How to create an acoustic jet with a metamaterial lens

We think of music and other sounds as spreading out from their sources to reach our ears wherever we might be sitting. But it’s possible in principle to create an acoustic jet—that is, a beam of sound whose full width at half maximum is narrower than the sound’s wavelength.

Applications for acoustic jets are already on the drawing board. For example, if ambient acoustic energy could be harvested and focused, an acoustic jet could then direct it to a piezoelectric transponder for conversion into electricity.

Liuxian Zhao, Timothy Horiuchi, and Miao Yu of the University of Maryland have recently proposed a way to generate an acoustic jet that’s up to 30 times as long as the sound’s wavelength. Underlying their method is a spherical lens of radially varying refractive index. Named after its inventor, Rudolf Luneburg (1903–49), the lens is a generalized version of the optical fish-eye lens that James Clerk Maxwell described in 1854.

Zhao, Horiuchi, and Yu’s lens is made of an acoustic metamaterial, not glass. Whereas Luneburg’s original lens focuses plane waves onto a point on its surface, the focus of the Maryland researchers’ lens lies beyond the surface. What’s more, their lens consists of two nested Luneburg lenses. The focus of the outer lens is farther from the mutual center of the two lenses than from the center of the inner lens. The notional line between the two focal points is where the jet forms—or at least where it is supposed to form.

To demonstrate that their lens could in principle produce a jet, Zhao, Horiuchi, and Yu turned to numerical simulation. Their starting point was a pair of analytic expressions for the refractive index in the inner and outer lenses. Feeding the expressions into simulation software yielded the sound field in and around a grapefruit-sized lens. The input frequency was 17 kHz, which is close to the top of humans’ hearing range. As the figure shows, the intensity of the sound was indeed concentrated in a narrow jet.

The analytic expressions for the refractive index in the proof-of-principle simulation were smooth continuous functions. Metamaterials, however, are made up of small discrete objects—unit cells—arrayed in a lattice. Could Zhao, Horiuchi, and Yu’s lens be fabricated even if only in principle? To find out, the researchers turned again to numerical simulation.

To realize the requisite radial variation in the refractive index, the lens was constructed as a series of nested shells. An individual unit cell consisted of three orthogonal beams 5 mm long and crossing each other at their centers. Cells in the same shell had the same mechanical properties. Although the researchers used sound with a frequency range of 0–20 kHz as input, the shells’ and cells’ dimensions were such that the lens operated in the range of 11–17 kHz.

Gratifyingly, the results of the second set of simulations resembled the first; the lens produced a jet. The simulations also quantified one of the researchers’ concerns. Making a lens out of discrete unit cells rather than a continuous medium introduces an impedance mismatch between adjacent cells. Some of the incident acoustic energy is reflected by the lens, but only around 15%. (L. Zhao, T. Horiuchi, M. Yu, JASA Express Lett. 1, 114001, 2021 .)