## 3 Experimental Design and Analysis of Results
### Determination of the Optimal Operating Point for FP-ECDL  
Considering the need to select appropriate laser communication bands in the field of inter-satellite laser communication, this paper primarily adopts the ITU-prescribed \(\mathcal{C}\), \(L\), and \(H\) bands with a 100 GHz frequency spacing [27]. Figure 16 shows some of these channels. Accordingly, the proposed optimal operating point for the FP-ECDL refers to the wavelength closest to the one read at 25 \({}^{\circ}\)C among the channel wavelengths when the FP-ECDL operates at a certain temperature and current. At this point, the linewidth is relatively small, and the optical power needs to be greater than 10 mW. Considering that the long-term operation of the laser and changes in the external environment can cause slight wavelength fluctuations, a wavelength error less than 1 pm compared to the expected  
Figure 14: The Lorentzian linewidths of two FP-ECDLs with different F-P etalon precisions. Figure 15: Power-injection characteristics of two FP-ECDLs with different F-P etalon precisions. channel wavelength in actual measurements can be considered as meeting the wavelength requirements of the optimal operating point [28]. Choosing the high-F-P-etalon-precision FP-ECDL, the actual temperature scanning curve is shown in Figure 17, with a fixed operating current of 200 mA and a scanning range of 10-35 \({}^{\circ}\)C. During both the heating and cooling processes, wavelength jumps can be observed. This is because, with an increase in temperature, the gain peak of the diode laser shifts towards longer wavelengths. Simultaneously, the rise in temperature leads to thermal expansion, causing an increase in the laser cavity length, which also results in a change in the longitudinal mode wavelength. The reverse occurs during the cooling process. Additionally, within a certain range (for the same mode), the longitudinal mode of the diode laser linearly changes with temperature. Beyond this range, the laser will jump to the next mode, causing a sudden wavelength jump. This phenomenon is known as mode hopping. Power is supplied to the FP-ECDL, and its operating temperature is set to 25 \({}^{\circ}\)C, with the working point labeled as \(O\). At this point, the wavelength is 1550.5853 nm, and by analysis, it is closest to the \(H33\) channel with a wavelength of 1550.52 nm. Considering \(O\) as the initial state, the linear segment passing through \(O\) represents the FP-ECDL's initial mode. Through heating and cooling scans, the wavelength-temperature change rates during heating and cooling are calculated to be 0.195 pm/0.01 \({}^{\circ}\)C and 0.198 pm/0.01 \({}^{\circ}\)C, respectively. Since the heating scan precedes the cooling scan, the temperature of FP-ECDL after the scan reaches the minimum value of 10 \({}^{\circ}\)C. At this juncture, it is observed that during the heating scan, FP-ECDL undergoes a mode jump to the initial mode at the lowest temperature of approximately 22.3 \({}^{\circ}\)C. Setting the temperature to 23 \({}^{\circ}\)C and then 25 \({}^{\circ}\)C restores the initial mode without the issue of secondary mode hopping caused by overshooting. Returning to the initial \(O\) point and setting the temperature to 21.57 \({}^{\circ}\)C using the known wavelength-temperature change rate results in a wavelength of 1550.5204 nm, with a wavelength error of only 0.4 pm, meeting the requirement of less than 1 pm. Additionally, using the linewidth testing system mentioned earlier, the Lorentzian linewidth at this working point is approximately 2.5314 kHz, denoted as point \(A\). Testing points  
Figure 16: Partial channels with a 100 GHz interval. Figure 17: Curves of the bidirectional temperature-scanning of the FP-ECDL. \(P1\), \(P2\), and \(P3\), with the same wavelength as \(A\), yields actual linewidths of 3.2019 kHz, 2.9742 kHz, and 2.9713 kHz, respectively, all greater than the linewidth at point \(A\).