## 1 Introduction  
Polarization-maintaining fibers (PMFs) with lengths of hundreds of meters have been applied in many fields, such as ultrafast all-optical switching and ultrashort pulse generation [1; 2]. In these applications, the group birefringence dispersion (GBD) of a PMF governs the temporal profiles of amplitudes and spectra of optical pulses through nonlinear optical effects. The characterization of the GBD of the PMF helps to control the properties of the optical pulses. PMFs have also been employed in distributed stress sensors [3]. The sensor measures the stress by detecting the polarization model coupling induced by the external transverse forces. The usage of a long PMF ensures distributed stress sensing over a long distance. Because of the GBD of the PMF, the spatial resolution of stress measurements deteriorates with fiber distance. Characterization of the GBD of the long PMF mitigates the impact of birefringence dispersion on distributed stress measurements.  
White-light-interferometry-based techniques, including spectrum-domain and time-domain techniques, are widely used to characterize the GBD of a PMF [4; 5; 6; 7; 8; 9; 10]. The interferogram of optical intensity as a function of wavelength or scanning length is detected in a spectrum-domain/time-domain technique. The phase of the interferogram is retrieved, which leads to the phase birefringence, group birefringence and the GBD of the PMF. The accuracy of these techniques is determined by the accuracy of the phase retrieval. For a long PMF, the interference contrast of the interferogram is low because of the short coherent length of the employed white light source. Low interference contrast results in the large error of the retrieved phase and, hence, has an impact on the accuracy of birefringence dispersion measurement. To implement precise measurements, the maximum measurable fiber length of the white-light-interferometry-based technique is severely shortened.  
Kerr phase-interrogators have been reported for measuring the differential group delay (DGD) of two sinusoidally modulated optical signals (SMOSs) [11; 12], and they have been employed to measure the GBD of a Panda PMF by directly measuring the wavelength-dependent DGD of two SMOSs polarized along the principal axes of the Panda PMF [13]. The reported approach utilizes the Kerr effect instead of the interference between two polarization modes to measure the GBD, and hence removes the limitation of laser coherence length on the maximum measurable fiber length. Unfortunately, the reported approach fails when the GBD of the PMF under test is so low that the detected optical power cannot oscillate over one sinusoidal circle as the laser wavelength of the SMOSs scans. In addition, the performance of this approach has not been rigorously discussed.  
In the present study, the Kerr-phase-interrogator-based technique is systematically studied for measuring the GBD of a PMF. The GBD of a Panda PMF and an elliptical core PMF are measured by the proposed technique to demonstrate the high GBD measurement and the low GBD measurement. In addition, the performance of the proposed technique is rigorously analyzed. With the compensation for the intensity loss of the SMOSs, the proposed approach is capable of characterizing a PMF that is tens of kilometers long.