Study On Focused Acoustic Vortex Based On Self-bending Airy Beam

Acoustic vortex(AV)beam is a kind of special sound wave with helical wavefronts.It has annular pressure distribution and a pressure zero with phase singularity at the center.The orbital angular momentum(OAM)carried by the AV can be transferred to objects,showing potential applications in particle manipulation.The pressure and phase of acoustic radiation play key roles in the formation of AV.Based on the phased control and acoustic focusing technologies,an AV of millimeter scale can be formed with higher radial gradient force and axial acoustic radiation force,which can be used to realize accurate and stable object manipulation.However,in practical applications,acoustic reflections and scattering occur during beam propagation when it encounters obstacles,which will reduce the efficiency of acoustic transmission,weaken the energy of acoustic focusing and even destroy the phase spiral of the focused AV beam.As a non-diffraction beam,the Airy beam has attracted intensive attentions in the past decades due to its unique abilities of self-bending and self-healing.It can be used to bypass obstacles by propagates along a designed trajectory and realize a self-bending acoustic focus using multiple Airy beams.In thi study,based on the Airy beam and phase-controlled AV technologies,the method of constructing a self-bending auto-focused AV beam is proposed.A bottle-shaped cavity generated by self-bending Airy beams can be used to produce acoustic focus behind the obstacles.The obstacle-avoidant focused AV can be applied to reduce the interferences of tissues,organs and bones,exhibiting a good application prospect in medical ultrasound.First,the diffraction-free Airy function solution based on the helmholtz equation is studied.The envelope of the finite-energy Airy function with an incident angle is constructed,and the propagation trajectory of the Airy beam is derived.Based on the acoustic radiation of point sources,the phase difference of the incident acoustic beam is converting to the distance variation and a one-dimensional phase modulated ripple structure of Airy function is designed to regulate the initial phases of acoustic sources Then,by rotating the one-dimensional phase modulation structure,a two-dimensional sector or ring-shaped phase modulation structure is designed with the pressure formula deduced through the integral of surface elements.Based on the phase-code technique,a focused AV beam with a bottle-shaped cavity is obtained.The acoustic distributions generated by the linear,sector and ring-shaped ripple structures are numerically studied and the factors that affect the trajectory are also analyzed.Resultsshow that,the bottle-shaped beam propagates closer to the source plane with theincrease of the incident angle of the Airy function.The bending degree of the trajectory increases with the transverse scale,but keeps almost invariant for the angle changing of the sector sources.A wider hollow axis of vortex center with pressure zero of the focused AV beam is achieved for a higher non-zero topological chargeThen,the controllability and obstacle-avoidant ability of the focused AV based on the self-bending Airy function is discussed.By changing the parameters of Airy function to regulate the phase modulation structure,the distance of the focal point and the configuration of the bottle-shaped cavity are achieved to analyze the effects of obstacles.Result proves that there is little influence on the pressure and phase distributions of the focused AV when obstacles are located completely in the bottle-shaped cavity,which provides a theoretical basis for the obstacle-avoidant object manipulation using the focused AV beam.Lastly,an experimental setup is established using an 8-elemnet sector transducer array.Eight direct digital synthesis(DDS)devices are employed to send out sinusoidal signals with a controllable initial phase difference,which are used to drive the sector transducers in sequence after power amplification.Through the phase modulation using the ring-shaped structure,the focused AV beam with a bottle-shaped cavity is generated a hollow center axis of pressure zero.Based on the pressure and phase distributions,the factors that affect the curvature of the self-bending beams and the shapes of the focused AVs are obtained.It is proved that the radius of the vortex center goes wider with the increase of the topological charge.Through comparisons of the focal length,focal region and focal pressure,the controllability of the focused AV is demonstrated.In addition,the influence of rigid spheres with different sizes at different locations in the bottle-shaped cavity is also verified by the experimental measurements of the focused AV.In conclusion,a novel method of generating a self-bending focused AV with a bottle-shaped cavity is proposed by applying the phase modulation of the Airy function on a sector-transducer array.The theoretical and experimental results demonstrate that the self-accelerating acoustic beam can drive particles to propagate along curved parabolic trajectory and accumulate in the focal region with the capability of avoiding bones and important organs,which provide a new technique of obstacle-avoidant object manipulation in biomedical applications.