered in the figure. This means that the employed fiber length does not alter the results significantly when characterizing the dispersion of POFs. Despite the high coefficients of determination in Table 2, one of them (corresponding to the 25 m Toray fiber) is lower than the other two; but this lower value could be improved by reducing the temporal window of the Streak Camera while maintaining the number of temporal pixels. That procedure would increase the temporal resolution. However, it would imply a more complex synchronization process, thus leading to a longer measurement time. For the choice of a more appropriate fiber length, it should also be taken into account that the 75 m fiber is affected by the detrimental effect of the higher attenuation on the quality of the pulses. In order to partially compensate for this loss of quality, we also tried to employ higher integration times. However, this implied longer measurement times and the improvement achieved was small. Consequently, the most suitable fiber length among the three considered was 50 m in the conditions employed for this work. In any case; it is worth mentioning that the optimum fiber length would depend on the excitation and measurement conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(A\) & \(B\) (nm\({}^{2}\)) & \(R^{2}\) \\ \hline TORAY 25 m & 1.470 & 5006 & 0.9917 \\ TORAY 50 m & 1.472 & 4907 & 0.9979 \\ TORAY 75 m & 1.473 & 4851 & 0.9976 \\ MITSUBISHI 25 m & 1.474 & 4707 & 0.9908 \\ MITSUBISHI 50 m & 1.476 & 4627 & 0.9943 \\ MITSUBISHI 75 m & 1.477 & 4580 & 0.9954 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coefficients \(A\) and \(B\) of Equation (3) together with the corresponding coefficient of determination of the fittings (\(R^{2}\)). It should be noted that the dispersion results were obtained by using Equation (4), which is only valid when the considered wavelength interval \(\Delta\lambda\) is small, as was explained in Section 2.