[Tanaka, Fujimoto, Saito]

After aligning the sub-laser, the single-pass beam profile became much cleaner than before the lens-height adjustment (Fig. 1 in klog:37121). The SRX and SRY lengths were then measured following the same procedure as in klog:37260. The deviations from the design values were found to be −3.01(18) cm for SRX and −3.516(42) cm for SRY. Compared with the results of klog:37250 and klog:37260, namely 2.80(13) cm for SRX and 1.757(50) cm for SRY, the differences are -3.01(18) cm-2.80(13) cm=−5.81(22) cm for SRX and -3.516(42) cm-1.757(50) cm−5.273(65) cm for SRY, indicating a significant discrepancy. The cause is currently unknown. In addition, the maximum beat-signal amplitude was only about 1 mV, whereas it had been about 4 mV in klog:37250 and klog:37260, suggesting that the mode-matching ratio may have degraded. Using the same procedure as in klog:37260, the SRC length and Schnupp asymmetry were also calculated, yielding 66.55867(92) m and 3.33486(185) m, respectively. Compared with the klog:37260 results of 66.61409(70) m for SRC and 3.34023(139) m for the Schnupp asymmetry derived from SRC, the differences are 66.55867(92) m-66.61409(70) m=−5.54(12) cm for SRC and 3.33486(185)m-3.34023(139)m=0.537(231) cm for the Schnupp asymmetry, indicating that the SRC result also differs significantly.
 

• First, the irises were repositioned so that the sub-laser alignment could be performed using only the sub-laser beam. Two irises were installed between the lens and the mirror whose heights had been adjusted in klog:37369, with the largest possible separation, and the main-laser beam was centered through both irises. SRY was then locked, and the main laser was turned off. Next, the sub-laser PZT was driven with a 10 Hz, 4 Vpp triangular waveform, and the sub-laser alignment was adjusted using the mirror and BS while monitoring the OMC REFL DC PD signal. When the beam was centered through both irises, the OMC REFL DC PD signal changed, so the alignment was further optimized to maximize the signal. After misaligning the SRM and observing the OMC REFL camera, the beam profile appeared as shown in Fig. 1. Before the lens-height adjustment, the mode had been horizontally elongated, as shown in Fig. 1 of klog:37121, whereas it became nearly circular after the adjustment.
   
• The main laser was then turned on, and SRY was measured following the same procedure as in klog:37260. The sub-laser PZT was driven with a 0.3 Hz, 4 Vpp triangular waveform, and the spectrum analyzer's Max Hold function was used to acquire transmitted-power data as a function of frequency near beat frequencies of 1.6 GHz (Fig. 2), 800 MHz (Fig. 3), −800 MHz (Fig. 4), and −1.6 GHz (Fig. 5). Negative frequencies indicate that the sub-laser frequency was lower than the main-laser frequency.

• The same procedure was then attempted for SRX. However, near 1.6 GHz, the beat signal exhibited two clearly separated peaks (Fig. 6). The sub-laser alignment was therefore readjusted (Fig. 7), but little improvement was observed, suggesting that higher-order modes of the main laser may be affecting the measurement. Data were then acquired near beat frequencies of 1.6 GHz (Fig. 8), 800 MHz (Fig. 9), −800 MHz (Fig. 10), and −1.6 GHz (Fig. 11). Figures 8–11 also suggest that the relative heights of the two peaks vary with the beat frequency.
   

• The measured peaks were fitted both with and without a linear background. The fitting results for the individual peaks will be posted separately. From the fitted peak frequencies and their uncertainties, the minimum and maximum frequencies within the uncertainty range were determined, and the overall uncertainty was defined as the combined range from both fitting methods. The following frequency ranges were then used to determine the SRX and SRY lengths.

  SRX
  Minimum (MHz) Maximum (MHz)
  1625.3644  1625.4925
  806.5704   806.6633
  -782.6801  -782.5577
  -1603.6842 -1603.5300

  SRY

  Minimum (MHz) Maximum (MHz)
  1630.4411  1630.5146
  824.9937   825.0215
  -834.3554  -834.3158
  -1600.5609 -1600.5409

  The midpoint of each frequency range was divided by the FSR calculated from the design lengths of 68.2562 m for SRX and 64.9264 m for SRY. 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:

  SRX (Fig. 12)
  A: 2.197053(57) MHz
  B: −0.036(30) MHz

  SRY (Fig. 13)
  A: 2.309961(15) MHz
  B: 0.1600(86) MHz

  Since A corresponds to the FSR, the cavity lengths are:

  SRX
  Fitted length: 68.2261(18) m
  Design length: 68.2562 m
  Difference (fitted − design): −3.01(18) cm

  SRY
  Fitted length: 64.89124(42) m
  Design length: 64.9264 m
  Difference (fitted − design): −3.516(42) cm

  Compared with the klog:37250 and klog:37260 results of 2.80(13) cm for SRX and 1.757(50) cm for SRY, the differences are:

  SRX: -3.01(18) cm - 2.80(13) cm = −5.81(22) cm
  SRY: -3.516(42) cm - 1.757(50) cm = −5.273(65) cm

  These discrepancies are substantial, and their cause remains unknown. Furthermore, the maximum beat-signal amplitude was only about 1 mV, compared with about 4 mV in the previous measurements（klog:37250, klog:37260）, suggesting that the mode-matching ratio may have decreased.
   

• Using these results, the SRC length and Schnupp asymmetry were calculated following the same procedure as in klog:37260.

  SRC
  Calculated length: 66.55867(92) m
  Design length: 66.5913 m
  Difference (calculated − design): −3.263(92) cm

  Schnupp asymmetry
  Value derived from SRC: 3.33486(185) m
  Design value: 3.3298 m
  Difference (derived − design): 0.506(185) cm

  Compared with the klog:37260 results of 66.61409(70) m for SRC and 3.34023(139) m for the Schnupp asymmetry derived from SRC, the differences are:

  SRC: 66.55867(92) m - 66.61409(70) m = −5.54(12) cm

  Schnupp asymmetry derived from SRC: 3.33486(185) m - 3.34023(139) m = 0.537(231) cm

  Thus, the SRC result also differs significantly from the previous measurement.