【正文】 This shows that singleSagnacloop transmissivity is related to the polarization deflection angle and the phase difference between two axes. As shown in the simulated results in Fig. 2, the filter period is shorter and the filter bandwidth is narrower when the length of the PMF is increased. However, the period and bandwidth cannot be tuned independently. In addition, with the PMF birefringences higher, the filter period is shorter and the filter bandwidth is narrower. For the double Sagnac loops, a fiber isolator is mounted between two Sagnac loops for eliminating the reflective light. So, the transmissivity of double loops can be described as （5）Obviously, the transmissivity of double Sagnac loopsis related to the length or the refraction difference of two segments of PMFs based on Eq. (5). Then, the filter period and bandwidth are determined by a shorter PMF and a longer PMF, respectively, and the output laser can be tuned by adjusting the PCs and the lengths of the PMFs. In a doubleSagnacloop structure, two segments of PMF were 2 m long and 1 m long. Figure 3(a) shows the simulated result. From the figure we can see that the filter period can be changed while the filter bandwidth is unchanged. Keeping a 2 m long PMF in one Sagnac loop, Fig. 3(b) shows that the filter bandwidth can be changed while the filter period is unchanged by changing the length of a longer PMF (2 m) in another Sagnac loop. Thus, by using double Sagnac loops in the fiber laser, both the wavelength spacing and the bandwidth can be tuned independently.Fig. 1. (a) Tunable multiwavelength fiber laser based on a double Sagnac HiBi fiber loop interferometer. (b) Sagnac interference loop.Fig. 2. (Color online) Transmissivity spectrum of single Sagnac loop.Fig. 3. (Color online) Transmissivity spectrum of double Sagnac loop. (a) Tunable filter period without changing filter bandwidth.(b) Tunable filter bandwidth without changing filter period.3. Experiments and ResultsIn experiments, isolator 1 was used to ensure the unidirectional propagation of the light and decrease the noise. The length, cutoff wavelength, numerical aperture, and peak absorption near 1530 nm of the EDF are 12 m, 960 nm, , and 7 dB∕m, respectively. Lengths of PMFs are 5 and 2 m, and the birefringence beat length is less than mm. To be pumped at 300 mW, we used an optical spectrum analyzer (AQ6370B) to monitor the output laser. Based on simulated results, the filter period can be tuned by changing the length of the short PMF, and multiple lasers will be produced by all the transmitted light of the filter. Since gain spectrumflatness and polarization attenuation are limited, part of the light in the filter bandwidth will be suppressed. The number of lasing wavelengths was sensitive to the PC. The operation of three wavelengths with the center wavelength at nm is illustrated in Fig. 4, and the SMSR of the laser is greater than 50 dB. The irregular output spectrum of the multiwavelength laser was mainly caused by inaccurate refractive difference of PMFs, inaccurate length of PMFs, and the splicing loss. Fig. 4(b) shows the repeated scans of the output spectrum with , , and nm at 2 min intervals over a 10 min period. Stable output power and wavelength can be observed. A measurement of the optical powers at three wavelengths showed that the maximum power fluctuation was less than dB and the wavelength fluctuation was less than nm. The polarization deflection angle can be tuned by adjusting PC1 and PC2. Then the wavelength and the wavelength spacing of the output laser can be tuned. As shown in Fig. 5, the multiwavelength output laser was observed in (a) the short wavelength and (b) the long wavelength within the Cband by adjusting two PCs. The multiwavelength output laser can be observed in the whole Cband in Fig. 5(c), and the laser stability was decreased with the increasing of the oscillation modes.In the experiment, we observed that the output wavelength spacing can be tuned by adjusting two PCs. As shown in Fig. 6, the wavelength spacing of the multiwavelength fiber lasers changed from (panel a) to nm (panel b). By adjusting the PC, parts of the light in the filter bandwidth were not up to threshold. Then the number of wavelengths and the wavelength spacing could be tuned by the PC. Hence, by adjusting the PCs, we observed that six wavelengths was the maximum number of stable output peaks. The wavelength spacing can be tuned by changing the length of the short PMF based on Eq. (5). In the experiment, with a 5 m length for the long PMF and 1 m length for the short PMF, we observed that the wavelength spacing was nm, as shown in Fig. 7(a). Therefore, with a 2 m length of the short PMF, we observed that the wavelength spacing was nm, as shown in Fig. 7(b). Based on both simulated and experimental results, the wavelength spacing is be narrowed by increasing the length of the short PMF while the linewidth is unchanged. The laser linewidth could be tuned by changing the length of the long PMF based on simulated results. When the lengths of the two segments of the PMFs were 1 m, nm of 3 dB linewidth was observed, as shown in Fig. 8(a).With 5mlength of the long PMF, nm of 3 dB linewidth was observed, shown in Fig. 8(b). The experimental results show that the linewidth will be narrower when the length of the long PMF is increased, without a change in wavelength spacing. Thus, the simulated results [Fig. 3(b)] were verified by the experimental results. With smaller peak linewidth, the fiber laser was more vulnerable to environmental perturbations, but the jitter range was less than nm.Fig. 4. (Color online) Output optical spectrum of the multiwavelength fiber laser. (a) Three wavelength laser spectrum. (b) Repeated scans of the output spectrum in