KAGRA Logbook

[Kawaguchi, Sugimoto, Michimura, Fujimoto]

Abstract

On 12/2, we performed a calibration of the polarization monitor system at TMS-Y.
The purpose of this calibration was to obtain the calibration factors for converting the p-pol PD and s-pol PD spectra (V/rtHz measured by DL950, cnt/rtHz measured by CDS) into the polarization rotation spectra (rad/rtHz).
The measurement and analysis procedures are the same as those used for the calibration of TMS-X polarization monitor system (klog #35743, klog #35758).

Preparation: Dark offsets of PDs

We measured the output offsets of each PD in the polarization monitor system at TMS-Y using both the DL950 and CDS.
For CDS, we used the channels K1:TMS-Y_IR_PDA1_OUT_DQ, K1:TMS-Y_IRSPOL_PDA1_OUT_DQ, and K1:TMS-Y_IRPPOL_PDA1_OUT_DQ.
Note that CDS internally adds offsets before the dewhitening filter (after the ADC).

DL950 CDS
Y_IR 6(1)e-3 V 0(1) cnt
Y_IRSPOL 18(1)e-3 V -6.20(3) cnt
Y_IRPPOL 23(1)e-3 V 1.43(2) cnt

HWP dependence of PDs

We rotated the HWP in the polarization monitor system and measured the output voltages of the p-pol PD, s-pol PD and Y_IR PD with the DL950 and CDS.
During the measurement, the average output of the Y_IR PD was 3.77(2) V and 1.473(2)e4 cnt.
Figure 1 and Figure 2 show the measurement results obtained with DL950 and CDS respectively, where the vertical axis is the measured PD output after subtracting the PD offsets, and the horizontal axis is the HWP scale value.

Calibration: p-pol PD to polarization rotation (V/rtHz → rad/rtHz)

Model: $V_\mathrm{p} = A(1-\cos (4(\theta_\mathrm{HWP}-B)))+C$

Fitting parameters: A[V], B[deg], C[V]

Result:
A = 11.71(5) V
B = 71.35(4) deg
C = 1.808(7) V

Calibration factor:
$\frac{d\phi}{dV_{p}} = \frac{1}{2A\sin(4(\theta_\mathrm{HWP}-B))}\times\frac{3.77(2)\,\mathrm{V} - 6(1)\times10^{-3} \mathrm{V}}{V_\mathrm{IR}- 6(1)\times10^{-3} \mathrm{V}}$
$=0.072(3) \,\mathrm{rad/V}\quad (\mathrm{at}\, \theta_\mathrm{HWP} = 80.5(5)\,\mathrm{deg}, V_\mathrm{IR}=3.77(2)\,\mathrm{V})$

Calibration: p-pol PD to polarization rotation (cnt/rtHz → rad/rtHz)

Model: $C_\mathrm{p} = A(1-\cos (4(\theta_\mathrm{HWP}-B)))+C$

Fitting parameters: A[cnt], B[deg], C[cnt]

Result:
A = 1.910(7)e4 cnt
B = 71.32(3) deg
C = 2940(7) cnt

Calibration factor:
$\frac{d\phi}{dC_{p}} = \frac{1}{2A\sin(4(\theta_\mathrm{HWP}-B))}\times\frac{1.473(2)\times10^4 \mathrm{cnt} - 0(1)\,\mathrm{cnt}}{C_\mathrm{IR}- 0(1)\,\mathrm{cnt}}$
$=4.4(2) \times 10^{-5}\,\mathrm{rad/cnt}\quad (\mathrm{at}\, \theta_\mathrm{HWP} = 80.5(5)\,\mathrm{deg}, C_\mathrm{IR}=1.473(2)\times10^4 \mathrm{cnt})$

Calibration: s-pol PD to polarization rotation (V/rtHz →rad/rtHz)

Model: $V_\mathrm{s} = A(1+\cos (4(\theta_\mathrm{HWP}-B)))+C$

Fitting parameters: A[V], B[deg], C[V]

Result:
A = 1.224(3) V
B = 71.39(8) deg
C = 0.182(2) V

Calibration factor:
$\frac{d\phi}{dV_{s}} = -\frac{1}{2A\sin(4(\theta_\mathrm{HWP}-B))}\times\frac{3.77(2)\,\mathrm{V} - 6(1)\times10^{-3} \mathrm{V}}{V_\mathrm{IR}- 6(1)\times10^{-3} \mathrm{V}}$
$=-0.69(3) \,\mathrm{rad/V}\quad (\mathrm{at}\, \theta_\mathrm{HWP} = 80.5(5)\,\mathrm{deg}, V_\mathrm{IR}=3.77(2)\,\mathrm{V})$

Calibration: s-pol PD to polarization rotation (cnt/rtHz → rad/rtHz)

Model: $C_\mathrm{s} = A(1+\cos (4(\theta_\mathrm{HWP}-B)))+C$

Fitting parameters: A[cnt], B[deg], C[cnt]

Result:
A = 1.988(3)e3 cnt
B = 71.48(6) deg
C = 297(2) cnt

Calibration factor:
$\frac{d\phi}{dC_{s}} = -\frac{1}{2A\sin(4(\theta_\mathrm{HWP}-B))}\times\frac{1.473(2)\times10^4 \mathrm{cnt} - 0(1)\,\mathrm{cnt}}{C_\mathrm{IR}- 0(1)\,\mathrm{cnt}}$
$=-4.3(2) \times 10^{-4}\,\mathrm{rad/cnt}\quad (\mathrm{at}\, \theta_\mathrm{HWP} = 80.5(5)\,\mathrm{deg}, C_\mathrm{IR}=1.473(2)\times10^4 \mathrm{cnt})$

Polarization ellipticity

For reference, the ellipticity (semi-minor/semi-major axis) of the polarization incident to the polarization monitor system at TMS-Y can be estimated as

Ellipticity = sqrt(V_p_min/V_p_max)=sqrt(C/(2*A+C))=0.2677(7)

using A = 11.71(5) V and C = 1.808(7) V.
The above value gives an upper limit on the ellipticity of the cavity transmitted light.

We will use the obtained calibration factor above to convert the PD spectra into the polarization spectra.
After that, we are planning to search for the axion dark matter signal in the polarization spectra.