[Kawakami, Komori, Tanaka, Saito]

The SRY cavity was scanned by directly driving the sub-laser PZT while monitoring the beat signal in the OMC REFL. Using the Max Hold function of the spectrum analyzer, transmission power as a function of beat frequency was obtained around 1.6 GHz, 800 MHz, −800 MHz, and −1.6 GHz. The measurement data are stored in:

Dropbox → All files/Dropbox KAGRA/Measurements/IFO/SRCL/SRCL_OMC_REFL_beat_signal_PZT_sweep/2026_07_23_SRY

The data were fitted both with and without a linear background, and the maximum and minimum values within the fitting uncertainties were used to estimate the uncertainty. From these results, the SRY cavity length was determined by fitting. The measured length differs from the design value by 1.757(50) cm, which is consistent with the previous result of 1.58(82) cm reported in klog:37209.
 

• First, a new spectrum analyzer was installed to monitor the beat signal at the OMC REFL. A PLL was established using the down-converted beat signal when the original beat frequency was approximately 450 MHz, and it was confirmed that the SRY cavity could be scanned by frequency-modulating the LO. Next, although the mixer used for down-conversion has a nominal upper frequency limit of 500 MHz, it was expected that PLL operation would still be possible at higher frequencies with only increased conversion loss. Therefore, the beat frequency was increased to approximately 800 MHz, and it was confirmed that the SRY cavity could again be scanned by frequency-modulating the LO while using the down-converted signal for the PLL.
   
• Furthermore, since the PLL is not required for the OMC REFL beat-signal measurement itself, the PLL was turned off and the sub-laser PZT was driven directly to scan the SRY cavity. This worked successfully when the beat frequency was around 800 MHz. Therefore, the sub-laser PZT was driven directly, and the Max Hold function of the spectrum analyzer was used to obtain transmission-power data as a function of beat frequency around 1.6 GHz, 800 MHz, −800 MHz, and −1.6 GHz (Fig. 1). Here, the negative frequencies correspond to the case in which the sub-laser frequency is lower than the main laser frequency. In addition, while observing the maximum beat-signal level in the OMC REFL during the PZT sweep, the alignment was optimized using a single mirror. As a result, the peak shapes became noticeably cleaner. This suggests that the relatively large uncertainty of the SRY measurement in klog:37209 was likely caused by imperfect alignment. After acquiring the data around 1.6 GHz and 800 MHz, the temperature of the sub-laser was increased to reduce its frequency. The beat signal disappeared at approximately 29.8°C. According to klog:36777, the sub-laser undergoes a mode hop between 29.5°C and 30°C, so the disappearance of the beat signal is attributed to this mode hop. The temperature was then increased further, and at approximately 31.64°C, data around −800 MHz were acquired. Before and after this point, data around 1.6 GHz and −1.6 GHz were also obtained.
   

• The peaks in the measured data were fitted with and without a linear background, following the same procedure as in klog:37209. The fitting results for the individual peaks are listed below. The measurement data are also stored in:

  Dropbox → All files/Dropbox KAGRA/Measurements/IFO/SRCL/SRCL_OMC_REFL_beat_signal_PZT_sweep/2026_07_23_SRY

  Fig. 2: Around 1.6 GHz, without a linear background. Using data from 1518.25 MHz to 1519.1 MHz, the fitted peak frequency is 1518.7773(42) MHz.
  Fig. 3: Around 1.6 GHz, with a linear background. Using data from 1518.25 MHz to 1519.1 MHz, the fitted peak frequency is 1518.725(13) MHz.
  Fig. 4: Around 800 MHz, without a linear background. Using data from 872 MHz to 873.6 MHz, the fitted peak frequency is 872.8561(45) MHz.
  Fig. 5: Around 800 MHz, with a linear background. Using data from 872 MHz to 873.6 MHz, the fitted peak frequency is 872.8274(81) MHz.
  Fig. 6: Around −800 MHz, without a linear background. Using data from 823.3 MHz to 824.25 MHz, the fitted peak frequency is 823.7654(15) MHz.
  Fig. 7: Around −800 MHz, with a linear background. Using data from 823.3 MHz to 824.25 MHz, the fitted peak frequency is 823.7819(48) MHz.
  Fig. 8: Around −1.6 GHz, without a linear background. Using data from 1555 MHz to 1556 MHz, the fitted peak frequency is 1555.3774(33) MHz.
  Fig. 9: Around −1.6 GHz, with a linear background. Using data from 1555 MHz to 1556 MHz, the fitted peak frequency is 1555.3867(99) MHz.
   

• From the fitted peak frequencies and their uncertainties, the maximum and minimum frequencies within the uncertainty range were determined. The overall uncertainty range was taken as the union of the results obtained with and without a linear background. The following values were therefore used to determine the SRY cavity length:

  Minimum (MHz)    Maximum (MHz)
  1518.7120    1518.7815
  872.8193    872.8606
  −823.7866    −823.7639
  −1555.3967    −1555.3768

  The midpoint frequency between the minimum and maximum values was divided by the FSR calculated from the SRY design length of 64.9264 m. The resulting values were rounded to the nearest integers, and the measured frequencies were fitted with the function AN + B, where A and B are fitting parameters and N is an integer. The fitting results are shown in Fig. 10:

  A: 2.308085(18) MHz
  B: 0.2480(98) MHz

  Since A corresponds to the FSR, the SRY cavity length was calculated from this value:

  Fitted length: 64.94397(50) m
  Design value: 64.9264 m
  Difference (fitted − design): 1.757(50) cm

  This result is consistent with the previous result reported in klog:37209, which gave a difference from the design value of 1.58(82) cm.