[Paper Review] Off-axial acoustic radiation force of pressor and tractor Bessel beams on a sphere

Glauber T. Silva, J. H. Lopes+2 more|arXiv (Cornell University)|Aug 14, 2012

Microfluidic and Bio-sensing Technologies29 references4 citations

TL;DR

This study investigates the off-axial acoustic radiation force of zero- and first-order Bessel beams on a silicone-oil sphere using 3D partial wave expansion methods. It reveals that tractor beam forces weaken with radial displacement from the beam axis, and transverse force fields exhibit both stable and unstable equilibrium regions depending on the size parameter $ka$, crucial for designing acoustical tweezers and tractor beam devices.

ABSTRACT

Acoustic Bessel beams are known to produce an axial radiation force on a sphere centered on the beam axis (on-axial configuration) that exhibits both "pressor" and "tractor" behaviors. The pressor and the tractor forces are oriented along the beam's direction of propagation and opposite to it, respectively. The behavior of the acoustic radiation force generated by Bessel beams when the sphere lies outside the beam's axis (off-axial configuration) is unknown. Using the 3D radiation force formulas given in terms of the partial wave expansion coefficients for the incident and scattered waves, both axial and transverse components of the force exerted on a silicone-oil sphere are obtained for a zero- and a first-order Bessel vortex beam. As the sphere departs from the beam's axis, the tractor force becomes weaker. Moreover, the behavior of the transverse radiation force field may vary with the sphere's size factor $ka$ (where $k$ is the wavenumber and $a$ is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found depending on $ka$ values. These results are particularly important for the design of acoustical tractor beam devices operating with Bessel beams.

Motivation & Objective

• To investigate the axial and transverse radiation forces exerted by zero- and first-order Bessel beams on a sphere when the sphere is displaced from the beam axis.
• To determine how the size parameter $ka$ and beam half-cone angle $\beta$ influence the transition between pressor and tractor beam behavior.
• To identify stable and unstable equilibrium regions in the transverse radiation force field for different $ka$ values.
• To evaluate the decay of the axial tractor force as the sphere moves off the beam axis.
• To support the design of acoustical tweezers and tractor beam devices using Bessel beams for biomedical and particle manipulation applications.

Proposed method

• Utilizes 3D radiation force formulas expressed via beam-shape and scattering coefficients in partial wave expansion.
• Employs the discrete spherical harmonic transform (DSHT) algorithm to compute beam-shape coefficients for Bessel beams.
• Applies acoustic boundary conditions to determine scattering coefficients for the silicone-oil sphere.
• Numerically computes axial and transverse radiation force components for both on- and off-axial configurations.
• Analyzes force fields across varying $ka$ values and beam offsets ($kx_0, ky_0$) to map equilibrium regions.
• Visualizes transverse force fields overlaid on beam intensity to assess trapping stability.

Experimental results

Research questions

• RQ1 How does the axial radiation force of a Bessel beam change when the sphere is displaced from the beam axis?
• RQ2 What is the dependence of the transverse radiation force field on the sphere’s size parameter $ka$?
• RQ3 Under what conditions does the transverse force field exhibit stable or unstable equilibrium regions near the beam axis?
• RQ4 How does the strength and direction of the tractor beam force vary with radial offset from the beam axis?
• RQ5 Can first-order Bessel beams generate stable transverse trapping for a silicone-oil sphere at specific $ka$ values?

Key findings

• The axial tractor force decreases significantly as the sphere is displaced radially from the beam axis, with a drop in strength by one order of magnitude at $kx_0 = 1.6$.
• For $ka = 0.1$, the first-order Bessel beam creates a stable equilibrium region in the beam's central spot, with transverse forces pointing inward toward the axis.
• At $ka = 3$, the transverse force field exhibits outward-pointing forces that rotate clockwise with radial displacement, indicating no stable trapping region.
• The transverse force field for $ka = 0.1$ shows inward-pointing forces in regions between the first minimum and second maximum of beam intensity, suggesting potential trapping.
• For $ka = 2$, the zero-order Bessel beam produces an unstable equilibrium at the beam center, with force lines diverging outward.
• The islands of attractive axial force shift toward higher $ka$ values and shrink in size when the sphere is offset by $kx_0 = 1.6$.