Fig. 1. Ideal polarization evolution in (a) the Sagnac loop and (b) the cavity. Polarization rotator formed with the (c) PM fiber or (d) the Faraday rotators. PBS, polarization beam splitter; CW, clockwise; CCW, counterclockwise; FR, Faraday rotator.

Fig. 2. Schematic of the NPE mode-locked fiber laser with the PBS-formed Sagnac loop. LD, laser diode; WDM, wavelength division multiplexer; col, collimator; EDF, Er-doped fiber; ISO, isolator; λ/2, half-wave plate.

Fig. 3. Calculated correlation between the nonlinear loss and the nonlinear phase bias with different α of 0°, 15°, 30°, 45°, 60°, 75°, and 90°.

Fig. 4. (a) Corrected nonlinear loss with a 20% insertion loss to the CCW pulses. Simulated evolution processes of (b) the pulse duration and (c) the spectral width in this cavity. Positions A, B, C, D, and E denote the ISO, the left PBS, the right PBS, and both ends of EDF marked in Fig. 2, respectively. The fiber length of AB, CD, DE, EC, and BA are 0.3, 0.1, 0.8, 0.5, and 0.3 m respectively. The lengths of the isolator and wavelength division multiplexer are 0 m. The distance between the two PBSs is 0.04 m (equivalent fiber length). At the left fiber loop, the CW pulse (green line) and CCW pulse (blue line) have different evolution processes.

Fig. 5. (a) Experimental schematic of the figure-8 APM fiber laser with a specially designed fiber coupler. (b) Designed 7.5-cm-long PBS-based fiber coupler. Integrated NPE-based mode-locked laser with (c) the design drawing and (d) the proto-model picture.

Fig. 6. (a) Measured temporal electronic pulse trace, (b) radio frequency spectrum, (c) optical spectrum, and (d) pulse autocorrelation of the fiber laser. RBW, resoultion bandwidth.

Fig. 7. (a) Measured single-band phase noise and (b) RIN of the repetition rate signal.