T-matrix evaluation of three-dimensional acoustic radiation forces on nonspherical objects in Bessel beams with arbitrary order and location

T-matrix evaluation of three-dimensional acoustic radiation forces on nonspherical objects in Bessel beams with arbitrary order and location Zhixiong Gong1,2,†, Philip L. Marston2,‡, Wei Li1,* 1School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 2Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164-2814, United States † Present address: Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Polytechniques Hauts-de-France, UMR 8520-IEMN, International laboratory LIA/LICS, F-59000 Lille, France zhixiong.gong@iemn.fr ‡ marston@wsu.edu

• Corresponding author: hustliw@hust.edu.cn

Acoustic radiation forces (ARFs) induced by a single Bessel beam with arbitrary order and location on a nonspherical shape are studied using the T-matrix method (TMM) in three dimensions. Based on the radiation stress tensor approach and the multipole expansion method for the arbitrary Bessel beam, the ARF expressions are derived in terms of the incident and scattered beam shape coefficients independently with the corresponding homemade code packages. Several numerical experiments are conducted to verify the versatility of the TMM. The axial acoustic radiation forces (ARFs) of several typical shapes are considered in the analysis with the emphasis on the axial ARF reversal 2

and the corresponding physical mechanism. This study may guide the experimental set-up to find negative axial ARFs quickly and effectively based on the predicted parameters with TMM. Relatively elongated shapes may be helpful for pulling forces in Bessel beams. Furthermore, the lateral ARFs for both convex and concave nonspherical shapes are also investigated with different topological charges, cone angles and offsets of the particle centroid to the beam axis in a broadband frequency regime. A brief theoretical derivation of the incident beam shape coefficients for the standing Bessel beams is also given. The present work could help to design the acoustic tweezers numerical toolbox which provides an acoustical alternative to the optical tweezers toolbox. 1 Introduction Acoustic tweezers1-4, an appropriate counterpart to optical tweezers5, could be used for levitation6,7, pulling forces8-12, particle trapping13,14, and even dynamic controls15,16 in the fields of microfluidics and life sciences. Compared with optic tweezers, acoustic tweezers tend to exert a larger force over larger length scales with the same intensity since the radiation force is proportional to the ratio of the intensity to the velocity in the medium2,17. In general, there are two main schemes to design acoustic tweezers: the (quasi)standing wave scheme with dual beams1,2,4 and the single beam structure3. Single-beam tweezers may be superior to general plane standing-wave tweezers in some respects, for instance, single-beam tweezers can continuously pull or push a particle over a large region because there are no multiple equilibrium positions10,17. Negative radiation force single-beam 3

device could pull the target towards the source, which is of interest in both acoustical8-12,17 and optical fields18. The physical mechanism is due to the asymmetric scattering of the incident fields on the target such that the scattering into the forward direction is relatively stronger than the scattering into the backward direction8-10,18,19. This is understood by the conservation of momentum and Newton’s third law regarding reaction force between the acoustic field and the inside particle.19,20 Beams having the local properties of acoustic Bessel beams are candidates for single-beam tweezers which have been examined in theoretical8-10,21 and experimental approaches17,22. The ordinary Bessel beam (OBB) possesses the axial maximum and azimuthal symmetry, while the helicoidal Bessel beams (HBBs) have an axial null and azimuthal phase gradient. Hefner and Marston conducted the experimental demonstration for the acoustical vortices by using simple four-panel piezoelectric transducers23. Recently, the transducer arrays17,24, active spiral transducer25,26, diffraction gratings27 and metasurfaces28 have been demonstrated to produce the local Bessel beams which coincide with the theoretical or simulation results. These fabrication technologies facilitate the experimental studies of Bessel beams and the possible applications in the fields of particle manipulations. In addition, the exact series solutions have been solved for the axial ARFs of spherical objects in an on-axis incident Bessel beam for both the ordinary8,9 and helicoidal (vortex)10,17 Bessel beams. The ARF produced by a Bessel vortex beam has also been studied via the optical theorem29-33 which gives the 4

relationship between the extinction and the scattering at the forward direction of the beam’s plane wave components. However, it is still necessary to develop efficient and versatil

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