Birefringence of AlGaAs/GaAs Coatings under Above-Band-Gap Illumination, GR Noise and Photo-Optic Transfer Function

TL;DR

The paper addresses dynamic birefringence in AlGaAs/GaAs crystalline coatings under above-band-gap illumination and its implications for gravitational-wave detectors. It combines cavity-based measurements of illumination to birefringence transfer with a master equation model that captures the observed frequency dependence and intensity effects, including a DC gain that decreases and a pole that moves with illumination. The theory predicts generation-recombination noise and photo-optic noise, with GR noise expected to be white below the pole and to scale with power similarly to shot noise, offering a distinct signature for crystalline coatings. These results inform noise modeling and material choices for next-generation GW detectors employing crystalline coatings.

Abstract

AlGaAs/GaAs coatings are being considered as coating candidates for gravitational-wave detectors. In this paper we investigate the birefringence properties of this crystalline semiconductor material by modulating the optical illumination on the mirror coating and monitoring the induced birefringence. While the measured low-frequency birefringence values align with previous studies, we observed a frequency-dependent behavior in the illumination-to-birefringence coupling, characterized by a pole increasing with illumination intensity and a DC gain decreasing with illumination intensity. We developed a theoretical mode based on a master equation to characterize the measurement results by considering photon-induced electric fields and electro-optical effects. This model reproduces the frequency and intensity dependencies of the induced birefringence. Additionally, this model predicts a generation-recombination noise (GR noise) will be observable in the coatings birefringence. While the presented measurement cannot predict the exact level of GR noise, for the frequency band and spot sizes relevant for gravitational-wave detectors we expect GR noise to be white below the pole frequency, scale with power the same way laser shot noise does, and for fixed power be independent of spot size.

Figures (9)

• Figure 1: Experiment Scheme. The optical cavity is 4-cm long, with its output coupler coated with $\rm Al_{0.92}Ga_{0.08}As/GaAs$. To monitor the frequency splitting between orthogonal polarizations induced by the illumination, we measured the beat note between two independent lasers, one locked to the cavity in p- polarization and the other in s- polarization.
• Figure 2: Typical transfer function from LED illumination to beat note noise. The solid line shows the raw data and the dashed line is a fitting to a first-order low-pass filter. 1064 nm intensity: $2.0\,\rm MW/m^2$, LED wavelength: 700 nm, LED intensity: $1.5\,\rm W/m^2$ DC, plus a modulation of $\rm \pm 1W/m^2$ (modulation index $m=0.67$).
• Figure 3: Fitting results at different illumination intensity levels: The wavelength of the illumination is 700 nm. The solid green lines are measured raw data after calibration. The noise peaks at $\sim$ 500 Hz and $\sim$ 600 Hz are due to the mechanical resonance of the cavity mirror posts. The dashed lines are the fitting results obtained by the four-parameter global fit described in section \ref{['sec:GlobalFit']} and appendix \ref{['sec:MASTERTheory']}. This plot shows data for a 1064nm carrier light intensity of 2.0MW/m^2. See FIG. \ref{['fig:globalfit']} (a) and (b) for other 1064nm intensities.
• Figure 4: DC gain values for the induced birefringence under various of 700 nm and 1064 nm intensities. The x-axis is the intensity of 700 nm illumination and different colors represent varying 1064 nm intensities. The data points come from the measurements shown in FIG. \ref{['fig:change DC2']} and FIG. \ref{['fig:globalfit']}. The dashed lines and shaded uncertainties are calculated based on the model described in Appendix \ref{['sec:MASTERTheory']}.
• Figure 5: Transfer functions from 430 nm LED intensity to beat note noise. Solid lines represent measurement data under different illumination intensities. Dashed lines indicate fitted curves for the raw data. Each of the fitted curves here is not simply a pure first-order low-pass filter, but consists of a series of superimposed first-order low-pass filters. This is the expected response if the distribution of effective lifetimes of the involved carriers is spread out.