Invariance of waveguide grating mirrors to lateral displacement phase shifts

We present a method to analyze the coupling of lateral displacements in nanoscale structures, in particular waveguide grating mirrors (WGMs), 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.