Objective Distributed feedback (DFB) fiber lasers (DFB-FLs) are the seed source of high-power narrow linewidth fiber lasers, which are widely employed in LIDAR, gravitational wave detection, beam combination, and other applications. Phase-shifted fiber gratings (PS-FBG) are the key devices of DFB-FLs, whose coupling strength has a direct impact on the output performance of DFB- FLs. Therefore, it is essential to study the coupling strength of the PS-FBG to obtain the best DFB-FL output performance. Methods Using the transmission matrix theory and the energy level rate equation, a transmission model of the DFB-FL was established, and the output characteristics of the DFB-FL were analyzed by simulation. Experimentally, PS-FBGs with varying coupling coefficients and grating lengths were fabricated using the light scanning method of a phase mask. Based on PS-FBGs, DFB- FLs were constructed and tested. Finally, to introduce additional birefringence in the PS-FBG phase-shift region, a stress point was applied during the packaging process. This approach was aimed at suppressing dual-polarization states and enhancing the polarization extinction ratio of the laser. Results and Discussions The simulation results indicate that the transmission slit bandwidth of the PS-FBG decreases with an increase in the coupling strength. The pumping efficiency of the DFB-FL first increases and then decreases with an increase in the PS- FBG coupling strength. The output polarization state of the DFB-FL is influenced by the coupling strength of the PS-FBG and birefringence within the fiber. Thus, reducing the coupling strength of the PS-FBG or increasing the internal birefringence of the PS- FBG is advantageous for achieving the single polarization state output of the DFB-FL. The relaxation oscillation frequency of the DFB-FL increases as the PS-FBG coupling strength increases while the relative intensity noise (RIN) decreases. The experimental results show that the output performance of DFB-FL is closely related to PS-FBG coupling strength kappa L. First, the output laser linewidth of DFB-FL exponentially reduces with the increase of PS-FBG coupling strength kappa L. When kappa L<5, the output laser linewidth of DFB-FL narrows rapidly with the increase in kappa L; when kappa L>5, the laser linewidth decreases slowly; when kappa L=6.65, the linewidth reaches the minimum of 2.2 kHz (Fig. 6); at kappa L=4.84, the pumping efficiency of DFB-FL reaches the maximum of 0.16 degrees o (Fig. 7). However, further increase in coupling coefficient leads to a faster decline in pumping efficiency after the maximum pumping efficiency. Under the same coupling strength, long grating length and small coupling coefficient are more conducive to obtaining laser output with high pumping efficiency. When kappa L<5, the DFB-FL operates in a single polarization mode, the polarization extinction ratio achieving 20 dB (Table 1). With increasing kappa L, the polarization extinction ratio decreases, and DFB-FL gradually transitions to dual-polarization operation (Fig. 8). When kappa L=6.65, the relaxation oscillation frequency of the laser is 1.59 MHz, and the lowest RIN peak is-120.6 dB/Hz (Fig. 9). Therefore, achieving a single-polarization laser output with a narrow linewidth, high pumping efficiency, and low-intensity noise is challenging when relying solely on the PS-FBG coupling strength design. Finally, by optimizing the package structure design, a narrow linewidth fiber laser with output laser linewidth of 4. 1 kHz, peak RIN <-120 dB/Hz, polarization extinction ratio of 23 dB, and pumping efficiency of 0.17 degrees o is achieved (Fig. 11). Conclusions The effect of PS-FBG coupling strength on the output performance of the DFB-FL is investigated theoretically and experimentally. The results show that the output laser linewidth of DFB-FL decreases with the increase of PS-FBG coupling strength kappa L. The relaxation oscillation frequency shifts to a higher value and the RIN peak value decreases. Simultaneously, the polarization extinction ratio decreases and the phenomenon of dual-polarization output gradually appears. In addition, with an increase in the PS- FBG coupling strength, the pumping efficiency initially increases and then decreases. In the experiment, when kappa L=4.84, the pumping efficiency of DFB-FL reaches the maximum value of 0.16 degrees o. Depending on the design of the PS-FBG coupling strength, obtaining a single-polarization laser output with a narrow linewidth, high pumping efficiency, and low-intensity noise is challenging. Finally, the DFB-FL is constructed using a PS-FBG with a grating length of 40 mm and a coupling coefficient of 120.9 m-1. By applying a stress point in the package area of PS-FBG, DFB-FL with a linewidth of 4.1 kHz, RIN peak value <-120 dB/Hz, polarization extinction ratio of 23 dB, pumping efficiency of 0.17 degrees o, and maximum output power of 750 mu W is obtained.
