Trapping Force of Acoustical Bessel Beams on a Sphere and Stable Tractor Beams

We seek stable tractor beams that not only axially pull objects but also transversely trap the object. Transverse force acting on a spherical particle centered on the axis of acoustic Bessel beams is examined using the Gor'kov potential and partial wave expansion. The results suggest flexibility of trapping both relatively dense and stiff particles and relatively light and soft particles at the pressure maximum of the axisymmetric Bessel beam in the Rayleigh regime. This trapping is more flexible than trapping by standing waves and focused beams used in acoustic tweezers. The flexibility is interpreted by the contribution of axial velocity to the force potential and by momentum projection. We then reveal parameters (paraxiality, density ratio, and bulk modulus ratio) for simultaneous trapping and pulling of an elastic object and droplet in and beyond the Rayleigh regime. The results reveal the capability and conditions to simultaneously trap and pull a Rayleigh particle even in the situation when losses are accounted for. Our study guides designs of stable tractor beams and drives development of acoustic tweezers.