Designing Luneburg lenses. (a) The building blocks of the Luneburg lens: 3D-crosses with varying geometric coefficient a0 lead to a range of refractive index. In the inset, the dimension of a0D is marked (D is the length of the unit cell, which is 2 mm for the ultrasonic version). (b) The refractive index profile of a 40 kHz Luneburg lens. (c) A 2.5D sample design for 40 kHz airborne ultrasound. There are three layers of the 3D-cross unit cells along the out-of-plane dimension. (d) A full 3D sample design for 8 kHz airborne sound.