Lateral input-optic displacement in a diffractive Fabry-Perot cavity

Abstract

All-reflective configurations have been suggested for future laser-interferometric gravitational wave detectors. Diffraction gratings would be required as core elements of any such design. In this paper, coupling of lateral grating displacement to the output ports of a diffractive Fabry-Perot cavity was derived using a steady-state technique. The signal to noise ratio versus a potential gravitational wave signal was compared for each cavity output port. For a cavity featuring parameters similar to the planned Advanced Virgo instrument, we found the forward-reflected port offers the highest SNR at low frequencies. Furthermore, the lateral isolation suspension requirements were relaxed by a factor of twenty at a frequency of 10Hz versus the transmitted port.