Acoustic Macroscopic Rigid Body Levitation by Responsive Boundary Hologram

Propagated acoustic waves, which generate radiation pressure, exert a non-contact force on a remote object. By suitably designing the wave field, remote tweezers are produced that stably levitate particles in the air without any mechanical contact forces[23, 3, 5]. Recent works have revealed that holographic traps can levitate particles even with a single-sided wave source[8, 7, 24, 11]. However, the levitatable objects in the previous studies were limited to particles smaller than the wavelength, or flat parts placed near a rigid wall[1]. Here, we achieve a stable levitation of a macroscopic rigid body by a holographic design of acoustic field without any dynamic control. The levitator models the acoustic radiation force and torque applied to a rigid body by discretising the body’s surface, as well as the acoustic wave sources, and optimizes the acoustic field on the body surface to achieve the Lyapunov stability so that the field can properly respond to the fluctuation of the body position and rotation. In an experiment, a 40 kHz (8.5 mm wavelength) ultrasonic phased array levitated a polystyrene sphere and a regular octahedron with a size of ∼50 mm located 200 mm away from acoustic elements in the air. This method not only expands the variety of levitatable objects but also contributes to microscopic contexts, such as in-vivo micromachines, since shorter-wavelength ultrasound than the size of target objects can be used to achieve higher controllability and stability. ∗inoue@hapis.k. u-tokyo.ac. jp 1 ar X iv :1 70 8. 05 98 8v 1 [ ph ys ic s. ap pph ] 2 0 A ug 2 01 7 Acoustic radiation pressure is a static pressure applied to an object in a propagating or standing sound wave, and can apply a force to a remote object. Acoustic tweezers trap particles at points in space by utilizing acoustic radiation pressure. Compared with optical radiation force tweezers for nanoparticles or magnetic levitation targeting ferromagnetic materials, acoustic levitation by ultrasonic waves can levitate various materials, opening up the possibility of a wide range of applications, such as crystallography[15], chemistry[17], microbiology[4] and human–computer interfaces[14, 16]. However, previous midair acoustic levitation was limited to particles smaller than the wavelength of the sonic wave, where the wave field is designed under an assumption that sound field disturbance by the target object is negligible. An exceptional example of macroscopic object levitation is squeeze-film levitation. An ultrasonic vibrator can reduce the friction and lift an object larger than the wavelength using squeeze-film effect. However, the levitation distance is much smaller than the wavelength in typical designs[21]. Another approach is to create a standing wave between wave sources and the target object [25, 1]. Although it has been theoretically predicted that this approach can levitate an object at a distance of half the wavelength or integer multiples thereof, no experiments have been reported that demonstrate stable levitation in a three-dimensional space beyond distances equal to the wavelength. Basically, this approach cannot stabilize the transverse orientation of the object to the wave direction. A typical levitator for particles uses a standing waves generated by a pair of transducers or a set of a transducers and a reflector[23, 3, 5]. A recent research has expanded its degrees of freedom of manipulation into threedimensions[14]. In addition, single-sided traps formed by travelling waves have been realized recently, by extending the technique used in optical tweezers, first for lateral trapping[8] and also for full dimensional trapping[11]. The main approach used in acoustic tweezers is to apply an approximation model, such as the Gor’kov potential, that holds on a sphere significantly smaller than the wavelength, assuming the field is not affected by the scatterer[3, 7, 5, 11, 12, 10]. This approach is often highly effective for sparse particles because it becomes a free space problem, which is analytically solvable. Another approach is to employ a cloaking technique, where the wave avoids an object and is scattered less[24]. However, it yields less force, and it has not been reported that this technique gives a force sufficient to lift a solid in the air because the acoustic radiation pressure results from the scattered energy density[22]. Levitation by shorter wavelengths than the object size will not only expand the variety of levitatable targets but will also enable precise control of small particles. Levitation of a rigid body with a large clearance while stabilizing its orientation will be of benefit in a wide range of applications, including industrial assembly such as electronics, drug delivery, micro-machine control and multiple bodies control, and will make it possible to manipulate