Adjustable Phase-Amplitude-Phase Acoustic Metasurface for the Implementation of Arbitrary Impedance Matrices

Impedance metasurfaces enable accurate regulation of acoustic fields. However, they can hardly supply a flexible response as such perfect operation is accompanied by stringent requirements on the design of unit cells. Actually, an arbitrary lossless and passive target impedance matrix requires the tuning of 3 independent real parameters. The set composed of a reflection phase, a transmission amplitude, and a transmission phase, enables the representation of an arbitrary impedance matrix, possibly possessing singular elements. In this paper, a mechanism of phase-amplitude-phase modulation (PAP modulation) is developed for the generic design of the unit cells of acoustic impedance metasurfaces. Adjustable acoustic impedance metasurfaces are further available under this framework. An impedance unit with 3 mobile parts is designed based on this idea. The assembled metasurface can handle different incidences for acoustic field manipulation at a given frequency. Beam steering and beam splitting are considered as demonstration examples and are verified by numerical simulation and experiment. PAP modulation enriches the design of acoustic impedance metasurfaces and extends the range of application of impedance theory.