Focusing Profiles of Planar Si-SiO2 Metamaterial GHz Frequency Ultrasonic Lens

Advancesin machine learning and signal processing have increased the demand for power-efficient and high-performance computation. Two-dimensional Fast Fourier transform is one of the most widely used mathematical algorithms in modern science that requires computation on the scale of O(N
²
logN). It has been demonstrated that ultrasonic waves can be used to compute 2D Fourier Transforms owing to the wave diffraction propagation properties. The use of ultrasonic waves requires an ultrasonic lens. Here we demonstrate an ultrasonic lens that can focus ultrasonic waves at a focal length of 500µm. In order to show the focusing effect, we fabricated a planar GHz-scale lens by etching spatially varying posts inside a silicon wafer and thermally growing SiO2 inside the trenches that can generate gradually changing phase shifts over different radii. The fabricated lenses were tested by attaching piezoelectric GHz transducer chips to the lens chips. Preliminary wave propagation was measured using an optical interferometer, and focused wavefronts agree with the analytical calculations.