Hemispherical acoustic Luneburg lens with the acoustic Goos–Hänchen shift and Fresnel filtering effect

A two-dimensional (2D) slice of a 3D hemispherical acoustic Luneburg lens using a quasi-conformal transformation and face-centred-orifice-cubic (FCOC) unit cells is designed and fabricated. With the system, the focusing characteristics of acoustic waves with frequencies that satisfy the homogeneous medium condition of the metamaterial are observed, such as focusing of acoustic plane waves at the antipodal point on the transformed surface of the opposite side for the incident direction and focus spreading due to total internal reflection at the focus point. The attenuation losses of the system are measured and compared with those of an untransformed system with respect to frequency. The value of the acoustic Goos–Hänchen shift is determined by comparing the experimental and theoretical and simulated values of the focus points with respect to the incident angle. The effect of acoustic Fresnel filtering due to the angular distribution of the incident waves at the flat surface boundary is verified by comparing the results of the experiment and a simulation.