Translational, rotational, and vibrational coupling into phase in diffractively coupled optical cavities

All-reflective optical systems are under consideration for future gravitational wave detector topologies. A key feature of these all-reflective systems is the use of Fabry-Perot cavities with diffraction gratings as input couplers; however, theory predicts and experiment has shown that translation of the grating surface across the incident laser light will introduce additional phase into the system. This translation can be induced through simple side-to-side motion of the coupler, yaw motion of the coupler around a central point (i.e., rotation about a vertical axis), and even via internal resonances (i.e., vibration) of the optical element. In this Letter we demonstrate on a prototype-scale suspended cavity that conventional cavity length-sensing techniques used to detect longitudinal changes along the cavity axis will also be sensitive to translational, rotational, and vibrational motion of the diffractive input coupler. We also experimentally verify the amplitude response and frequency dependency of the noise coupling as given by theory.