Numerical Optimization of Metasurface Cells for Acoustic Reflection

Metamaterials and metasurfaces disclosed new degrees of freedom in controlling the acoustic field. Exploiting the generalized Snell law and the generalized law of reflection, the assembly of subwavelength unit cells is able to achieve extraordinary refraction and reflection by means of a controlled phase delay introduced in the field by the treated boundaries. The space-coiling design is one of the most powerful for cells in this metadevice class, providing effective low-thickness metasurfaces. However, space-coiling suffers from a narrow frequency operating range due to the intrinsic connection between the design operating wavelength and the characteristic dimensions of the metasurface. This work defines a procedure based on numerical optimization for designing space-coiling cells for modular acoustic metasurfaces, extending the frequency range in which the metasurface is effective. The set comprises eight different unit cells, each introducing a tailored phase shift in the reflected field that can be arranged to produce the desired acoustic effect. The broadband design is obtained by minimizing the dependency on the operating frequency of phase delay introduced by the cells, keeping the overall thickness below a quarter of the design wavelength. Results are shown for the benchmark problem of a metasurface modifying the reflection angle from a boundary.