## 5 Results and Discussion  
When the pump power is greater than 300 mW, by adjusting PC1 and PC2, the mode-locked laser output with two central wavelengths of 1038.97 nm and 1067.72 nm can be realized. When the central wavelength is 1038.97 nm, the output of the mode-locked CVB fiber laser is as shown in Figure 8. Figure 8a shows the output spectrum, which yields a 3 dB linewidth of 2.99 nm. Figure 8b is a pulse train, wherein the pulse interval is 113.8 ns and the repetition frequency is 8.78 MHz, which is consistent with the theoretical calculation value of 23 m cavity length, referring to the formula f = c/nL. Figure 8c is the corresponding single pulse; the single pulse has Gaussian distribution, and the pulse width is 660 ps. Figure 8d is the change curve of laser output power with pump power. It can be seen that the average output power of the laser is linearly positively correlated with the pump power. This experiment is limited by cavity loss and pump power; the maximum average output power of the LP\({}_{11}\) mode is 5.56 mW. When PC3 is properly adjusted, we obtain CVBs with a maximum output average power of 5.2 mW. This is illustrated in the mode intensity distribution of the laser output. When the central wavelength is 1067.72 nm, the output of the mode-locked CVB fiber laser is as shown in Figure 9. The laser output pulse train and repetition rate are consistent with the output results when the central wavelength is 1038.97 nm; the pulse width of the single pulse is 656 ps. Figure 9d is the change curve of laser output power with pump power. We can see that the average output power of the laser and the pump power also have a linear positive correlation, also limited by cavity loss and pump power; the maximum average output power of the LP\({}_{11}\) mode is 5.5 mW and the maximum output average power of CVBs is 5.2 mW. This is illustrated in the mode intensity distribution of the laser output. Figure 7: CVB all-fiber mode-locked experimental setup. Figure 8: The output characteristics of mode-locked fiber laser at a pump power of 300 mW (central wavelength: 1038.97 nm): (**a**) spectrum; (**b**) output pulse train; (**c**) single pulse; (**d**) the change curve of output power with pump power. Figure 9: The output characteristics of mode-locked fiber laser at a pump power of 300 mW (central wavelength: 1067.72 nm): (**a**) spectrum; (**b**) output pulse train; (**c**) single pulse; (**d**) the change curve of output power with pump power. The relatively low CVB output power is determined by the design and production process of the STMC itself. The specific reason is that in order to obtain a high-purity LP\({}_{11}\) mode during the production process of the STMC, the LP\({}_{11}\) mode should leak into the cladding as much as possible, while the LP\({}_{01}\) mode should be restricted in the fiber core. Thus, the separation of LP\({}_{01}\) and LP\({}_{11}\) modes is maximized, which requires a specific fiber diameter range in the coupling region, thus limiting the CVB output power of the STMC. According to the simulation results above, when the diameter of the STMC-coupling region is larger than 75 \(\upmu\)m, both LP\({}_{01}\) and LP\({}_{11}\) modes are bound in the fiber core and are not coupled to the second TMF. When the diameter of the STMC-coupling region was 29-75 \(\upmu\)m, the evanescent field of the LP\({}_{11}\) mode was not strong, while the LP\({}_{01}\) mode was still bound in the fiber core, and the optical power coupling was very weak, which resulted in low optical power coupling efficiency and CVB output power. When the diameter of the fiber in the coupling region is further reduced to less than 29 \(\upmu\)m, the LP\({}_{01}\) mode begins to be coupled to the second TMF. At this time, the output power is increased, but the increased power is the power of the LP\({}_{01}\) mode, and the purity of the LP\({}_{11}\) mode is reduced.