DC response of an interferometer topology with an L-shaped cavity: a tabletop study

TL;DR

The paper tackles the challenge of kilohertz gravitational-wave detection by analyzing a folded L-shaped cavity interferometer pumped by a Sagnac-like vortex. It presents a theoretical DC response model showing that, with the L-shaped common mode on resonance and ideal end mirrors, the topology acts as a folded Michelson, while a finite end-mirror transmission yields a Sagnac mode and two independent pumping paths. A tabletop demonstration validates these predictions, yielding best-fit reflectivities $R_{ m ITM} \\approx 97.8\%$ and $R_{ m ETM} \\approx 99.7\%$, and identifying mode-mismatch–induced offsets that agree with simulations. The work provides a clear, lock-friendly physical picture of the topology and informs the design and control strategies for future kilohertz GW detectors, including approaches to incorporating squeezing and higher-power operation. Overall, it connects analytic predictions with experimental validation to support scalable development of this interferometer concept for high-frequency gravitational-wave astronomy.

Abstract

A new interferometer topology for kilohertz gravitational-wave detection was recently proposed in [Zhang et al. Phys. Rev. X 13, 021019 (2023)]. The design is based on an L-shaped optical cavity pumped through a Sagnac-like vortex. We report a tabletop experiment that characterizes the interferometer's optical response near DC. When the laser frequency is locked to the resonance of the L-shaped cavity, we observe that the cavity input coupler becomes effectively transparent, yielding a simple Michelson-like response. Moreover, the Sagnac vortex separates into upper and lower paths, which behave as two independent pumping paths driving the cavity. These observations are in agreement with theoretical predictions. Our results provide an intuitive physical picture of this interferometer topology and offer insight into its lock acquisition strategy.

Figures (4)

• Figure 1: Layout of the new topology with an L-shaped cavity and Sagnac-like vortex. BS:beam splitter; PRM: power recycling mirror; SRM: signal recycling mirror; ITM: input test mass; ETM: end test mass. The part enclosed by the dashed black box is the focus of the experimental study.
• Figure 2: (a) Schematic showing that the interferometer with an L-shaped cavity can be regarded as equivalent to a Michelson interferometer. The left panel of the figure only illustrates the circulation of the clockwise incident beam within the L-shaped cavity. The counterclockwise incident beam, indicated by the dashed line, has a symmetric circulation inside the cavity that is not shown. (b) Schematic showing that the input laser can be equivalent to two in-phase beams injected into the interferometer, traveling along the clockwise and counterclockwise paths of the Sagnac vortex, separately, and subsequently pump the L-shaped cavity from opposite directions.
• Figure 3: Optical layout (a) and setup (b) of the experiment. The L-shaped interferometer contains two main parts, the Sagnac vortex and the L-shaped optical cavity. PBS: polarization beam splitter; EOM: electro-optic modulator; PD: photodetector.
• Figure 4: Measured output power at the (a) bright, (b) dark, and (c) transmission ports. Data were fitted based on Eqs. \ref{['eq:darkDC when re<1']}-\ref{['eq:intra-cavityDC when re<1']}, yielding reflectivities of $R_{\mathrm{i}} = 97.8\%$ for the ITM and $R_{\mathrm{e}} = 99.7\%$ for two ETMs.