Level-set topology optimization of electrode-patterned piezoelectric metasurfaces for far-field ultrasonic focusing via the Kirchhoff–Helmholtz integral method

Abstract

Conventional focusing methods using acoustic lenses have limitations, such as low transmittance and mechanical crosstalk, which degrade the on-demand focusing performance. This study presents a level-set topology optimization framework for designing electrode patterns on a planar piezoelectric metasurface. In the proposed framework, the electrode topologies are implicitly represented by a signed-distance function and evolved through the Hamilton-Jacobi equation using boundary point sensitivities calculated by the adjoint variable method. A parameterization scheme for the electric potential boundary condition is devised to parameterize the electrode patterns through topological design variables, i.e., area fractions of design elements cut by the zero level-set contour. The far-field acoustic pressure is efficiently evaluated using the Kirchhoff-Helmholtz integral method, leading to significant computational cost savings during optimization. Numerical investigations demonstrate that the proposed framework achieves well-defined focusing in both on- and off-axis configurations, which supports its use as a lens-free approach for far-field ultrasonic focusing.