Abstract
Phase gradient acoustic metasurfaces often exhibit pronounced structural dependence in imaging applications, with significant performance variations arising from differences in the negative effective parameters of resonant unit cells. However, the relationship between imaging performance and negative effective parameters near resonance frequencies-particularly in multi-band nested structures-remains insufficiently studied. To address this knowledge gap, this work combines effective parameter theory with local resonance characteristics to construct a comparative model investigating how negative effective mass density and modulus influence the imaging quality of single-band and dual-band nested metasurfaces in series and parallel configurations. The results demonstrate that (1) for single-band structures, imaging performance positively correlates with the absolute value of negative effective parameters; (2) in dual-band configurations, smaller inter-band differences in negative parameter values yield more stable imaging; and (3) series-type nested structures exhibit superior reflection imaging performance compared to parallel-type structures, though with marginally reduced design flexibility. This study elucidates the fundamental mechanisms through which negative parameters govern acoustic metasurface imaging and provides theoretical foundations for designing multi-band acoustic devices.