In situ substrate birefringence characterization in gravitational wave detectors using a heterodyne polarimetry method

TL;DR

The paper addresses in-situ characterization of substrate birefringence in gravitational wave detectors using a heterodyne polarimetry approach implemented with a polarization phase camera. It develops a Jones-matrix framework and RF heterodyne detection to extract birefringence parameters $|\alpha_-|$ and $|\theta|$, demonstrated on a tabletop setup with a known sample and conditions mimicking detector optics. The results show consistent 2D maps with mean values $|\alpha_-| \approx 0.79$ rad and $\theta \approx -4.83^{\circ}$, with typical uncertainties around $\sim 6\%$, and discuss the method’s applicability to Advanced LIGO, KAGRA, Cosmic Explorer, and Einstein Telescope, including detectability limits near $\mathscr{L} \sim 0.05\%$. The technique enables non-invasive, in-situ monitoring of birefringence that can influence power-recycling gain and interferometer controls, informing commissioning strategies and material studies for next-generation detectors.

Abstract

High-quality test mass substrates play essential roles in laser interferometric gravitational wave detectors. Inhomogeneous birefringence distribution in test mass substrates, however, can degrade the sensitivity of the detector by introducing the optical loss and disturbing the interferometer controls. In this paper, we present a heterodyne polarimetry method that enables in situ birefringence characterizations, hence diagnosing the gravitational wave interferometer. We experimentally demonstrate the proposed method with a tabletop setup. We also discuss its applicability to current and future gravitational wave detectors and the detectable limit.

Figures (7)

• Figure 1: Schematic of the definition. The mirror substrate has two orthogonal refractive index axes, $n_{x}$ and $n_{y}$, which are rotated by $\theta$ from s- and p-polarization axes, respectively.
• Figure 2: Contour maps of systematic errors in differential phase retardation and orientation. Since there is a symmetry, only the first quadrant is plotted for each case. The blue curve in each plot corresponds to the optical loss ($\sin^2\alpha_-\sin^22\theta$) of $5\%$.
• Figure 3: Schematic of the experimental setup. The input beam is conditioned to be an s-polarized beam using polarizers. A non-polarizing beamsplitter (NPBS1) divides the beam into two paths. The frequency of the reference beam is shifted using a fiber AOM. The test and the reference beams are combined by NPBS2, and then split into s- and p-polarized beams. PBS1 is installed after the fiber output to remove the unwanted polarization component. Then the reference beam power on each PD is adjusted by HWP1.
• Figure 4: Schematic of the data acquisition system. The beatnote signals are demodulated by analog RF circuits. The demodulated signals are filtered by low-pass filters (LPFs), and then converted to digital signals by analog-to-digital converters (ADCs). The post-processing and data storage are performed on the digital system.
• Figure 5: 2D birefringence distribution maps and their histograms. Red dashed circles in distribution maps describe the test beam diameters at the PDs. Red dashed lines in histograms are the fitted curves, and black dashed lines are the expected values. The distributions within the beam diameters are highlighted.