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.

Experimental demonstration of a suspended diffractively coupled optical cavity.

All-reflective optical systems are under consideration for future gravitational wave detector topologies. One approach in proposed designs is to use diffraction gratings as input couplers for Fabry-Perot cavities. We present an experimental demonstration of a fully suspended diffractively coupled cavity and investigate the use of conventional Pound-Drever-Hall length sensing and control techniques to maintain the required operating condition.

Optical characterization of ultrahigh diffraction efficiency gratings.

We report on the optical characterization of an ultrahigh diffraction efficiency grating in a first-order Littrow configuration. The apparatus used was an optical cavity built from the grating under investigation and an additional high-reflection mirror. The measurement of the cavity finesse provided precise information about the grating's diffraction efficiency and its optical loss. We measured a finesse of 1580 from which we deduced a diffraction efficiency of (99.635+/-0.016)% and an overall optical loss due to scattering and absorption of just 0.185%. Such high-quality gratings, including the tool used for their characterization, might apply for future gravitational wave detectors. For example, the demonstrated cavity itself presents an all-reflective, low-loss Fabry-Perot resonator that might replace conventional arm cavities in advanced high-power Michelson interferometers.

Demonstration of three-port grating phase relations.

We experimentally demonstrate the phase relations of three-port gratings by investigating three-port coupled Fabry-Perot cavities. Two different gratings that have the same first-order diffraction efficiency but differ substantially in their second-order diffraction efficiency have been designed and manufactured. Using the gratings as couplers to Fabry-Perot cavities, we could validate the results of an earlier theoretical description of the phases at a three-port grating [Opt. Lett. 30, 1183 (2005)].

Three-port beam splitters-combiners for interferometer applications.

We derive generic phase and amplitude coupling relations for beam splitters-combiners that couple a single port with three output ports or input ports, respectively. We apply the coupling relations to a reflection grating that serves as a coupler to a single-ended Fabry-Perot ring cavity. In the impedance-matched case such an interferometer can act as an all-reflective ring mode cleaner. It is further shown that in the highly undercoupled case almost complete separation of carrier power and phase signal from a cavity strain can be achieved.

Input-output relations for a three-port grating coupled Fabry-Perot cavity.

We analyze an optical three-port reflection grating by means of a scattering matrix formalism. Amplitude and phase relations among the three ports, i.e., the three orders of diffraction, are derived. Such a grating can be used as an all-reflective, low-loss coupler to Fabry-Perot cavities. We derive the input-output relations of a three-port grating coupled cavity and find distinct properties that are not present in two-port coupled cavities. The cavity relations further reveal that the three-port coupler can be designed such that the additional cavity port interferes destructively. In this case the all-reflective, low-loss, single-end Fabry-Perot cavity becomes equivalent to a standard transmissive, two-port coupled cavity.

Ultra low-loss low-efficiency diffraction gratings.

The realization of ultra low-loss dielectric reflection gratings with diffraction efficiencies between 7% and 0.02% is presented. By placing the grating beneath the highly reflective layerstack scattering was significantly reduced. This concept allows the all-reflective coupling of high laser radiation to high finesse cavities, thereby circumventing thermal effects caused by absorption in the substrate.

Low-loss grating for coupling to a high-finesse cavity.

A concept for a low-loss all-reflective cavity coupler is experimentally demonstrated at a wavelength of 1064 nm. A 1450-nm period dielectric reflection grating with a diffraction efficiency of 0.58% in the - 1st order is used in the 2nd-order Littrow configuration as a coupler to form a cavity with a finesse of 400. The application of such reflective low-loss cavity couplers in future generations of gravitational-wave detectors and implementation issues are discussed.