## 4 Results and Discussion
### Optimization of the RIN  
In the process of measurement, we found that air convection in the laboratory and intrinsic light heating may lead to temperature fluctuations in the fiber splitters and photodetector, which would bring fluctuations in the coupling ratio of the fiber splitters and the responsivity of the photodetectors. To verify this, we measured the temperatures of the laboratory and interior of the amplifier, the voltages used for monitoring the actual temperature of the fiber splitter, and the voltage of the PD\({}_{\text{out}}\). As shown in Figure 8, the temperatures of the laboratory and interior of the fiber amplifier change synchronously with a period of approximately 9000 s. The temperature change of the fiber splitters is consistent with that in the interior of the fiber amplifier. When the temperature of the fiber splitter decreases, the power of the out-of-loop increases. The measured voltage of PD\({}_{\text{out}}\) also shows periodic fluctuations under the influence of the temperatures of the fiber splitters and interior of the amplifier. Figure 8: Measurements of temperature fluctuations and voltage fluctuations. To reduce the temperature fluctuations of the fiber splitters, we carefully designed a temperature control system, including a copper encapsulation jacketed by a thermal isolation coating and a precise temperature controller (Thorlabs, TED200C, Newton, NJ, USA) with a temperature stability of 1 mK. The temperature controller (TED200C) is operated with a thermistor temperature sensor (10 k\(\Omega\)), and the analog output delivers a DC voltage, proportional to the actual temperature. For further measurement, we monitored the internal temperature of the amplifier after operating for 4 h, and set the temperature points for the pump LD and fiber couplers to be the same as the internal temperature of the amplifier. Then, the voltage fluctuations of the in-loop and out-of-loop are recorded as shown in Figure 9. The voltage fluctuations of the in-loop and out-of-loop are approximately 0.15 mV and 1 mW when the stable state in the amplifier is achieved. Compared to the out-of-loop voltage in Figure 8, the voltage fluctuations are reduced significantly. Figure 10 shows the measured RIN of the in-loop and out-of-loop. The out-of-loop RIN is measured to be \(-63.2\) dBc/Hz @ 1 mHz and \(-105.8\) dBc/Hz @ 1 Hz. In the frequency range from 1 mHz to 1 Hz, the RIN can be reduced to \(-60\) dBc/Hz, with a further improvement of approximately 16 dBc/Hz @ 1 mHz compared to the out-of-loop RIN without temperature stabilization of the fiber splitters (the black curve). Another important noise source in the feedback loop is the temperature-dependent responsivity of the photodetector, which deteriorates the performance of the power stabilization feedback loop. The photodetector PD\({}_{\text{in}}\) can induce electronic and thermal noise, which affects the intensity noise of the amplified laser. In the feedback loop, the noise of PD\({}_{\text{in}}\) adds to the control signal and impresses equivalent fluctuations with the opposite sign onto the output laser beam. To verify the influence of different photodetectors, a temperature-stabilized detector with a one-stage TE-cooled system (Hamamatsu, G12180-130A, Hamamatsu, Japan) is employed to replace the detector (Thorlabs, DET01 DFC/M, NJ, USA) used in the RIN measurement system. Table 1 shows their typical specifications. Figure 9: Measurements of the voltage fluctuations with temperature stabilization of the fiber splitters. Figure 12 shows the measured voltage fluctuations and RINs employing G12180-130A with 1.2 V bias voltage. The photodetector is temperature-stabilized at 283.15 K and the temperature fluctuations are within 0.7 mK during the measurements. When the internal temperature of the amplifier reaches a steady state, the voltage fluctuations for the out-of-loop detector are approximately 0.3 mV and the out-of-loop RIN is \(-72.5\) dBc/Hz @ 1 mHz and \(-90\) dBc/Hz @ 0.1 Hz, as shown in Figure 12b.