Negative refraction and focusing of ultrasound in two-dimensional phononic crystals

Abstract

We present experimental demonstrations of negative refraction and focusing of ultrasonic waves in two-dimensional phononic crystals made of stainless steel rods assembled in a triangular lattice and immersed in a liquid. Negative refraction is achieved for the range of frequencies in the second band, where the directions of the wave vector and group velocity are antiparallel to each other due to circular equifrequency contours. Negative refraction is unambiguously observed using a prism-shaped crystal. By exploiting the circular equifrequency contours in the second band, focusing of the ultrasonic field emitted by a pointlike source was demonstrated using a flat phononic crystal filled with and immersed in water. During these experiments, the importance of imaging in the regime of all angle negative refraction (AANR) was established for obtaining high-quality images. The regime of AANR was achieved in a similar flat crystal, in which the liquid inside the crystal (methanol) was different from the outside medium (water). This design resulted in matching circular equifrequency contours at the frequency of $0.55\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, implying that a flat ultrasonic lens with an effective refractive index of $\ensuremath{-}1$ was realized. By imaging a subwavelength line source with this crystal, a resolution of $0.55\ensuremath{\lambda}$ was observed, which is just above the diffraction limit.