A modified angular spectrum method for rapid on-demand design of axisymmetric acoustic metalenses

The angular spectrum method (ASM) is rarely employed directly in the rapid design of acoustic metalenses, due to significant aliasing artifacts in long-distance diffraction calculations. For axisymmetric systems, although ASM based on radial transforms holds promise for dimensionality reduction and acceleration, its application in on-demand focusing design remains underdeveloped. This paper presents a modified ASM that significantly enhances both the speed and accuracy of diffraction simulations. Compared to the finite-element method as the accuracy benchmark, the modified method reduces the relative error by a factor of 2-3 and is approximately 100 times faster than the direct Hankel transform ASM. Additionally, it produces results consistent with the Rayleigh-Sommerfeld integral, with a 95 times speed increase, enabling millisecond-scale computation at a grid size of λ/15 on a standard desktop. By integrating the method with an evolutionary algorithm, this method efficiently optimized binary acoustic metalenses and experimentally demonstrated complex focal shapes. This approach provides a practical, cost-effective, and efficient solution for the rapid on-demand design of axisymmetric acoustic focusing devices.