Abstract

We measured the sensing noise (dark noise and shot noise) of the CARM RFPD at REFL as part of the CARM noise budget.
By analyzing the power dependence of the demodulated noise spectra, we extracted the dark noise level and the shot noise coefficient, as well as the effective transimpedance of the RFPD.

Details

As part of the CARM noise budget, we measured the sensing noise (dark noise + shot noise) of the CARM RFPD at REFL.
The procedure was as follows: the reflected beam from the PRM was injected into the CARM RFPD, and the demodulated noise spectrum was measured for several PD input powers.
By fitting the power dependence of these spectra, we estimated the dark noise and the coefficients associated with shot noise.
The demodulated spectra were first amplified with a SR560 (high-pass @ 3 Hz, gain = 100) and then measured with a Moku:Lab.

Figure 1 shows the demodulated noise spectra taken at different PD input powers (the amplification by the SR560 has been corrected).
To extract the noise-floor values for each input power, we computed the mean and standard error over the frequency band from 50 kHz to 100 kHz for each spectrum.
This frequency region was selected to avoid the peak near 40 kHz.

Figure 2 shows the power dependence of the obtained noise-floor values.
The data were fitted using the following model to extract the power dependence of the PD dark noise and shot noise:

Fitting model:
$\delta V_\mathrm{RFPDnoise} = \sqrt{\delta V_\mathrm{dark}^2+\delta V_\mathrm{shot}^2}$
Definitions:
$\delta V_\mathrm{dark}$ : Dark noise of the RFPD
$\delta V_\mathrm{shot} \equiv R\sqrt{2e\alpha}\times\sqrt{P_\mathrm{in}}$: Shot noise after RFPD demodulation
$R$: effective transimpedance including demodulation
$e$: elementary charge
$\alpha$ : responsivity [A/W]
$P_\mathrm{in}$: input power to the RFPD

Result of fitting:
$V_\mathrm{dark}=3.96(1)\times10^{-8}\,\mathrm{V/\sqrt{Hz}}$
$R\sqrt{2e\alpha}=2.271(8)\times10^{-8}\,\mathrm{V/\sqrt{Hz\,mW}} =7.18(2)\times10^{-7}\,\mathrm{V/\sqrt{Hz\,W}}$

Assuming $\alpha=0.77\,\mathrm{A/W}$ (QE = 0.9), the effective transimpedance $R$ and the power-to-voltage conversion efficiency including demodulation $R\alpha$ are
$R=1.447(5)\times10^3\,\mathrm{\Omega}$
$R\alpha=1.114(4)\times10^3\,\mathrm{V/W}$

These results will be used for the CARM noise budget soon.