Realistic polarizing Sagnac topology with DC readout for the Einstein Telescope

The Einstein Telescope (ET) is a proposed future gravitational wave detector. Its design is original, using a triangular orientation of three detectors and a xylophone configuration, splitting each detector into one high-frequency and one low-frequency system. In other aspects the current design retains the dual-recycled Michelson interferometer typical of current detectors, such as Advanced LIGO. In this paper, we investigate the feasibility of replacing the low-frequency part of the ET detectors with a Sagnac interferometer. We show that a Sagnac interferometer, using realistic optical parameters based on the ET design, could provide a similar level of radiation pressure noise suppression without the need for a signal recycling mirror and the extensive filter cavities. We consider the practical issues of a realistic, power-recycled Sagnac, using linear arm cavities and polarizing optics. In particular, we investigate the effects of nonperfect polarizing optics and propose a new method for the generation of a local oscillator field similar to the DC readout scheme of current detectors.