Versatile acoustic topology optimization of sonic black holes for enhanced wavefocusing

Sonic black holes (SBHs) have been widely studied for sound-absorption applications due to their gradual structures that slow sound waves, which are then attenuated using dissipative materials. In addition to slowing sound waves, the amplitude of sound wave increases, which can be leveraged for wave-focusing applications. Recently, topology optimization has been used to design SBH devices that exhibit broadband wave focusing with the objective of maximizing the transmission bandwidth. However, such transmission-based designs often provide limited focusing performance, and the local phase velocity inside the SBH does not decrease monotonically as in an ideal configuration. Here, we show that by directly maximizing the pressure distribution inside the SBH while imposing pressure constraints, the wave-focusing performance is significantly improved. A three-point method is used to estimate the local phase velocity, revealing that the constraint-based designs closely approach ideal SBH behavior, with the local phase velocity approaching zero toward the end of the SBH. We further provide numerical evidence of their practical application for wave focusing in a free field using transient analysis with the designed SBH, achieving up to 30 dB acoustic amplification. Experimental measurements further validate the practical capability of the fabricated samples for weak signal amplification. This framework offers a versatile approach to designing SBHs with enhanced wave focusing and practical weak-signal amplification.