Fig. 1. Schematic of the experimental apparatus. CL, collimating lens; BS, beam splitter; λ/4, quarter wave plate; PD, photodetector; OPM, optically pumped magnetometer; PID, proportional-integral-differential module.

Fig. 2. VCSEL properties. (a) Intensity tuning of the VCSEL can be obtained by changing the injection current. The injection current tuning coefficient is 391.9 µW/mA. (b) The tuning coefficient is 224 GHz/mA at 47.5°C and 29.4 GHz/K at 1.8 mA.

Fig. 3. Absorption and dispersion curves (black and red lines, respectively). The vertical axis indicates the detection signal strength, and the horizontal axis represents the laser frequency detuning.

Fig. 4. Frequency shift as estimated by the wavemeter. The frequency shift rates under the free-running (black line), single-closed-loop (blue line), and double-closed-loop (red line) modes are 328.7, 19.0, and 12.5 MHz/h, respectively.

Fig. 5. Allan deviation calculated for three data sets under three running modes. The black, blue, and red lines represent the open-loop, single-closed-loop, and double-closed-loop modes, respectively.

Fig. 6. Light intensity noise in the time domain exposed to Gaussian white noise. The standard deviation is 1.5 and 0.24 mV under the free-running and single-closed-loop modes, respectively.

Fig. 7. NSD of the intensity exposed to Gaussian white noise. The black, blue, and red lines are the free-running, single-closed-loop, and double-closed-loop modes, respectively. The VCSEL intensity noises under the free-running, single-closed-loop, and double-closed-loop modes are approximately 1 × 10^-4, 1 × 10^-5, and 7 × 10^-6 V/Hz^1/2, respectively.

Fig. 8. Intensity NSD under the three running modes. The black, blue, and red lines represent the free-running, single-closed-loop, and double-closed-loop modes, respectively.