## 3 Results and Discussion
### Transmission Properties Using Green Light as a Function of Fiber Length  
In this subsection we present a thorough characterization of the transmission properties of the fibers, including spatial properties, time/frequency properties and overall transmission performance. The spatial properties of light at the outputs of the fibers were characterized in terms of encircled angular flux (EAF) obtained from FFP measurements, and the fiber frequency response was calculated from measurements of the S\({}_{21}\) transmission parameter of the link. Finally, the measurement of BER as a function of data rate completed the characterization, giving a full picture not only of the fiber but of the whole link. In order to ease the comparison of the different fibers, numerical parameters were extracted from these characterization measurements: optical power; EAF width; fiber 3-dB bandwidth; and maximum data rates for a given BER value were obtained as a function of fiber length and allowed us to evaluate the influence of the numerical aperture. The EAF, obtained from the measured FFP, is a particularly interesting way to represent the spatial distribution of optical power because it represents the portion of power contained in a given solid angle [21]. Figure 2 displays the EAFs obtained for the MH on the left, for the GH in the middle and for the BH on the right, at several selected lengths: 100, 50, 20 15 and 1 m, and at the maximum measured length, which was different for each fiber. The graphs illustrate the different behavior of the fibers. First, we can observe that the EAFs for the 1-m MH and the 1-m BH are very narrow, suggesting an underfilled launch, and the EAF for the 1-m GH is wider. As we said before, the direct launch is rather variable, and it is possible to get very different launching conditions depending on the fiber termination and connector position [20]. The EAFs for the two POFs with wider NAs, GH and BH exhibited steady widening with increasing fiber length, as should be expected by power diffusion [18]. For the longest fiber lengths, BH and GH EAFs only show small changes, which indicates that the equilibrium mode distribution was reached at the maximum measured length for both fibers. However, MH dis  
Figure 2: EAFs at selected fiber lengths. (**a**) MH fiber, (**b**) GH fiber and (**c**) BH fiber. there is not a monotonous increase of EAF width with length, and the widest EAFs was found at 100 m rather than at 130 m. During the experiments, we observed that, particularly for this fiber, the end polishing produced relevant changes both in the output power and in the shape of the FFP, which introduced high variability over these measurements. We suggest that this behavior can be explained by alterations in its double-cladding structure incurred when applying the sandpaper. As for the frequency response, it was obtained from the measurement of the S\({}_{21}\) transmission parameter, for a given length L, according to:  
\[H_{L}(f)=\left(\frac{S_{21,\;L}(f)}{S_{21,\;REF}(f)}\right)^{\frac{1}{2}} \tag{1}\]  
where \(S_{21,\;L}(f)\) is the link transmission parameter measured for a fiber length L, and \(S_{21,\;REF}(f)\) is the transmission parameter for a 1-m fiber segment. This last measurement was taken at the end of the cut-back experiment under the same launching conditions, and was used as a reference to account for the frequency responses of the active devices. The frequency responses for the MH, GH and BH fibers are represented on the left, middle and right plots of Figure 3, respectively. The lines show the averages of five measurements, and the error bars their standard deviations. The graphs show selected lengths of all fibers used: 100, 70, 50, 30, 20 and 15 m. The frequency responses for the longest measured lengths are also shown for MH (130 m) and GH (150 m). All graphs show that the frequency response narrowed with increasing fiber length by the effect of modal dispersion.