Invariance of waveguide grating mirrors to lateral displacement phase shifts

Abstract

We present a method to analyse the coupling of lateral displacements in nanoscale structures, in particular waveguide grating mirrors (WGM), into the phase of a reflected Gaussian beam using a finite-difference time-domain simulation. Such phase noise is of interest for using WGMs in high-precision interferometry. We show that, to the precision of our simulations (10 −7 rad), waveguide mirrors do not couple lateral displacement into phase noise of a reflected beam and that WGMs are therefore not subject to the same stringent alignment requirements as previously proposed layouts using diffraction gratings.

Gravitational radiation detection with laser interferometry

“…Work in this area has resulted in impressive performance in recent years (Brückner et al, 2008;Friedrich et al, 2011;Kroker et al, 2011) approaching power reflectivities of up to 99.9%. Incorporating gratings into interferometers for gravitational-wave detection require substantial hurdles to be overcome: the coupling of mirror alignment fluctuations (Freise, Bunkowski, and Schnabel, 2007;Kroker et al, 2013) and transverse mirror motions (Wise et al, 2005;Brown et al, 2013) into longitudinal phase noise, the control of microroughness to reduce the diffuse scattered light (Woods et al, 1994;Magaña-Sandoval et al, 2012), the control of the large scale flatness to control the mirror figure error, and reducing the transmission losses by another factor of 10 (R ¼ 99:999%).…”

Upper limit to the transverse to longitudinal motion coupling of a waveguide mirror

“…The assumptions made for each free parameter in the model can be found in Table 4. The upper bound on coupling was assumed to be a factor 10 better than the grating mirror measured in [32], given the indication from [33] that no coupling is present. The bounds on the scaling factor and spot smearing standard deviation were chosen from earlier observations of the behaviour of the signals during the experiment.…”

Concepts and research for future detectors

“…Previous efforts with 2nd order Littrow configurations found that an additional phase effect is produced on the reflected light [31,32], resulting in stringent technical requirements. Recent simulations of a 0th order waveguide [33] have shown that this effect can be avoided. The authors aim to demonstrate this result experimentally.…”