## 3 Experimental Results
This difference is attributed to the fact that the FSR of the TDLI can be adjusted arbitrarily to change the excitation points of the lasers, which should be close to the wave crests of the sub-interferences. The graph in Figure 3c depicts the regular tuning of the wavelength position of a dual-wavelength laser with almost all wavelength spacings of 1.42 nm. The shorter and longer wavelengths of the five dual-wavelength lasers are as follows: 1529.62 nm and 1531.04 nm (light blue pattern); 1529.92 nm and 1531.33 nm (light green pattern); 1530.22 nm and 1531.55 nm (dark current pattern); 1530.42 nm and 1531.84 nm (light current pattern); and 1530.72 nm and 1532.14 nm (yellow pattern), respectively. The difference in the positions of each pair of dual-wavelength lasers is approximately 0.3 nm. The position of the third pair of dual-wavelength lasers is slightly off due to the effects of sub-interference generated by the BS. It is worth noting that the dual-wavelength laser in the yellow spectrum of Figure 3b and the dual-wavelength laser in the light blue spectrum of Figure 3c have the same wavelength position and spacing, and their interference patterns are complementary. One is that the two lasers arise on the same lobe of the interference pattern, and the other is that the two lasers separately arise on the neighboring lobe of the interference pattern. This proves that the interference pattern position can be shifted; as long as the node of the interference pattern corresponds to the peak of the sub-interference, the same two dual-wavelength lasers can arise. Figure 3c illustrates a dual-wavelength laser featuring a narrow tuning range. To showcase a dual-wavelength laser with an extended tuning range, it is essential to fully utilize the TBF function to filter out unnecessary wavelengths and prevent mode competition. The outcomes, depicted in Figure 3d, demonstrate dual wavelengths and their respective spacings: 1527.71 nm and 1529.12 nm (light blue pattern), with a spacing of 1.41 nm; 1529.91 nm and 1531.32 nm (light green pattern), with a spacing of 1.41 nm; 1531.85 nm and 1533.29 nm (dark current pattern), with a spacing of 1.44 nm; and 1533.9 nm and 1535.03 nm (yellow pattern), with a spacing of 1.13 nm. In the yellow part of the spectrum, the lasers have a smaller wavelength spacing because the power of EDFA is higher in the range of 1527 nm to 1534 nm. This makes it challenging for the laser to be stimulated at wavelengths beyond 1535 nm. Figure 4 shows the case where the dual-wavelength laser position remains the same under different interferometric FSRs, and the laser spectrum at different times under this experimental scheme is verified to verify the stability of the system. The wavelengths of the dual-wavelength lasers in Figure 4a,b are both 1530.14 nm and 1531.56 nm, but the FSR of Figure 4a is 1.45 nm, while the FSR of Figure 4b is 0.9 nm. As mentioned in Figure 3, the same interference FSR, but with complementary phases, can produce the same dual-wavelength lasers. Here, the same dual-wavelength laser can be generated with different FSRs, and any point in the interference pattern cannot correspond to each other neatly. This serves as confirmation that the experimental setup is capable of generating multi-format lasers, indicating that the same laser wavelength can coexist with different interference states, a doing that has not been previously demonstrated in previous studies. Figure 5a shows the dual-wavelength laser case with the narrowest wavelength spacing, and Figure 5b shows the dual-wavelength laser case with several interfering lobes in the lasing wavelength gap. Additionally, the dual-wavelength laser states are recorded at different times to confirm their stability. Figure 5a shows a dual-wavelength laser with wavelengths of 1531.85 nm and 1532.15 nm at a wavelength spacing of 0.3 nm, which is achieved by filtering out unnecessary bands with TBF and setting the trough of the interferometric pattern between the two lasing wavelengths to maintain a balanced  
energy distribution.