Abstract
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.
Highlights
Grating movements within these interferometers or beam movements on the grating affect the phase of the light differently to movements of mirrors and beam splitters in conventional interferometers
When a four-port grating is used for a beam splitter the outgoing beams are given by the interference between a zero- and a first-order diffracted beam
Diffraction gratings have been proposed as replacements of traditional mirrors and beam splitters for interferometric gravitational-wave detectors
Summary
A surface with a periodic modulation of optical properties, so-called grooves, defines a diffraction grating. The analogue to a transmissive mirror with two ports (in the case of normal incidence) is given by a first-order Littrow configuration In this case only one additional order exists but the diffracted beam coincides with the incoming beam (α = β1). Parameters can likewise be chosen to allow for a second-order Littrow configuration (two additional orders and α = β2) This results in a beam splitter with three ports, which can be used to construct a linear Fabry–Perot interferometer (figure 2). Its maximal finesse is limited by the specular reflectivity of the grating rather than the diffraction efficiency Such a three-port splitter has no simple analogue to a conventional transmissive mirror and its input–output phase relations are more complex [12]. The resulting properties of such resonators are well understood and controllable [13]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
