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

Waveguide mirrors (WGMs) 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 the 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 WGM 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.