Li Quan

Apple Inc.

Research Motivation

Sound waves are very common in our daily lives. Strong interactions between matter and sound waves not only provide an extra degree of freedom to manipulate sound waves, but they also provide a useful tool to extract information from unknown bodies. Common applications are ultrasound imaging used in medical diagnosis, non-destructive testing used in industry diagnosis, underwater communications, etc. Acoustic metamaterials have been providing new opportunities in acoustics, enabling scientists to explore opportunities in sound-matter interactions that are not available in nature and discover exotic phenomena that were considered impossible in traditional views. For example, acoustic metamaterials with negative dynamic bulk modulus and negative dynamic mass can support negative refraction of sound waves, which may have a large impact on sound imaging. Acoustic non-reciprocal metamaterials, which allow asymmetric transmission of sound in opposite propagation directions, have potential applications in sound communication and noise control. Acoustic radiation pattern control, such as low-frequency sound collimation technologies, not only can save energy, but also keep the transmitted signal confidential. The discovery of acoustic metamaterials is only about two decades old, and several fundamental questions remain unsolved and/or unexplored in the field. However, the design of novel acoustic devices with special properties is based on the full understanding of the interaction between matter and sound waves. My research goals are motivated by addressing basic open questions in the explorations of acoustic metamaterials, shedding light on the underlying physical mechanisms behind exotic sound phenomena and design novel acoustic devices.

Current Research Interests

At present, my research goal has been focusing on the understanding of bianisotropy in acoustics, i.e., pressure-velocity coupling, and its implications in wave propagation and device engineering. In acoustics, typically the volume compression degree is only a function of the applied pressure, and the unit mass momentum is only dependent on the applied velocity. The pressure-velocity coupling, also known as Willis coupling, explores an extra degree of freedom in sound wave manipulation, by relating volume compression and unit mass momentum with both applied pressure and velocity. Although Willis coupling has been initially proposed in the 1980s, this effect was for a long time considered a higher-order perturbation, which is in most instances negligible, thus the research and applications of this effect have been quite slow in the past decades. The treatment of Willis coupling has been mainly based on higher-order perturbation approximations. In my recent research, I have worked on addressing some of the outstanding questions in this area: what is the ultimate bound for Willis coupling? Can the effect of Willis coupling overcome the perturbation limitation and become as strong as the direct coupling between pressure and compression? How to systematically design inclusions with Willis coupling that provide the maximum effect? I have recently developed a theory to derive the bounds of Willis coupling, indicating that the previous higher-order perturbation assumption is not necessarily valid, and actually the Willis coupling effect can be as strong as the direct coupling terms. By fully understanding the physical mechanism of this effect, several sub-wavelength scale inclusions can be designed to yield the maximum possible Willis coupling. With these inclusions reaching maximum coupling, I am exploring their application to realize unitary-efficient acoustic metasurfaces that can fully redirect the incident acoustic energy into desired directions with the use of only passive media.

Selected Projects

Nonlocal acoustic metasurface

Hyperbolic metasurfaces, supporting extreme anisotropy of the surface impedance tensor, have recently been explored in nanophotonic systems for robust diffractionless propagation over a surface, offering interesting opportunities for subdiffraction imaging and enhanced Purcell emission. In acoustics, due to the longitudinal nature of sound transport in fluids, these phenomena are forbidden by symmetry, requiring the acoustic surface impedance to be inherently isotropic. Here we show that nonlocalities produced by strong coupling between neighboring impedance elements enable extreme anisotropic responses for sound traveling over a surface, supporting negative phase and energy velocities, as well as hyperbolic propagation for acoustic surface waves.

Related Publications:

Physical Review Letters, 123, 244303 (2019).
Physical Review Applied, 11, 054077 (2019).

Maximum Willis coupling

Acoustic bianisotropy effect, also known as Willis coupling effect, was considered has a higher-order perturbation in traditional view. In this project, a fundamental theory has been proposed about the bound of Willis coupling and indicating the previous higher-order perturbation assumption of Willis coupling effect was a misconception in the field, and actually, the Willis coupling effect can be as strong as the direct polarizabilities. A systematic design approach to reach the bound of Willis coupling effect has also been proposed.

Related Publications:

Physical Review Letters, 120, 254301 (2018).
Nature Communications, 10, 3148 (2019).
Nature Communications, 12, 2615 (2021).

Non-reciprocal Imaging System

Mechanical motion can break the symmetry in which sound travels in a medium, but significant non-reciprocity is typically achieved only for very large motion speeds. In this project, we combine moving media with zero-index acoustic propagation, yielding extreme non-reciprocity and induced bianisotropy for modest applied speeds. The metamaterial is formed by an array of waveguides loaded by Helmholtz resonators, and it exhibits opposite signs of the refractive index sustained by asymmetric Willis coupling for propagation in opposite directions. We use this response to design a non-reciprocal acoustic lens focusing only when excitation from one side, with applications for imaging and ultrasound technology.

Related Publications:

Physical Review Letters, 123, 064301 (2019).

Effective Impedance Modulation

Boundary impedance is the most important parameters determining acoustic waves propagation properties along the surface. In this project, we proposed an approach to arbitrary control the acoustic impedance of a surface and realizing acoustic directivity pattern control. By decorating Helmholtz Resonators on the surface of a plate, we realized a soft boundary condition on the surface of a hard plate.

Our proposed effective impedance modulation approach has motivated and inspired researchers' work in the field of theoretical physics focusing on General Relativity. See Phys. Rev. Lett. 117, 271101 (2016).

Related Publications:

Nature Communications, 5, 3188 (2014).
Physical Review B, 92, 104105 (2015)
The Journal of the acoustical society of America, 138, 782-790 (2015).

Nonlinear ultrasound non-destructive testing

Nondestructive testing is an important tool to ensure product quality and performance, and ultrasonic testing is one of the most popular methods for nondestructive testing. However, the traditional linear ultrasound techniques have difficulty in detecting microcracks within a solid. In this project, we propose a new technique based on the vibration amplitude of the higher harmonics, which is capable of determining the locations of multiple cracks. The boundary condition of the rod structure is set to be free on one side while mass-loading conditions are introduced on the other side, which provides nonuniformly spaced eigenfrequencies of the specimen. Using this method, the analytical relationship between the amplitude of the higher harmonics and the crack position is obtained. The locations and the sizes of the cracks can be determined if the higher harmonic amplitudes are measured.

Related Publications:

Journal of Applied Physics, 112, 054906 (2012).

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