Phase and alignment noise in grating interferometers

Diffraction gratings have been proposed as core optical elements in future laser interferometric gravitational-wave detectors. In this paper, we derive equations for the coupling between alignment noise and phase noise at diffraction gratings. In comparison to a standard reflective component (mirror or beam splitter) the diffractive nature of the gratings causes an additional coupling of geometry changes into alignment and phase noise. Expressions for the change in angle and optical path length of each outgoing beam are provided as functions of a translation or rotation of the incoming beam with respect to the grating. The analysis is based entirely on the grating equation and the geometry of the set-up. We further analyse exemplary optical set-ups which have been proposed for the use in future gravitational-wave detectors. We find that the use of diffraction gratings yields a strong coupling of alignment noise into phase noise. By comparing the results with the specifications of current detectors, we show that this additional noise coupling results in new, challenging requirements for the suspension and isolation systems for optical components