I measured the gouy phase of HOMs of the IMC and calculated the ROC of MCe mirror and the injection angle to. The result is as below
ROC : 37.8(8) m
injection angle : 0.15(13) rad
The ROC measured by Hirose-san was 37.3(1) m, so those two data are consistent. But the design value of injection angle is 0.0095 rad, so this measured value is not consistent and the error is very large
1. Measurement
To know the HOM frequency difference from TEM00, tuned the side band frequency so that the error signal of side band resonance coincide with each HOMs. First of all the laser frequency was swept with 10 Hz 10Vpp signal (I swept all time long in this measurement). And then I missaligned the MCe mirror to yaw and pitch direction and identify which peak are which HOM with using a IMC TRANS signal.. The attached picture are taken when the MCe mirror was missaligned to each direction. I measured three times for each HOMs.
It is similar method with klog #616. I tuned such that the error signal of HOM resonance has smallest amplitude, because error signals of HOM resonance and aideband resonance are sign inversion signal. But it was not as accurate as this measurement because it doesn't have as good reference as FSR measurement. At FSR measurement, we tuned such that an error signal disappeared. But anyway the side band frequency which coincide with each HOMs are as below.
- TEM10(vertical) :[52.434 52.415 52.427]MHz
- TEM20 [52.638 52.637 52.642] MHz
- TEM01(horizontal) : [51.6642 51.6642 51.6638]MHz
- TEM02 : [52.6931 52.6991 52.700] MHz
2. Calculation
I converted those results to the HOM frequency.
- TEM10(vertical) : 1.81(1) MHz
- TEM20 3.605(3) MHz
- TEM01(horizontal) : 4.5795(2) MHz
- TEM02 : 9.171(4) MHz
Those frequency has one DOF and it has been predicted by calculation. And from those results the gouy phase for each direction, vertical and horizontal, could be calculated.
- Gouy phase for horizontal direction : 5.116(10)
- Gouy phase for vertical direction ; 2.01(7)
The reason why each direction has different gouy phase are that the phase got 180 degree difference at reflection on a mirror only in horizontal modes. And also the effective ROC of the MCe are different by the direction such as
ROC_ver = ROC*cos(injection angle), ROC_hor = ROC/cos(injection angle)
And the ROC can be calculated by
ROC_ver = L / (1-cos(gouy_ver)), ROC_hor = L/(1+cos(gouy_hor))
The effective ROC are calculated as below
- ROC_ver = 37(2)
- ROC_hor = 38.3(2)
ROC was calculated as ROC = sqrt(ROC_ver*ROC_hor), injection angle = acos(sqrt(ROC_ver/ROC_hor)).
3. Discussion
As I mentioned the calculated injection angle is too large. It would be come from the bad accuracy on pitch direction measurement. At that time I haven't got used to this measurement. I guess we could do more precise measurement. Or we could estimate by cavity scan data more precisely. Kambara-kun would do that calculation in near future.
