Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase

The fine manipulation of sound fields is critical in acoustics yet is restricted by the coupled amplitude and phase modulations in existing wave-steering metamaterials. Commonly, unavoidable losses make it difficult to control coupling, thereby limiting device performance. Here we show the possibility of tailoring the loss in metamaterials to realize fine control of sound in three-dimensional (3D) space. Quantitative studies on the parameter dependence of reflection amplitude and phase identify quasi-decoupled points in the structural parameter space, allowing arbitrary amplitude-phase combinations for reflected sound. We further demonstrate the significance of our approach for sound manipulation by producing self-bending beams, multifocal focusing, and a single-plane two-dimensional hologram, as well as a multi-plane 3D hologram with quality better than the previous phase-controlled approach. Our work provides a route for harnessing sound via engineering the loss, enabling promising device applications in acoustics and related fields.