# A Spaceborne Mounting Method for Fixing a Cubic Fabry-Perot Cavity in Ultra-Stable Lasers
## 3 Experimental Results and Discussion
In order to analyze whether the WS could withstand the vibration tests, three criteria were proposed. First, we monitored the direct current (DC) component of the voltage of the PD2. The PD2 is based on a silicon PIN photodiode (S9055, Hamamatsu). The width of the photosensitive area of the PD2 is 0.2 mm. In order to capture more laser power, a focus lens with a focal length of 2.75 mm was used in front of the photodiode chip of the PD2. Consequently, the chip was fixed to the focal point of the lens. The diameter of the laser beam radiated on the PD2 (before the focus lens) is ca. 400 \(\upmu\)m. Based on the Gaussian distribution and above-measured diameter of the laser beam, the diameter of the laser spot at the focal point of the lens is ca. 9.34 \(\upmu\)m (calculated using Wyrowski VirtualLab Fusion software). Considering the focal length of the lens, the voltage of the PD2 can remain the same when the tilt angle of the laser beam is within range of  
\[\pm\theta=\pm tan^{-1}[(100-9.34)/2750]=\pm 33\;mrad \tag{1}\]  
Therefore, monitoring the voltage of the PD2 can roughly determine whether the optical system, especially the fixed FP cavity, has a severe tilt or not during aerospace vibration tests. This is important for protecting the system because of the high expense of the FP cavity. During the vibration tests, a frequency tunable laser was connected to the fiber from the CL. The laser power at the position of the PD2 was ca. 55 \(\upmu\)W. The voltage of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{3}{c}{**Sinusoidal Vibration**} & \multicolumn{5}{c}{**Random Vibration**} \\ \hline
**Frequency Range (Hz)** & **Amplitude** & \begin{tabular}{c} **Sweep Rate** \\ **(oct/min)** \\ \end{tabular} & \begin{tabular}{c} **Frequency** \\ **Range (Hz)** \\ \end{tabular} & \
\begin{tabular}{c} **Power Spectral** \\ **Density** \\ \end{tabular} &
\begin{tabular}{c} **Acceleration** \\ **RMS (Grms)** \\ \end{tabular} & **Time (s)** \\ \hline
4–10 & 9 mm & 3 & 10–50 &
\begin{tabular}{c} 3 dB/oct \\ (rising slope) \\ \end{tabular} & 3.055 & 90 \\
10–17 & 3.6 g & 3 & 50–300 &
\begin{tabular}{c} 0.25 g\({}^{2}\)/Hz \\ (holding value) \\ \end{tabular} & 3.055 & 90 \\
17–60 & 6.6 g & 3 & 300–2000 &
\begin{tabular}{c} \(-12\) dB/oct \\ (falling slope) \\ \end{tabular} & 3.055 & 90 \\
60–100 & 4.8 g & 3 & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of the vibration tests. Figure 4: Whole system (WS) during vibration tests. (The non-English term in the upper left corner of the figure is the safety instructions. Whereas, that in the bottom of the figure is the company’s name in Chinese). the PD2 was always within the range of 2.13 \(\pm\) 0.01 V during the vibration tests, indicating that the FP cavity did not have a severe offset. Second, we monitored the voltage of the PD3 while performing laser frequency tuning over 1 free spectral range (FSR). The FSR of the cavity can be determined by the following equation:  
\[FSR=c/(2L) \tag{2}\]  
where \(c\) is light speed and \(L\) is the length of the cavity. Therefore, the FSR of the 100 \(\times\) 100 \(\times\) 100 mm cubic cavity is 1.5 GHz. Because the voltage of the PD2 can only indicate whether the FP cavity has a severe offset or not, the voltage of the PD3 was used to judge the offset of the FP cavity more precisely. When the laser is aligned well with the FP cavity, modes are excited. Tuning the laser frequency causes the laser to resonate with the FP cavity at certain frequencies. At these frequencies, the laser is transmitted through the FP cavity. Then, the voltage will be generated on the PD3. using this criterion, a few milliradians of tilt can be identified (as simulated in the OSCAR toolbox in MATLAB) [24]. The WS was first adjusted to a condition under which only the TEM00 mode could resonate with the FP cavity in 1 FSR before the vibration tests. Figure 5 shows the voltage of the PD3 and the frequency of the laser when the laser is being tuned at a certain speed.