Analytical-Numerical Optimization of a Reflective Acoustic Metalens Using PSO

This paper presents an analytical-numerical framework for designing and optimizing a reflective acoustic metalens embedded in a rigid cavity. The goal is to steer the reflected beam by tailoring the spatial phase or effective impedance of the metalens surface. The model is based on the Helmholtz equation with a Neumann boundary for the rigid wall and continuity-jump conditions across the metalens interface. Using the half-space Green's function, an integral relation for the surface pressure is derived and discretized into a stable Fredholm equation of the second kind. The particle-swarm optimization (PSO) algorithm is then applied to find the optimal phase distribution that maximizes reflected energy at the target angle. Numerical results show that the optimized metalens produces a controlled phase gradient that redirects normal reflection into an oblique beam with high accuracy. The framework combines analytical rigor, numerical stability, and computational efficiency, and can be extended to electromagnetic and other wave systems.

کلیدواژه ها:

Acoustic metalens ، beam steering ، Green's function ، PSO optimization ، Fredholm integral