Coupling of lateral grating displacement to the output ports of a diffractive Fabry-Perot cavity

TL;DR

This paper analyzes how lateral displacements of diffraction gratings affect the output signals of a Fabry-Perot cavity, relevant for gravitational-wave detectors, and compares noise contributions at different ports.

Contribution

It introduces a steady-state method to quantify lateral grating displacement coupling and evaluates the signal-to-noise ratio at various output ports for a gravitational-wave detector model.

Findings

Forward-reflecting port has highest SNR at low frequencies.

Lateral isolation requirements can be relaxed by observing the forward-reflected port.

Potential 20-fold reduction in suspension requirements at 10Hz.

Abstract

Diffraction gratings have been proposed as core elements in future laser-interferometric gravitational-wave detectors. In this paper, we use a steady-state technique to derive coupling of lateral grating displacement to the output ports of a diffractive Fabry-Perot cavity. By introducing a signal to noise ratio (SNR) for each of the three cavity output ports the magnitude of the noise sidebands originating from lateral grating displacement are compared to the magnitude of a potential gravitational wave signal. For the example of a 3km long Fabry-Perot cavity featuring parameters similar to the planned Advanced Virgo instrument, we found that the forward-reflecting grating port offers the highest SNR at low frequencies. Furthermore, for this example suspension requirements for lateral isolation were computed, and a factor of twenty relaxation at a frequency of 10Hz can be gained over the transmitted port by observing the forward-reflected port.