Wave-field shaping with elastic metasurfaces via the iterative angular-spectrum approach

Metasurface designs are often based on the generalized Snell's law, which controls wave refraction but lacks the capability for complex wavefront shaping. Combining it with advanced engineering techniques enables more complex wave trajectories, though achieving fully customized trajectories remains challenging and requires extensive design efforts. The holographic iterative angular spectrum approach (IASA) is based on the iterative computation of the forward and backward propagation of acoustic waves, allowing the realization of custom arbitrary patterns by considering numerous target planes. In this work, IASA is used as a unique metasurface inverse design approach, allowing for precise and conformal control over the phase of transmitted waves via designed unit cells. Various forms of wave manipulation are achieved, including self-bending and bottle beams. We demonstrate that the IASA, which involves reconstructing the complex field, enables successive beam steering. This capability is demonstrated by tailoring the unit cell profiles in the elastic host media, thereby creating thickness profiles that generate the desired phase gradients while allowing for near-perfect transmission of the wave energy. Experiments are conducted to validate the numerical predictions of the IASA for successive patterning.