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

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.