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 setup. We further analyse exemplary optical setups 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 the optical components.

Optical characterization of ultra-high diffraction efficiency gratings

We report on the optical characterization of an ultra-high diffraction efficiency grating in 1st order Littrow configuration. The apparatus used was an optical cavity built from the grating under investigation and an additional high reflection mirror. Measurement of the cavity finesse provided precise information about the gratings diffraction efficiency and its optical loss. We measured a finesse of 1580 from which we deduced a diffraction efficiency of (99.635$pm$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 3-port grating phase relations

We experimentally demonstrate the phase relations of 3-port gratings by investigating 3-port coupled Fabry-Perot cavities. Two different gratings which have the same 1st order diffraction efficiency but differ substantially in their 2nd 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.

Diffractive Optics for Gravitational Wave Detectors

All-reflective interferometry based on nano-structured diffraction gratings offers new possibilities for gravitational wave detection. We investigate an all-reflective Fabry-Perot interferometer concept in 2nd order Littrow mount. The input-output relations for such a resonator are derived treating the grating coupler by means of a scattering matrix formalism. A low loss dielectric reflection grating has been designed and manufactured to test the properties of such a grating cavity.

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 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 as well as some implementation issues are discussed.