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shun.saito - 22:48 Thursday 20 August 2026 (37393) Print this report
Comment to Improving the sub-laser alignment for the PRCL/SRCL measurements (37369)

Following Fujimoto-san's result in klog:37384, the FSR index assignment was changed to a method based on the frequency differences between the measured resonance peaks. With this revised method, the deviations from the design values became 3.01(18) cm for SRX and 2.385(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 SRX result is considered consistent, while the SRY result is closer than the previous value reported in klog:37381 but still shows a small discrepancy. Using the same procedure as in klog:37381, the SRC length and Schnupp asymmetry derived from SRC were also calculated, yielding 66.61828(92) m and 3.33605(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 agreement improved relative to klog:37381, although small differences remain. Furthermore, the beat frequency closest to 0 Hz, as obtained from the fitting results, was found to be approximately four times larger than that obtained in klog:37250 and klog:37260. Since this value should ideally be 0 Hz, the larger offset observed here is unexpected, and its cause is currently unknown.
 

  • Following Fujimoto-san's result in klog:37384, the FSR index assignment was revised. The peak near −1.6 GHz was assigned an FSR index of 0, and the frequency difference between adjacent peaks was divided by the design FSR. The resulting values were rounded to the nearest integer to assign the FSR indices. The measured frequencies were then fitted with AN+B where A and B are fitting parameters and N is the FSR index. The fitting results are as follows.

    SRX (Fig. 1)
    A: 2.195115(57) MHz
    B: −1603.604(57) MHz

    SRY (Fig. 2)
    A: 2.307862(15) MHz
    B: −1600.5506(94) MHz

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

    SRX
    Fitted length: 68.2863(18) m
    Design length: 68.2562 m
    Difference (fitted − design): 3.01(18) cm

    SRY
    Fitted length: 64.95025(42) m
    Design length: 64.9264 m
    Difference (fitted − design): 2.385(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 SRX result is considered consistent. The SRY result is closer than the value reported in klog:37381, although a small discrepancy remains.
     

  • Using these results, the SRC length and Schnupp asymmetry were calculated following the same procedure as in klog:37381.

    SRC
    Calculated length: 66.61828(92) m
    Design length: 66.5913 m
    Difference (calculated − design): 2.698(92) cm

    Schnupp asymmetry
    Value derived from SRC: 3.33605(185) m
    Design value: 3.3298 m
    Difference (derived − design): 0.625(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, these values are closer than those reported in klog:37381, although small differences remain.
     

  • In addition, in the previous fitting (klog:37381), adding +1 to the FSR indices of the two positive-frequency peaks, or subtracting 1 from the FSR indices of the two negative-frequency peaks, reproduces the same results obtained here. This indicates that the FSR indices of two resonance peaks had been assigned incorrectly for both SRX and SRY in the previous analysis.
     

  • Following this revision, the analyses in klog:37250 and klog:37260 were also rechecked. No changes were found in any of those measurement results, indicating that the FSR indices used in klog:37250 and klog:37260 had been assigned correctly.
     

  • Finally, the beat frequency closest to 0 Hz was calculated from the fitting results for both the present analysis and the results of klog:37250 and klog:37260, yielding the following values.

    Present results
    SRX:1.025065 MHz
    SRY:1.105628 MHz

    klog:37250 and klog:37260
    SRX:0.25572 MHz
    SRY:0.24769 MHz
    PRX:−0.034825 MHz
    PRY:−0.042492 MHz

    Ideally, these beat frequencies should be 0 Hz, but the offsets in the present measurements are substantially larger. The reason for this discrepancy remains unknown.
     

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