Recent studies in photonics have indicated that structuring the spatial profile of light induces changes in the speed of light in vacuum [1,2,3]. As one can only reliably measure the time of arrival of a photon, this leads to ambiguity in the measurement of this effect. To offer a clarifying perspective, we investigate the analogous changes in rate of energy flow that arise from the spatial shaping of sound. Unlike photonics, one can easily simultaneously measure of phase and intensity of sound. Hence, we spatially shape an acoustic pulse through the use of a bespoke 28-element phased array transducer operating at 40 kHz. When the pulse is measured, after 60 mm of propagation, a distinctive amplitude profile is observed, consistent with a beating pattern between waves traveling at different velocities. For an acoustic vortex beam, we directly measure an increase in the speed of sound in air by 6 m/s. Through geometrical analysis we conclude that the speed of sound across the wavefront changes, locally, to compensate for the local change in path length induced by wavefront shaping, thereby maintaining time of flight for the pulse to match that of a pulse with a planar wavefront. We propose that this is a general effect for shaped wavefronts, and suggest that only photons with a flat optical wavefront truly travel at c, the canonical speed of light.
References: 1. D. Giovannini, et al., Science 347, aaa3035 (2015).
2. F. Bouchard, et al., Optica 3, 351 (2016).
3. R.R. Alfano, et al., Optics Communications, 361, 25–27 (2016).