  Waveguide mirrors possess nano-structured surfaces which can potentially
provide a significant reduction in thermal noise over conventional dielectric
mirrors. To avoid introducing additional phase noise from motion of the mirror
transverse to the reflected light, however, they must possess a mechanism to
suppress the phase effects associated with the incident light translating
across the nano-structured surface. It has been shown that with carefully
chosen parameters this additional phase noise can be suppressed. We present an
experimental measurement of the coupling of transverse to longitudinal
displacements in such a waveguide mirror designed for 1064 nm light. We place
an upper limit on the level of measured transverse to longitudinal coupling of
one part in seventeen thousand with 95% confidence, representing a significant
improvement over a previously measured grating mirror.
