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

Rotation velocity measurement based on a self-mixing grating interferometer

A novel rotational velocity measurement method based on the self-mixing grating interferometer (SMGI) is explored and presented in this paper. In this method, the target object rotational velocity is measured by the Doppler frequency shift, which can be extracted through the power spectrum without measuring incident angles. The experimental results show that the relative errors are below 0.5%.

Interferometer phase noise due to beam misalignment on diffraction gratings

All-reflective interferometer configurations have been proposed for the next generation of gravitational wave detectors, with diffractive elements replacing transmissive optics. However, an additional phase noise creates more stringent conditions for alignment stability. A framework for alignment stability with the use of diffractive elements was required using a Gaussian model. We successfully create such a framework involving modal decomposition to replicate small displacements of the beam (or grating) and show that the modal model does not contain the phase changes seen in an otherwise geometric planewave approach. The modal decomposition description is justified by verifying experimentally that the phase of a diffracted Gaussian beam is independent of the beam shape, achieved by comparing the phase change between a zero-order and first-order mode beam. To interpret our findings we employ a rigorous time-domain simulation to demonstrate that the phase changes resulting from a modal decomposition are correct, provided that the coordinate system which measures the phase is moved simultaneously with the effective beam displacement. This indeed corresponds to the phase change observed in the geometric planewave model. The change in the coordinate system does not instinctively occur within the analytical framework, and therefore requires either a manual change in the coordinate system or an addition of the geometric planewave phase factor.

Invited review article: Interferometric gravity wave detectors

A direct detection of gravitational waves is still lacking today. A network of several earthbound interferometric detectors is currently operating with a continuously improving sensitivity. The window of interest for observation has a lower cut off in the frequency domain below some tens of hertz, determined by the effect of seismic motion. For larger frequencies, the sensitivity is limited by thermal effects below few hundreds of hertz and by the quantum nature of light above that value. Each of these sources of noise pose a big technological challenge to experimentalists, and there are big expectations for the next generation of detectors. A reduction of thermal effects by at least one order of magnitude will be obtained with new and carefully designed materials. At that point the quantum nature of light will become an issue, and the use of quantum non-demolition techniques will become mandatory. In this review, we discuss interferometric detection of gravitational waves from an instrumental point of view. We try to address conceptually important issues with an audience of non-experts in mind. A particular emphasis is given to the description of the current limitations and to the perspectives of beating them.

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.