[Tanaka, Fujimoto, Saito]

To observe the beat signal with the RFPD installed at OMC REFL, the vertical axis of the spectrum analyzer was set to a linear scale, and the number of frame averages was increased to make the peak height and frequency easier to identify. During the observation, the beat frequency occasionally shifted toward lower frequencies, sometimes as often as once every few seconds. The No. 3 sub-laser used in this experiment (as identified in the JGW DOC documentation) is known to exhibit frequency-noise events that increase its RMS frequency noise approximately once every 5 s to 2 min, and the occurrence rate closely matched that of the observed beat-frequency shifts. Therefore, these frequency shifts are considered to originate from the frequency noise of the sub-laser. The beat-signal amplitude also fluctuated, which is believed to be caused by fluctuations of PRX. Accordingly, when the beat signal was stable, the LO frequency was varied, and the minimum and maximum frequencies at which the beat-signal amplitude reached its maximum were measured around 160 MHz, 140 MHz, −160 MHz, and −140 MHz. Fitting these measurements yielded a PRX length of 68.27 ± 0.01 m, compared with the design value of 68.2563 m.
 

• The sub-laser was injected into PRX, the PLL was engaged, and the beat signal was observed with the RFPD installed at OMC REFL. The objective was to determine the minimum and maximum frequencies at which the beat-signal amplitude reached its maximum. For this purpose, the vertical axis of the spectrum analyzer was set to a linear scale, and the number of frame averages was increased to improve the visibility of the peak height and frequency. By varying the PLL LO frequency, both the resonance point (Fig. 1) and the anti-resonance point (Fig. 2) were observed. At the anti-resonance point, however, the beat-signal peak appeared to split into two peaks.
   
• During the measurements, the beat frequency occasionally shifted toward lower frequencies, sometimes as often as once every few seconds. The beat signal in the PLL path exhibited the same frequency shift. Initially, fluctuations of the Moku:Lab LO signal were suspected, so the LO source was switched from the Moku:Lab to the function generator that had originally been used. However, no change was observed. Fluctuations of the main laser were also considered, and an additional control loop was applied to suppress them, but this likewise produced no improvement. On the other hand, the No. 3 sub-laser used in this experiment (as described in the JGW DOC documentation) is known to exhibit frequency-noise events that increase its RMS frequency noise approximately once every 5 s to 2 min, and the occurrence rate closely matched that of the observed beat-frequency shifts. Therefore, the observed frequency shifts are considered to originate from the frequency noise of the sub-laser. The beat-signal amplitude also fluctuated, which is believed to be caused by fluctuations of PRX.
   

• Therefore, when the beat signal was stable, the LO frequency was varied, and the minimum and maximum frequencies at which the beat-signal amplitude reached its maximum were measured around 160 MHz, 140 MHz, −160 MHz, and −140 MHz. Negative frequencies correspond to the case where the sub-laser frequency is lower than the main-laser frequency. The measured values are listed below.

  Minimum    Maximum
  162.363 MHz    162.442 MHz
  140.366 MHz    140.494 MHz
  −140.683 MHz    −140.555 MHz (assuming ±0.064 MHz around −140.619 MHz)
  −160.435 MHz    −160.307 MHz (assuming ±0.064 MHz around −160.371 MHz)

  The midpoint between the minimum and maximum frequencies was then calculated for each measurement. Each midpoint was divided by the FSR calculated from the PRX design length of 68.2563 m. The resulting values were rounded to the nearest integers, and the measured frequencies were fitted with the linear function AN+B, where A and B are fitting parameters and N is the corresponding integer. The fitting results are shown in Fig. 3 and are summarized below:

  A = 2.1957 ± 0.0004 MHz
  B = −0.08 ± 0.03 MHz

  Since A corresponds to the FSR, the PRX length calculated from the fitted FSR is

  Fitted PRX length: 68.27 ± 0.01 m
  Design value: 68.2563 m

[Tanaka, Hirose, Fujimoto, Saito]

Following the same procedure as in the previous measurement (klog:37185), the lengths of PRY, SRY, and SRX were measured. The differences between the measured and design values were 0.6 ± 1.2 cm for PRY, 1.5 ± 1.3 cm for SRY, and 2.8 ± 1.6 cm for SRX. Therefore, the PRY measurement is consistent with the design value within the measurement uncertainty of 1.2 cm, whereas the differences for SRY and SRX exceed their respective uncertainties, suggesting that their actual lengths may differ from the design values.
 

• As in the previous measurement (klog:37185), the sub-laser was injected into PRY, SRY, and SRX, the PLL was engaged, and the beat signal was observed with the RFPD installed at OMC REFL. The minimum and maximum frequencies at which the beat-signal amplitude reached its maximum were measured. The results are summarized below.

  PRY
  Minimum    Maximum
  161.501 MHz    161.583 MHz
  138.351 MHz    138.485 MHz (assuming ±67 kHz around 138.418 MHz)
  −140.999 MHz    −140.865 MHz (assuming ±67 kHz around −140.932 MHz)
  −161.783 MHz    −161.649 MHz (assuming ±67 kHz around −161.716 MHz)
  SRY
  Minimum    Maximum
  161.371 MHz    161.492 MHz
  140.6095 MHz    140.7305 MHz (assuming ±60.5 kHz around 140.67 MHz)
  −141.0055 MHz    −140.8845 MHz (assuming ±60.5 kHz around −140.945 MHz)
  −161.7595 MHz    −161.6385 MHz (assuming ±60.5 kHz around −161.699 MHz)
  SRX
  Minimum    Maximum
  −160.384 MHz    −160.244 MHz (assuming ±70 kHz around −160.314 MHz)
  −140.65 MHz    −140.51 MHz (assuming ±70 kHz around −140.58 MHz)
  162.316 MHz    162.456 MHz (assuming ±70 kHz around 162.386 MHz)
  140.33 MHz    140.47 MHz (assuming ±70 kHz around 140.400 MHz)

  During the measurements, the sub-laser temperature was changed significantly when switching the beat frequency from +160 MHz to −160 MHz. Under these conditions, the beat frequency observed at OMC REFL fluctuated much more frequently, suggesting that the fluctuations become significant until the sub-laser temperature stabilizes. In addition, after switching from +140 MHz to −140 MHz during the SRY measurement, the frequency fluctuations did not subside. However, when the MCE feedback was enabled during the subsequent SRX measurement, the fluctuations were noticeably reduced. This suggests that fluctuations of the main laser also contribute to the beat-frequency instability.
   

• For each cavity, the midpoint between the measured minimum and maximum frequencies was calculated and divided by the corresponding FSR calculated from the design lengths of 64.9265 m (PRY), 64.9264 m (SRY), and 68.2562 m (SRX). The resulting values were rounded to the nearest integers, and the measured frequencies were fitted with the linear function AN+B, where A and B are fitting parameters and N is the corresponding integer. The fitting results are as follows.

  PRY (Fig. 1)
  A = 2.30892 ± 0.00044 MHz
  B = −0.091 ± 0.030 MHz
  SRY (Fig. 2)
  A = 2.30818 ± 0.00046 MHz
  B = −0.136 ± 0.030 MHz
  SRX (Fig. 3)
  A = 2.19520 ± 0.00051 MHz
  B = −0.076 ± 0.035 MHz

  Since A corresponds to the FSR, the cavity lengths obtained from the fitted FSR values are

  PRY
  Fitted length: 64.921 ± 0.012 m
  Design length: 64.9265 m
  Difference (Fitted − Design): −0.6 ± 1.2 cm
  SRY
  Fitted length: 64.941 ± 0.013 m
  Design length: 64.9264 m
  Difference (Fitted − Design): 1.5 ± 1.3 cm
  SRX
  Fitted length: 68.284 ± 0.016 m
  Design length: 68.2562 m
  Difference (Fitted − Design): 2.8 ± 1.6 cm

  Therefore, the measured PRY length is consistent with the design value within the measurement uncertainty of 1.2 cm. In contrast, the differences between the measured and design values for SRY and SRX exceed their respective uncertainties, suggesting that their actual cavity lengths may differ from the design values.

[Aritomi, Ushiba, Tanaka, Saito]

The sub-laser was injected into SRY, and the PLL was engaged while the LO frequency was swept to scan the beat signal. Using the maximum hold function of the Moku:Lab spectrum analyzer, the SRY transmitted power was recorded as a function of frequency. Because the slopes on the two sides of the resonance peak were different, the data were fitted both with and without a linear background offset. The two fitting methods yielded resonance frequencies differing by approximately 47.9 kHz. If this difference is regarded as the fitting uncertainty, it is comparable to the measurement uncertainty reported previously (klog:37191). The PLL UGF was then reduced to narrow the beat-signal linewidth, and the measurement and fitting procedure was repeated. However, the fitted resonance frequencies with and without a linear background offset differed by approximately 143 kHz, indicating that the fitting uncertainty was not improved. To achieve more accurate fitting, it will likely be necessary to suppress fluctuations in the beat-signal amplitude and reduce the influence of higher-order modes.

• The sub-laser was injected into SRY, the PLL was engaged, and the beat signal was observed using the RFPD installed at OMC REFL. The LO frequency was then swept to scan the beat signal. The maximum hold function of the Moku:Lab spectrum analyzer was used to obtain the transmitted power of SRY as a function of beat frequency (Fig. 1). In Fig. 1, the orange trace represents the maximum-hold spectrum, while the red trace shows the instantaneous beat signal. The data between 163.5 MHz and 164.0 MHz were fitted using Φ=A*f−B,P_t​=C/(1+D(sin(Φ/2))^2), where f is the beat frequency. The fitted resonance frequency was 163.7443 ± 0.0017 MHz. However, as shown in Fig. 1, the slopes on the two sides of the resonance peak were asymmetric, and the fitted curve did not perfectly reproduce the measured data. Based on a suggestion from ChatGPT that a linear background should be included for such asymmetric data, the data were also fitted using Φ=A*f−B,P_t​=C/(1+D(sin(Φ/2))^2)+E*f+F, where E and F represent the linear background terms (Fig. 3). This fit yielded a resonance frequency of 163.7922 ± 0.0057 MHz. The fit including the linear background appears to reproduce the measured data better than the fit without the background. However, the resonance frequencies obtained from the two fitting methods differ by approximately 47.9 kHz. Therefore, if this difference is regarded as the fitting uncertainty, it is comparable to the uncertainty obtained in the previous measurement (klog:37191).
• Next, an attempt was made to perform the PLL using the SRMI signal, but the PLL could not be locked. The SRM gain was also increased while measuring SRY, but no noticeable improvement was observed. The SRM gain was then restored to its original value, and the PLL UGF was reduced in order to narrow the beat-signal linewidth and thereby improve the acquisition of the maximum-hold spectrum during the LO frequency sweep. The UGF was reduced by changing the gain of the Moku:Lab filter from 0 dB to −40 dB. The LO frequency was swept again, and another transmission spectrum of SRY was obtained (Fig. 4). The data between 165.6 MHz and 166.4 MHz were first fitted without a linear background, yielding the result shown in Fig. 5. The fitted resonance frequency was 166.0614 ± 0.0055 MHz. The same data were then fitted with a linear background, as shown in Fig. 6, resulting in a resonance frequency of 166.204 ± 0.049 MHz. As in the previous measurement, the fit including the linear background appears to reproduce the measured data more accurately. However, the resonance frequencies obtained with and without the linear background differ by approximately 143 kHz, indicating that the fitting uncertainty was not improved. These results suggest that achieving more accurate fitting will require suppressing fluctuations in the beat-signal amplitude and reducing the influence of higher-order transverse modes.

According to Saito-kun, HV amp (x10) was directly connected to the laser PZT input for the PLL lock. According to my past experiences, the direct connection tends to excite PZT at high frequency.

To solve this problem, we inserted a passive LPF that is set as one of the filters for the control servo between the PZT input and the HV. According to my memory, 10Hz ?? LPF and 100kHz?? LPF were used as one of the control filters. So what I can suggest is to set a passive LPF btw the PZT and the HV, and remove the same LPF in the control filters. I have a ponoma case and a film condenser (400V?) in my room.

Another concern is that the UGF at 10kHz for the PLL control might to excite some resonances of the PZT as in the main laser frequency stabilization servo.

[Aritomi, Ushiba, Tanaka, Saito]

Sub-laser light was injected into the SRY, PRY, PRX, and SRX, and a PLL was established. The LO frequency was then swept to scan the beat signal. Using the maximum hold function of the Moku:Lab spectrum analyzer, transmission power as a function of frequency was recorded around 190 MHz, 160 MHz, 140 MHz, −140 MHz, −160 MHz, and −190 MHz. The data were fitted both with and without a linear background, and the maximum and minimum peak frequencies within the corresponding fitting uncertainties were determined. The cavity lengths were then calculated from these results. The differences between the measured cavity lengths and the design values were 0.15 ± 0.33 cm for PRY and 1.58 ± 0.82 cm for SRY. Therefore, the PRY measurement is consistent with the design value within its uncertainty of 0.33 cm, whereas the SRY measurement differs from the design value by more than the estimated uncertainty, suggesting that the actual cavity length may differ from the design value. The results for PRX and SRX will be reported after the analysis is completed.
 

• As in the previous measurement (klog:37201), sub-laser light was injected into the SRY, PRY, PRX, and SRX, and a PLL was established. The beat signal was observed using the RFPD installed at OMC REFL. The LO frequency was then swept to scan the beat signal. Using the maximum hold function of the Moku:Lab spectrum analyzer, transmission power as a function of frequency was measured around 190 MHz, 160 MHz, 140 MHz, −140 MHz, −160 MHz, and −190 MHz for each cavity. Here, negative frequencies correspond to the case where the sub-laser frequency was lower than that of the main laser.
   

• For the data near each resonance peak, fitting was performed both with and without a linear background, following the same procedure as in the previous analysis (klog:37201). From the fitted peak frequencies and their uncertainties, the maximum and minimum frequencies within the fitting uncertainty were determined. The overall uncertainty range was then defined as the largest and smallest values obtained from both fitting models. The following data were used to determine the PRY and SRY cavity lengths.

  PRY
  Minimum (MHz)    Maximum (MHz)
  186.9049    186.9561
  163.8426    163.8974
  131.4761    131.5159
  -115.5105    -115.4909
  -157.0807    -157.0589
  -189.4049    -189.3442
  SRY
  Minimum (MHz)    Maximum (MHz)
  186.8354    186.9305
  166.0559    166.2530
  131.4035    131.4918
  -127.2003    -126.2609
  -159.4324    -159.3557
  -189.3570    -189.2707
   

• From the measurement results, the midpoint between the minimum and maximum frequencies was calculated for each resonance. These midpoint frequencies were divided by the FSR calculated from the design cavity lengths (64.9265 m for PRY and 64.9264 m for SRY). The resulting values were rounded to the nearest integers, and the measured frequencies were fitted with the linear function AN+B, where A and B are fitting parameters and N is the rounded integer. The fitting results were as follows.

  PRY (Fig. 1)
  A: 2.30865 ± 0.00012 MHz
  B: −0.0741 ± 0.0074 MHz
  SRY (Fig. 2)
  A: 2.30815 ± 0.00029 MHz
  B: −0.092 ± 0.021 MHz
   

• Since A corresponds to the FSR, the cavity lengths were calculated from the fitted values of A.

  PRY
  Measured cavity length: 64.9280 ± 0.0033 m
  Design value: 64.9265 m
  Difference (measured − design): 0.15 ± 0.33 cm
  SRY
  Measured cavity length: 64.9422 ± 0.0082 m
  Design value: 64.9264 m
  Difference (measured − design): 1.58 ± 0.82 cm

  Therefore, the PRY measurement is consistent with the design value within the uncertainty of 0.33 cm. In contrast, the difference between the measured and design values for SRY exceeds the estimated uncertainty, suggesting that the actual SRY cavity length may differ from the design value. The results for PRX and SRX will be posted once the analysis has been completed.

Saito-kun,

Could you upload the overplot graphs of the raw data and the fitting functions similar to fig 2 and 3 in klog37201?

The fitting results for the individual SRY resonance peaks presented in klog:37209 are summarized below. The measurement data are stored in Dropbox → All files/Dropbox KAGRA/Measurements/IFO/SRCL/SRCL_OMC_REFL_beat_signal_LO_sweep/2026_07_14_SRY.

• Figure 1: Around 190 MHz, without a linear background. Using data from 186.4 MHz to 187.1 MHz, the fitted peak frequency is 186.8382 ± 0.0027 MHz.
  Figure 2: Around 190 MHz, with a linear background. Using data from 186.4 MHz to 187.1 MHz, the fitted peak frequency is 186.908 ± 0.022 MHz.
   
• Figure 3: Around 160 MHz, without a linear background. Using data from 165.6 MHz to 166.4 MHz, the fitted peak frequency is 166.0614 ± 0.0055 MHz.
  Figure 4: Around 160 MHz, with a linear background. Using data from 165.6 MHz to 166.4 MHz, the fitted peak frequency is 166.204 ± 0.049 MHz.
   
• Figure 5: Around 140 MHz, without a linear background. Using data from 130.96 MHz to 131.69 MHz, the fitted peak frequency is 131.4068 ± 0.0033 MHz.
  Figure 6: Around 140 MHz, with a linear background. Using data from 130.96 MHz to 131.69 MHz, the fitted peak frequency is 131.480 ± 0.012 MHz.
   
• Figure 7: Around −140 MHz, without a linear background. Using data from 126.8 MHz to 127.5 MHz, the fitted peak frequency is 127.0443 ± 0.0054 MHz.
  Figure 8: Around −140 MHz, with a linear background. Using data from 126.8 MHz to 127.5 MHz, the fitted peak frequency is 126.73 ± 0.47 MHz.
   
• Figure 9: Around −160 MHz, without a linear background. Using data from 159.1 MHz to 159.9 MHz, the fitted peak frequency is 159.4293 ± 0.0031 MHz.
  Figure 10: Around −160 MHz, with a linear background. Using data from 159.1 MHz to 159.9 MHz, the fitted peak frequency is 159.372 ± 0.016 MHz.
   
• Figure 11: Around −190 MHz, without a linear background. Using data from 189.1 MHz to 189.87 MHz, the fitted peak frequency is 189.3517 ± 0.0053 MHz.
  Figure 12: Around −190 MHz, with a linear background. Using data from 189.1 MHz to 189.87 MHz, the fitted peak frequency is 189.295 ± 0.024 MHz.

The fitting results for the individual PRY resonance peaks presented in klog:37209 are summarized below. The measurement data are stored in Dropbox → All files/Dropbox KAGRA/Measurements/IFO/PRCL/PRCL_OMC_REFL_beat_signal_LO_sweep/2026_07_14_PRY.

• Figure 1: Around 190 MHz, without a linear background. Using data from 186.5 MHz to 187.4 MHz, the fitted peak frequency is 186.9075 ± 0.0027 MHz.
  Figure 2: Around 190 MHz, with a linear background. Using data from 186.5 MHz to 187.4 MHz, the fitted peak frequency is 186.9512 ± 0.0049 MHz.
   
• Figure 3: Around 160 MHz, without a linear background. Using data from 163.4 MHz to 164.4 MHz, the fitted peak frequency is 163.8465 ± 0.0039 MHz.
  Figure 4: Around 160 MHz, with a linear background. Using data from 163.4 MHz to 164.4 MHz, the fitted peak frequency is 163.8930 ± 0.0044 MHz.
   
• Figure 5: Around 140 MHz, without a linear background. Using data from 131.05 MHz to 132.05 MHz, the fitted peak frequency is 131.4789 ± 0.0028 MHz.
  Figure 6: Around 140 MHz, with a linear background. Using data from 131.05 MHz to 132.05 MHz, the fitted peak frequency is 131.506 ± 0.010 MHz.
   
• Figure 7: Around −140 MHz, without a linear background. Using data from 115 MHz to 116 MHz, the fitted peak frequency is 115.5063 ± 0.0042 MHz.
  Figure 8: Around −140 MHz, with a linear background. Using data from 115 MHz to 116 MHz, the fitted peak frequency is 115.4978 ± 0.0068 MHz.
   
• Figure 9: Around −160 MHz, without a linear background. Using data from 156.6 MHz to 157.6 MHz, the fitted peak frequency is 157.0631 ± 0.0042 MHz.
  Figure 10: Around −160 MHz, with a linear background. Using data from 156.6 MHz to 157.6 MHz, the fitted peak frequency is 157.0710 ± 0.0098 MHz.
   
• Figure 11: Around −190 MHz, without a linear background. Using data from 189.1 MHz to 189.8 MHz, the fitted peak frequency is 189.3984 ± 0.0065 MHz.
  Figure 12: Around −190 MHz, with a linear background. Using data from 189.1 MHz to 189.8 MHz, the fitted peak frequency is 189.363 ± 0.018 MHz.

The PRX and SRX data measured in klog:37209 were analyzed. The cavity lengths were determined by fitting the measured resonance frequencies. The differences between the measured and design cavity lengths were 1.25 ± 0.46 cm for PRX and 2.56 ± 0.45 cm for SRX. Since these differences exceed the estimated uncertainties, the actual PRX and SRX cavity lengths may differ from their design values.
 

• The cavity lengths of PRX and SRX were determined using the following data.

  PRX
  Minimum (MHz)    Maximum (MHz)
  188.6412    188.6851
  162.2368    162.3230
  129.2967    129.3204
  -125.3945    -125.3351
  -158.3357    -158.2847
  -186.8535    -186.7711
  SRX
  Minimum (MHz)    Maximum (MHz)
  195.1800    195.3102
  162.2970    162.4341
  127.1905    127.2084
  -125.3685    -125.2040
  -158.2469    -158.1762
  -193.3183    -193.2740
   

• From the measurement results, the midpoint between the minimum and maximum frequencies was calculated for each resonance. These midpoint frequencies were divided by the FSR calculated from the design cavity lengths (68.2563 m for PRX and 68.2562 m for SRX). The resulting values were rounded to the nearest integers, and the measured frequencies were fitted with the linear function AN+B, where A and B are fitting parameters and N is the rounded integer. The fitting results were as follows.

  PRX (Fig. 1)
  A: 2.19568 ± 0.00015 MHz
  B: −0.2170 ± 0.0099 MHz
  SRX (Fig. 2)
  A: 2.19526 ± 0.00014 MHz
  B: −0.1252 ± 0.0092 MHz
   

• Since A corresponds to the FSR, the cavity lengths were calculated from the fitted values of A.

  PRX
  Measured cavity length: 68.2688 ± 0.0046 m
  Design value: 68.2563 m
  Difference (measured − design): 1.25 ± 0.46 cm
  SRX
  Measured cavity length: 68.2818 ± 0.0045 m
  Design value: 68.2562 m
  Difference (measured − design): 2.56 ± 0.45 cm

  Therefore, the differences between the measured and design values for both PRX and SRX exceed the estimated uncertainties, suggesting that the actual cavity lengths may differ from their design values.

The fitting results for the individual PRX resonance peaks presented in klog:37223 are summarized below. The measurement data are stored in Dropbox → All files/Dropbox KAGRA/Measurements/IFO/PRCL/PRCL_OMC_REFL_beat_signal_LO_sweep/2026_07_14_PRX.
 

• Figure 1: Around 190 MHz, without a linear background. Using data from 188.4 MHz to 189.0 MHz, the fitted peak frequency is 188.6436 ± 0.0024 MHz.
  Figure 2: Around 190 MHz, with a linear background. Using data from 188.4 MHz to 189.0 MHz, the fitted peak frequency is 188.6809 ± 0.0042 MHz.
   
• Figure 3: Around 160 MHz, without a linear background. Using data from 161.8 MHz to 162.7 MHz, the fitted peak frequency is 162.2408 ± 0.0040 MHz.
  Figure 4: Around 160 MHz, with a linear background. Using data from 161.8 MHz to 162.7 MHz, the fitted peak frequency is 162.3162 ± 0.0068 MHz.
   
• Figure 5: Around 140 MHz, without a linear background. Using data from 128.9 MHz to 129.8 MHz, the fitted peak frequency is 129.3171 ± 0.0033 MHz.
  Figure 6: Around 140 MHz, with a linear background. Using data from 128.9 MHz to 129.8 MHz, the fitted peak frequency is 129.3037 ± 0.0070 MHz.
   
• Figure 7: Around −140 MHz, without a linear background. Using data from 125.1 MHz to 125.7 MHz, the fitted peak frequency is 125.3904 ± 0.0041 MHz.
  Figure 8: Around −140 MHz, with a linear background. Using data from 125.1 MHz to 125.7 MHz, the fitted peak frequency is 125.346 ± 0.011 MHz.
   
• Figure 9: Around −160 MHz, without a linear background. Using data from 157.9 MHz to 158.7 MHz, the fitted peak frequency is 158.3322 ± 0.0035 MHz.
  Figure 10: Around −160 MHz, with a linear background. Using data from 157.9 MHz to 158.7 MHz, the fitted peak frequency is 158.2937 ± 0.0089 MHz.
   
• Figure 11: Around −190 MHz, without a linear background. Using data from 186.4 MHz to 187.2 MHz, the fitted peak frequency is 186.8475 ± 0.0060 MHz.
  Figure 12: Around −190 MHz, with a linear background. Using data from 186.4 MHz to 187.2 MHz, the fitted peak frequency is 186.7790 ± 0.0078 MHz.

The fitting results for the individual SRX resonance peaks presented in klog:37223 are summarized below. The measurement data are stored in Dropbox → All files/Dropbox KAGRA/Measurements/IFO/SRCL/SRCL_OMC_REFL_beat_signal_LO_sweep/2026_07_14_SRX.
 

• Figure 1: Around 190 MHz, without a linear background. Using data from 194.7 MHz to 195.5 MHz, the fitted peak frequency is 195.1834 ± 0.0034 MHz.
  Figure 2: Around 190 MHz, with a linear background. Using data from 194.7 MHz to 195.5 MHz, the fitted peak frequency is 195.293 ± 0.018 MHz.
   

• Figure 3: Around 160 MHz, without a linear background. Using data from 161.8 MHz to 162.6 MHz, the fitted peak frequency is 162.3010 ± 0.0040 MHz.
  Figure 4: Around 160 MHz, with a linear background. Using data from 161.8 MHz to 162.6 MHz, the fitted peak frequency is 162.415 ± 0.019 MHz.

• Figure 5: Around 140 MHz, without a linear background. Using data from 126.9 MHz to 127.48 MHz, the fitted peak frequency is 127.1931 ± 0.0026 MHz.
  Figure 6: Around 140 MHz, with a linear background. Using data from 126.9 MHz to 127.48 MHz, the fitted peak frequency is 127.2057 ± 0.0026 MHz.
   

• Figure 7: Around −140 MHz, without a linear background. Using data from 125.0 MHz to 125.8 MHz, the fitted peak frequency is 125.3625 ± 0.0061 MHz.
  Figure 8: Around −140 MHz, with a linear background. Using data from 125.0 MHz to 125.8 MHz, the fitted peak frequency is 125.235 ± 0.031 MHz.
   

• Figure 9: Around −160 MHz, without a linear background. Using data from 157.9 MHz to 158.7 MHz, the fitted peak frequency is 158.2421 ± 0.0048 MHz.
  Figure 10: Around −160 MHz, with a linear background. Using data from 157.9 MHz to 158.7 MHz, the fitted peak frequency is 158.1853 ± 0.0091 MHz.
   

• Figure 11: Around −190 MHz, without a linear background. Using data from 193.0 MHz to 193.8 MHz, the fitted peak frequency is 193.3150 ± 0.0033 MHz.
  Figure 12: Around −190 MHz, with a linear background. Using data from 193.0 MHz to 193.8 MHz, the fitted peak frequency is 193.2798 ± 0.0058 MHz.

[Tanaka, Saito]

The sub-laser was injected into the SRY cavity, and the PLL was locked. The LO frequency was then frequency-modulated by ±10 kHz at a modulation frequency of 1 kHz. As a result, a signal appeared at 1 kHz in the power spectrum of the OMC REFL DC PD. By adjusting the LO frequency to minimize this signal, its amplitude was reduced to approximately the noise floor. To further improve the frequency resolution, the frequency modulation amplitude was increased to ±30 kHz. However, the amplitude of the 1 kHz signal changed in response to spontaneous fluctuations in both the frequency and amplitude of the beat signal observed at the OMC REFL RF PD, making it difficult to determine the beat frequency with 1 kHz-level precision. Therefore, it is considered that the beat frequency can be determined with a precision on the order of 10 kHz.
 

• First, the SRY cavity was locked, and the main-laser intensity noise measured by the OMC REFL DC PD was reduced to a level comparable to that reported in klog:37144. The sub-laser was then injected into SRY, and the PLL was locked. A Moku:Lab was used as the LO source. Using its frequency modulation function, the LO frequency was swept by ±2 MHz at 10 mHz, and the LO frequency was adjusted to approximately maximize the beat signal observed at the OMC REFL RF PD.
   
• Next, the LO frequency was modulated by ±10 kHz at 1 kHz. A spectral peak approximately five times higher than the noise floor appeared at 1 kHz in the power spectrum of the OMC REFL DC PD. The LO frequency was then adjusted so as to minimize this peak, and at a certain frequency the peak became comparable to the noise floor. To improve the frequency accuracy further, the modulation amplitude was increased to ±30 kHz. This again produced a peak at 1 kHz, and the LO frequency was adjusted in 1 kHz increments to minimize it. However, the amplitude of the 1 kHz peak varied together with spontaneous changes in the frequency and amplitude of the beat signal observed at the OMC REFL RF PD. As a result, determining the beat frequency with 1 kHz-level precision proved difficult. It is therefore concluded that the beat frequency can be determined with a precision on the order of 10 kHz.
   
• The final power spectra of the OMC REFL DC PD are shown in Figures 1 and 2. In Figure 1, the red trace corresponds to the present measurement. Its higher noise level at high frequencies compared with the other traces is attributed to the additional intensity noise from the sub-laser. In Figure 2, the green trace was measured with the sub-laser injected but without LO frequency modulation; the blue trace was measured after initially adjusting the LO frequency to approximately maximize the OMC REFL beat signal; and the red trace was measured after increasing the modulation amplitude to ±30 kHz and fine-tuning the LO frequency with approximately 1 kHz resolution.

[Kawakami, Komori, Tanaka, Saito]

A mixer and a 140 MHz low-pass filter were inserted between the 20 dB RF amplifier and the 45 dB RF amplifier. By setting the mixer's LO frequency to 350 MHz, the beat signal at approximately 450 MHz was successfully down-converted to approximately 100 MHz. PLL operation was successfully achieved using this down-converted signal. In the next experiment, a spectrum analyzer will be installed at the OMC REFL port, and since the mixer supports input frequencies up to 500 MHz, beat signals up to approximately ±500 MHz will be analyzed. The cavity lengths of SRX, SRY, PRX, and PRY will then be measured by applying the same fitting procedure used in klog:37209.
 

• First, the signal after the 20 dB RF amplifier was monitored with a spectrum analyzer, and the sub-laser temperature was adjusted so that the beat frequency became approximately 450 MHz. A mixer and a 140 MHz low-pass filter were then inserted between the 20 dB RF amplifier and the 45 dB RF amplifier. In addition, the 10 dB attenuator located before the PFD was removed. The current control chain from the RFPD to the sub-laser PZT is as follows:

  RFPD → 12 MHz high-pass filter → 20 dB RF amplifier → mixer → 140 MHz low-pass filter → 45 dB RF amplifier → power splitter → PFD → 100 kHz low-pass filter → Moku:Lab (100 Hz integrator, 10 kHz low-pass filter) → SR560 (gain = 200, 1 Hz low-pass filter) → 20 dB high-voltage amplifier → sub-laser PZT
   

• With the mixer's LO frequency set to 350 MHz, the signal taken from the power splitter before the PFD was monitored using the Moku:Lab spectrum analyzer, and the beat signal was observed at approximately 100 MHz. When the mixer's LO frequency was decreased, the beat frequency increased, confirming that the original beat signal was at approximately 450 MHz. Since the PFD locks with an offset when the input frequency is too low, the sub-laser temperature was adjusted so that the down-converted signal became approximately 160 MHz. The mixer's LO frequency was then changed to 340 MHz, resulting in a down-converted beat frequency of approximately 135 MHz. Finally, by setting the PFD LO frequency to 135 MHz, stable PLL lock was successfully achieved.

• In the next experiment, a spectrum analyzer will be installed at the OMC REFL port. Since the mixer can process signals up to 500 MHz, beat signals up to approximately ±500 MHz will be measured. The same fitting procedure as in klog:37209 will then be applied to determine the lengths of the SRX, SRY, PRX, and PRY cavities.

[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.

[Kawakami, Tanaka, Saito]

Following the same procedure as in klog:37250, the lengths of SRX, PRX, and PRY were measured. The differences from the design values were found to be 2.80(13) cm for SRX, 0.677(11) cm for PRX, and −0.107(46) cm for PRY. Compared with the results reported in klog:37209 and klog:37223, the largest discrepancy is observed for PRX, but it corresponds to only about 1.25σ, indicating that the results are statistically consistent.

Furthermore, using these results together with the method described in klog:37248, the SRC length, PRC length, and Schnupp asymmetry were determined. The results are 66.61409(70) m for the SRC, 66.59425(24) m for the PRC, and 3.33791(45) m for the Schnupp asymmetry. Their differences from the design values are 2.279(70) cm for the SRC, 0.285(24) cm for the PRC, and 0.811(45) cm for the Schnupp asymmetry. Compared with the results of klog:37248, the largest discrepancy is found for the PRC, but it is only about 1.48σ, indicating that the two measurements are consistent.
 

• Following the same procedure as in klog:37250, the sub-laser PZT was driven directly for SRX, PRX, and PRY, 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. Here, the negative frequencies correspond to the case where the sub-laser frequency is lower than the main laser frequency. The peaks in the measured data were fitted both with and without a linear background. The fitting results for the individual peaks will be posted separately. The peak frequencies obtained from the fits and their uncertainties were used to determine the maximum and minimum values within the uncertainty range. The overall uncertainty range was taken as the union of the results with and without a linear background. The following data were therefore used to determine the lengths of SRX, PRX, and PRY.

  SRX
  Minimum (MHz)    Maximum (MHz)
  1543.4471    1543.4932
  884.8872    884.9360
  −856.1353    −855.8030
  −1654.9558    −1654.8394
  PRX
  Minimum (MHz)    Maximum (MHz)
  1631.4880    1631.4954
  867.3066    867.3270
  −874.0048    −873.9845
  −1646.9334    −1646.9256
  PRY
  Minimum (MHz)    Maximum (MHz)
  1627.6201    1627.6266
  868.0174    868.0423
  −882.0137    −881.9492
  −1632.3336    −1632.2710

• For each cavity, the midpoint frequency between the minimum and maximum values was divided by the FSR calculated from the design cavity length (68.2562 m for SRX, 68.2563 m for PRX, and 64.9265 m for PRY). 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 as follows.

  SRX (Fig. 1)
  A: 2.195180(42) MHz
  B: 0.256(25) MHz
  PRX (Fig. 2)
  A: 2.1958613(35) MHz
  B: −0.0348(25) MHz
  PRY (Fig. 3)
  A: 2.308744(17) MHz
  B: −0.042(11) MHz
   

• Since A corresponds to the FSR, the cavity lengths were calculated as follows.

  SRX
  Fitted length: 68.2842(13) m
  Design value: 68.2562 m
  Difference (fit − design): 2.80(13) cm
  PRX
  Fitted length: 68.26307(11) m
  Design value: 68.2563 m
  Difference (fit − design): 0.677(11) cm
  PRY
  Fitted length: 64.92543(46) m
  Design value: 64.9265 m
  Difference (fit − design): −0.107(46) cm

  Comparing these results with those reported in klog:37209 and klog:37223, namely, differences from the design values of 2.56(45) cm for SRX, 1.25(46) cm for PRX, and 0.15(33) cm for PRY, the largest discrepancy is found for PRX, but it corresponds to only about 1.25σ. Therefore, the results are considered to be consistent.
   

• Using these results together with the SRY measurement reported in klog:37250, the SRC length, PRC length, and Schnupp asymmetry were calculated following the same procedure as in klog:37248.

  SRC
  Calculated value: 66.61409(70) m
  Design value: 66.5913 m
  Difference (calculated − design): 2.279(70) cm
  PRC
  Calculated value: 66.59425(24) m
  Design value: 66.5914 m
  Difference (calculated − design): 0.285(24) cm
  Schnupp asymmetry
  Calculated from the SRC: 3.34023(139) m
  Calculated from the PRC: 3.337640(473) m
  Weighted average: 3.33791(45) m
  Design value: 3.3298 m
  Difference (weighted average − design): 0.811(45) cm

  Comparing these values with those reported in klog:37248, namely 66.6120(47) m for the SRC, 66.5984(28) m for the PRC, and 3.3405(48) m for the Schnupp asymmetry, the largest discrepancy is found for the PRC, but it corresponds to only about 1.48σ. Therefore, the present results are considered to be consistent with the previous measurements.

The fitting results for the individual SRX peaks in klog:37260 are shown below. The measurement data are stored in:
Dropbox → All files/Dropbox KAGRA/Measurements/IFO/SRCL/SRCL_OMC_REFL_beat_signal_PZT_sweep/2026_07_24_SRX

• Fig. 1: Around 1.6 GHz, without a linear background. Using data from 1542.7 MHz to 1544.4 MHz, the fitted peak frequency is 1543.4872(60) MHz.
  Fig. 2: Around 1.6 GHz, with a linear background. Using data from 1542.7 MHz to 1544.4 MHz, the fitted peak frequency is 1543.4558(87) MHz.
   
• Fig. 3: Around 800 MHz, without a linear background. Using data from 884.25 MHz to 885.75 MHz, the fitted peak frequency is 884.9328(32) MHz.
  Fig. 4: Around 800 MHz, with a linear background. Using data from 884.25 MHz to 885.75 MHz, the fitted peak frequency is 884.905(17) MHz.
   
• Fig. 5: Around −800 MHz, without a linear background. Using data from 855 MHz to 856.5 MHz, the fitted peak frequency is 855.8067(37) MHz.
  Fig. 6: Around −800 MHz, with a linear background. Using data from 855 MHz to 856.5 MHz, the fitted peak frequency is 856.046(89) MHz.
   
• Fig. 7: Around −1.6 GHz, without a linear background. Using data from 1654 MHz to 1656 MHz, the fitted peak frequency is 1654.8460(66) MHz.
  Fig. 8: Around −1.6 GHz, with a linear background. Using data from 1654 MHz to 1656 MHz, the fitted peak frequency is 1654.931(24) MHz.

The fitting results for the individual PRX and PRY peaks in klog:37260 are shown below. The measurement data are stored in:
PRX: Dropbox → All files/Dropbox KAGRA/Measurements/IFO/PRCL/PRCL_OMC_REFL_beat_signal_PZT_sweep/2026_07_24_PRX
PRY: Dropbox → All files/Dropbox KAGRA/Measurements/IFO/PRCL/PRCL_OMC_REFL_beat_signal_PZT_sweep/2026_07_24_PRY

PRX

• Fig. 1: Around 1.6 GHz, without a linear background. Using data from 1630.9 MHz to 1631.9 MHz, the fitted peak frequency is 1631.4893(13) MHz.
  Fig. 2: Around 1.6 GHz, with a linear background. Using data from 1630.9 MHz to 1631.9 MHz, the fitted peak frequency is 1631.4920(33) MHz.
   
• Fig. 3: Around 800 MHz, without a linear background. Using data from 866.75 MHz to 867.7 MHz, the fitted peak frequency is 867.30748(89) MHz.
  Fig. 4: Around 800 MHz, with a linear background. Using data from 866.75 MHz to 867.7 MHz, the fitted peak frequency is 867.3245(25) MHz.
   

• Fig. 5: Around −800 MHz, without a linear background. Using data from 873.6 MHz to 874.6 MHz, the fitted peak frequency is 874.0037(11) MHz.
  Fig. 6: Around −800 MHz, with a linear background. Using data from 873.6 MHz to 874.6 MHz, the fitted peak frequency is 873.9868(23) MHz.

• Fig. 7: Around −1.6 GHz, without a linear background. Using data from 1646.6 MHz to 1647.5 MHz, the fitted peak frequency is 1646.9300(17) MHz.
  Fig. 8: Around −1.6 GHz, with a linear background. Using data from 1646.6 MHz to 1647.5 MHz, the fitted peak frequency is 1646.9295(39) MHz.
   

PRY

• Fig. 9: Around 1.6 GHz, without a linear background. Using data from 1627 MHz to 1628.1 MHz, the fitted peak frequency is 1627.6227(26) MHz.
  Fig. 10: Around 1.6 GHz, with a linear background. Using data from 1627 MHz to 1628.1 MHz, the fitted peak frequency is 1627.6246(20) MHz.
   
• Fig. 11: Around 800 MHz, without a linear background. Using data from 867.5 MHz to 868.5 MHz, the fitted peak frequency is 868.0185(11) MHz.
  Fig. 12: Around 800 MHz, with a linear background. Using data from 867.5 MHz to 868.5 MHz, the fitted peak frequency is 868.0390(33) MHz.
   
• Fig. 13: Around −800 MHz, without a linear background. Using data from 881.5 MHz to 882.3 MHz, the fitted peak frequency is 882.0091(46) MHz.
  Fig. 14: Around −800 MHz, with a linear background. Using data from 881.5 MHz to 882.3 MHz, the fitted peak frequency is 881.9540(48) MHz.
   
• Fig. 15: Around −1.6 GHz, without a linear background. Using data from 1631.8 MHz to 1632.6 MHz, the fitted peak frequency is 1632.3286(49) MHz.
  Fig. 16: Around −1.6 GHz, with a linear background. Using data from 1631.8 MHz to 1632.6 MHz, the fitted peak frequency is 1632.2769(59) MHz.