Optimal beam displacement measurements using high-order structured light modes

Abstract

We develop a novel technique to measure small angular and lateral displacements of structured light beams. The technique relies on using high-order Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes, which have well-defined symmetry under inversion. We show that the displacements of such fields lead to a crosstalk with modes with opposite parity under inversion, which we measure optimally with an interferometric parity sorter. Using this technique, we achieve improvement factors of up 41 in the signal-to-noise ratio using Hermite-Gaussian modes and 21 using Laguerre-Gaussian modes with order up to 20, as compared to the fundamental Gaussian mode. Our results present a viable way of using structured light for metrology that does not demand quantum light or homodyne detection.