Sound beam diffraction4/9/2024 It has been strictly proved that, in the paraxial limit the HB beam recovers the Airy solution 29. Besides, different from the paraxial Airy beam, the HB beam is an exact solution of the 2D homogeneous Helmholtz equation, since all plane wave components correspond to the same magnitude of wavevector (as a requirement of the monochromatic field). As shown below, the superposition of numerous plane waves contributes a curved propagation trajectory in the x-y plane. (1) the integral from 0 to π means that the 2D HB beam consists of a series of plane waves with positive y-component of wavevectors, which is crucially different from the conventional Bessel beam, integrating from 0 to 2π. Where ψ 0 is a unitary velocity potential, α is an arbitrary real number and k = ( kcosτ, ksinτ) represents the 2D wavevector in the background fluid. The large-angle transport could be greatly useful in the contactless manipulation of microparticles, such as to deliver biomedicines under complex conditions. The bending angle of the transport trajectory is considerably large (exceeding 90 o), which is unattainable by using conventional sound beams. It is of particular interest that in some situations the particle can be attracted into the strong field region and guided stably along a circularly curved orbit. The phenomena can be explained qualitatively from the competing effect between the gradient force and the scattering force. Distinct manipulation behaviors have been observed for the particles with different sizes and acoustic parameters. In this paper, we present the first theoretical study of the ARF acting on spherical microparticles illuminated by an acoustic 2D HB beam. This is greatly beneficial for manipulating microparticles without hampering by obstacles 37. Therefore, compared to the Airy beam, these nonparaxial accelerating beams can be used to achieve larger bending angles over a longer distance. These novel beams are exact solutions of the 2D Helmholtz equation, which can preserve their shapes well while propagating along circular, elliptic or parabolic trajectories. Recently, a new family of self-accelerating optic beams, i.e., Half-Bessel (HB) 29, 30, 31, 32, Mathieu 33, 34, 35 and Weber 33, 35, 36 beams have been demonstrated theoretically and experimentally. This leads to a serious limitation in practical applications. This condition fails and diffraction occurs when the Airy beam travels along the parabola trajectory and eventually bends into a larger angle. It is worth pointing out that, the Airy beam is only a solution of the 2D Helmholtz equation in the paraxial limit. These properties endow the self-accelerating beams with new degree of freedoms in contactless manipulations, e.g., guiding microparticles along a curved trajectory 27, 28. The beams with lateral shift, called self-accelerating beams, have two peculiar features: diffraction-free while propagating and self-healing even if blocked by obstacles. This cognition was broken up by the observation of Airy beams in optics 25, 26: the main lobes of Airy beams propagate along a parabolic trajectory. A representative example can be referred to the acoustic pulling effects by utilizing Bessel beams 20, 21, 22 or crossed plane waves 23, 24.Ĭonventionally, it is believed that in homogenous space shape-invariant wave beams travel along a straight line only. Recently, the ARFs produced by nondiffracting acoustic beams (which preserve shape in propagation) have attracted much attention due to the capability of stable manipulation in a long distance. Besides the intrinsic properties of the objects, i.e., the geometry and acoustic properties, the ARF depends greatly on the property of the external sound source. Recent studies have also stated that, remarkable interactions can be induced by acoustic waves in multi-body systems 18, 19, through the aid of resonant coupling between artificial structures. This advantage enables the acoustic manipulation with wide applications, e.g., the DNA transfection and targeted drug delivery. In contrast to the other contactless manipulations, the acoustic radiation forces (ARFs) necessitate much less power and thus exhibit weaker damage to objects. Acoustic waves can also exert forces on illuminated objects by exchanging momentum between the objects and sound field 10, 11, 12, 13, 14, 15, 16, 17. Many different techniques have been proposed, such as optical tweezers 1, 2, 3, 4, 5 and dielectrophoresis 6, 7, 8, 9. In the past decades, great efforts have been devoted to manipulate microparticles and even living cells under contactless conditions.
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