Bandwidth and resolution of super-resolution imaging with perforated solids

Recent experiments on acoustic superlens and hyperlens found anisotropic metamaterials constructed from periodic perforated solids can be used for super-resolution imaging. Here, we present a theoretical study on the operational bandwidth of these imaging devices using the emerging framework of transformation acoustics. Within the transformation approach, both the microstructural superlens and hyperlens can be discussed using the transfer matrix method on the same footing. We show that the geometrical structure of the periodic metamaterials induces that an acoustics hyperlens has a very wide operational frequency bandwidth with its subwavelength resolution limited by the ratio of image magnification while an acoustics superlens has a very deep subwavelength resolution limited only by the periodicity of the perforations but intrinsically working at a narrow frequency bandwidth. Such investigation will become useful for designing future transformation acoustical imaging devices.