Shaping sound field through acoustic metasurfaces: An optimisation method for correcting loudspeaker emissions

In a loudspeaker system, the acoustic wave front modulation can be achieved using active control systems that adopt algorithms to modulate the acoustic wave front emitted, adapting to the environmental conditions or to the specific requirements of the sound source. To be efficient, a large number of loudspeakers and the digital processing of the signal are required. Acoustic metasurfaces are sub-wavelength structures that can manipulate sound, allowing the control of, e.g., the shape or direction of the wave front. In this work, we aim to reduce the number of speakers by coupling acoustic metasurfaces at the outlet of a single transducer. To design the metasurface for this task direct methods, which rely on unit cells geometrical parameters retrieved by finite element simulations, are traditionally used. This approach has to be repeated iteratively and demands significant efforts to investigate the enormous number of possible metamaterial combinations. More recent methods include topology optimization, physics-informed neural networks, and machine learning. These methods frequently limit their focus on optimization for unit cell structures and do not provide a design or strategy for the whole metasurface. In this work, the metasurface phase profile is instead retrieved by combining a finite element method to generate the search space and a gradient-free optimization algorithm to retrieve the best metasurface configuration required to satisfy a desired pressure distribution pattern in a 2D listening area.