## 3 Experimental Results
For an FUT with the low value of \(|D_{B}|\) over the wavelength range of interest, the difference of \(t_{d}\) among different wavelengths is small, and \(\Delta\phi^{max}\) is much smaller than \(2\pi\). In this scenario, \(\Delta\phi(\lambda)\) cannot be retrieved accurately, and the GBD measurement fails. To realize measurements in this scenario, the experimental setup in Figure 1 is modified. Rather than directly measuring the \(t_{d}\) of two orthogonally polarized SMOSs, the modified setup first measures the wavelength-dependent group delays of fast axis \(t_{f}(\lambda)\) and slow axis \(t_{s}(\lambda)\), respectively. Then, \(t_{d}(\lambda)\) is calculated by \(t_{d}(\lambda)=t_{s}(\lambda)-t_{f}(\lambda)\). Application of \(t_{d}(\lambda)\) to Equation (4) leads to \(B(\lambda)\). Accordingly, \(D_{B}(\lambda)\) is obtained by utilization of Equation (5). Figure 5 presents the modified measurement setup to interrogate \(t_{f}(\lambda)\) and \(t_{s}(\lambda)\). In the experiment, a 509.5 m elliptical core PMF (Draka) is under test. To measure \(t_{f}(\lambda)\), port 1 and port 3 of the PMC with the FUT and the reflector R are connected to the fast axis ports of the PBS and the PBC, respectively. Using this setup, the difference of \(t_{f}\) and \(t_{s-ref}\) is measured, where \(t_{s-ref}\) refers to the group delay of the SMOS propagating from the input of the PBS to the slow axis port of the PBC. The process of \(t_{f}(\lambda)-t_{s-ref}(\lambda)\) measurement is the same as that of \(t_{d}(\lambda)=t_{s}(\lambda)-t_{f}(\lambda)\) measurement in the case of the Panda PMF. Similarly, \(t_{s}(\lambda)-t_{f-ref}(\lambda)\) is obtained by connecting port 1 and port 3 of the PMC to the slow axis ports of the PBS and the PBC, respectively, where \(t_{f-ref}\) refers to the group delay of the SMOS propagating through the fast axes of the PBS and the PBC. Then, \(t_{d}(\lambda)\) is calculated by  
\[t_{d}=\left[t_{s}(\lambda)-t_{f}(\lambda)\right]-\left[t_{f-ref}(\lambda)-t_{ s-ref}(\lambda)\right]. \tag{6}\]  
Figure 4: (**a**) Experimental results of (**a**) \(t_{d}\), (**b**) \(B\) and (**c**) \(D_{B}\) as a function of \(\lambda\) in the case of Panda PMF characterization. Figure 5: Schematic of the modified measurement setup to interrogate \(t_{f}(\lambda)\) and \(t_{s}(\lambda)\) in the case of elliptical core PMF characterization. Considering that the fiber length of the connection between the PBS and the PBC is much shorter than the length of the FUT, \(\left|t_{f-ref}(\lambda)-t_{s-ref}(\lambda)\right|\) is much smaller than \(\left|t_{s}(\lambda)-t_{f}(\lambda)\right|\). As a result, the approximation of \(t_{d}(\lambda)=t_{s}(\lambda)-t_{f}(\lambda)\) is valid. With Equations (4) and (5), \(B(\lambda)\) and \(D_{B}(\lambda)\) are calculated. Figure 6a presents the measurement results of group delays \(t_{f}(\lambda)\), \(t_{s}(\lambda)\) and calculated DGD \(t_{d}(\lambda)\). It is shown that \(t_{f}\) and \(t_{s}\) decline as \(\lambda\) increases. In contrast, \(t_{d}\) declines in the beginning and then increases after a turning point at 1555 nm. Wavelength-dependent group birefringence \(B(\lambda)\) of the elliptical core fiber is calculated from \(t_{d}(\lambda)\) by usage of Equation (4) with \(L=509.5\) m, and the values are presented in Figure 6b. The results show \(B=4.553\times 10^{-4}\) at \(\lambda=1550\) nm. \(D_{B}\) is calculated from \(B(\lambda)\) by utilization of Equation (5), and the calculated values are presented in Figure 6c. The calculated results reveal that GBD is normal with \(D_{B}<0\) for \(\lambda<1555\) nm and anomalous with \(D_{B}>0\) for \(\lambda>1555\) nm.