## 3 Experimental Results  
The GBD of a 459.4 m Panda PMF (Fujikura) is experimentally investigated. The wavelength of the combined signals oscillating at \(f_{s}\) = 20 GHz is scanned from \(\lambda_{1}\) = 1540 nm to \(\lambda_{2}\) = 1565 nm in steps of 0.1 nm, and the power spectral densities (PSDs) of the optical signal at the output of the Kerr medium are recorded for each \(\lambda\) by the optical spectrum analyzer (OSA). The recorded values of \(P_{1}\) as a function of \(\lambda\) are presented in Figure 2a, showing a sinusoidal power variation as \(\lambda\) increases, which agrees with the theoretical analysis and the indication of Equation (1). The relative phase \(\Delta\phi(\lambda)\) is calculated from \(P_{1}(\lambda)\) with \(\lambda_{ref}=\lambda_{1}\), and is presented in Figure 2b. Figure 1: Schematic of the Kerr phase-interrogator for group birefringence dispersion (GBD) measurements. TL: tunable laser; EOM: electro-optic modulator; RF: radio frequency; PC: polarization controller; PBS: polarization beam splitter; PBC: polarization beam combiner; PMC: polarization-maintaining circulator; FUT: fiber under test; R: reflector; EDFA: erbium-doped fiber amplifier; OSA: optical spectrum analyzer; OBPF: optical band-pass filter; PD: photodiode; OSC: oscilloscope; PSD: power spectral density. To measure the absolute DGD of \(t_{ref}\), the reference wavelength is fixed at \(\lambda_{ref}=\lambda_{1}\). \(f_{\rm s}\) is linearly scanned at a rate of \(r\) = 80 GHz/s from \(f_{\rm s-}init\) = 16 GHz to \(f_{\rm s-}fin\) = 24 GHz, and the sideband power \(P_{1}\) as a function of time \(t\) is acquired by an oscilloscope. To obtain \(P_{1}\) as a function of \(f_{\rm s}\), \(t\) is replaced with \(f_{\rm s}=f_{\rm s-}init+rt\). Figure 3a presents the \(P_{1}(f_{\rm s})\) showing a sinusoidal variation of \(P_{1}\) as \(f_{\rm s}\) increases, in agreement with the indication of Equation (1). \(\Delta\phi(f_{\rm s})\) is demodulated from \(P_{1}(f_{\rm s})\) and is presented in Figure 3b. The linear fit \(\Delta\phi_{fit}(f_{\rm s})\) is also presented in Figure 3b. Applying \(\Delta\phi_{fit}(f_{\rm s})\) to Equation (3) gives an absolute DGD of \(t_{ref}\) = 1448 ps at \(\lambda_{ref}=\lambda_{1}\). Similarly, a value of \(t_{ref2}\) = 1493 ps is obtained at \(\lambda_{ref2}=\lambda_{2}\). Comparison of \(t_{ref}\) and \(t_{ref2}\) reveals the increment of \(t_{d}\) as \(\lambda\) increases. The values of absolute DGD are calculated using \(t_{d}(\lambda)=t_{ref}+\Delta t_{d}(\lambda)\) and are presented in Figure 4a. \(B(\lambda)\) is calculated from \(t_{d}(\lambda)\) by using Equation (4) and \(L\) = 459.4 m, and it is presented in Figure 4b showing a value of \(4.784\times 10^{-4}\) at \(\lambda=1550\) nm. Figure 4c presents the values of GBD, \(D_{B}\), calculated from the wavelength dependence of \(B(\lambda)\) by utilization of Equation (5), showing \(D_{B}=5.55\times 10^{-7}\)/nm at \(\lambda=1550\) nm. Figure 3: Measurement results of (**a**) \(P_{1}\) and (**b**) \(\Delta\phi\) as a function of \(f_{\rm s}\) when the laser wavelength is \(\lambda_{1}\) = 1540 nm in the case of Panda PMF characterization. Figure 2: Measurement results of (**a**) \(P_{1}\) and (**b**) \(\Delta\phi\) as a function of \(\lambda\) in the case of Panda polarization-maintaining fiber (PMF) characterization. Essentially, \(\Delta\phi(\lambda)\) retrieval is the key for the measurements of \(B(\lambda)\) and \(D_{B}(\lambda)\). Obtaining \(\Delta\phi(\lambda)\), one can easily calculate \(B(\lambda)\) and \(D_{B}(\lambda)\) directly from \(\Delta\phi(\lambda)\) using Equations (2)-(5). \(\Delta\phi(\lambda)\) is retrieved from the sinusoidal variation of \(P_{1}(\lambda)\)[12]. Accurate phase retrieval of \(\Delta\phi(\lambda)\) requires \(P_{1}(\lambda)\) to undergo at least one sinusoidal variation cycle as \(\lambda\) varies over the wavelength range of interest. In other words, a maximum relative phase of \(\Delta\phi^{max}\) larger than \(2\pi\) is expected.