Acoustic transmission through aberrating or reflecting layers has been a long-standing issue in medical ultrasounds and nondestructive evaluation. An example of acoustic transmission is transcranial ultrasound beam focusing, where the ultrasound needs to be transmitted through the skull for either imaging or therapy. During this process, a large portion of the energy is reflected because of the presence of the skull, and the acoustic field is severely distorted, compromising the quality of the image or the treatment efficacy. We propose a unique solution to solve this problem using an anisotropic, acoustic, nonresonant, complementary metamaterial that virtually removes the aberrating layer.

We present the first feasible design for making acoustic complementary metamaterials, which consist of aluminum membranes approximately 0.1 mm thick and branch openings in each unit cell. The operating frequency of the metamaterials is 50 kHz, and there are $120\times 10$ unit cells over the entire metamaterial. The membranes introduce negative densities, and the branch openings are characterized by negative compressibilities. More importantly, we assign a membrane in each $x$ or $y$ direction with different thicknesses in order to achieve a strong anisotropy for the density; parameters in both directions are treated as one-dimensional quantities. We show that this design does not rely on resonance, unlike conventional acoustic metamaterials, and therefore does not suffer from energy losses due to resonance. Our numerical wave simulations show that the acoustic field distortion from the aberrating layer can be significantly reduced by using complementary metamaterials, and, in fact, the sound transmission is enhanced by approximately a factor of 3.

Our study paves the way for realizing acoustic complementary metamaterials that have a wide range of applications, including cloaking, all-angle antireflection, ultrasound imaging, and therapy through aberrating layers.