Optical ranging and vibration sensing based on the lagging propagation phase of structured beams.

Recently, studies have shown that the spatial confinement on waves or photons with beam shaping techniques would modify the propagation speed of optical fields including both group and phase velocities. Particularly, for the monochromatic spatially structured beams, the reduced longitudinal wave vector enables the phase velocity to be superluminal, causing a lagging propagation phase. In this Letter, we propose a novel, to the best of our knowledge, scheme for optical ranging and vibration sensing with the lagging propagation phase of structured beams. We experimentally demonstrate the extraction of displacement from the rotating angles of interfering fringes of superposed Gaussian and higher-order Bessel beams with lagging propagation phase difference. The measuring range is 0.2 m with the limitation of the tested moving stage, but it can be extended to tens of meters in principle. The measuring resolution can reach sub-millimeters, which can be further improved by carefully designing the probe beam and using a finer camera. The results may provide potential applications in position sensing and monitoring.