Mitri F G
Department of Physiology and Biomedical Engineering, Ultrasound Research Laboratory, Mayo Clinic, College of Medicine, Rochester MN 55905, United States.
Ultrasonics. 2009 Dec;49(8):794-8. doi: 10.1016/j.ultras.2009.07.006. Epub 2009 Jul 23.
Particle manipulation using the acoustic radiation force of Bessel beams is an active field of research. In a previous investigation, [F.G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers, Annals of Physics 323 (2008) 1604-1620] an expression for the radiation force of a zero-order Bessel beam standing wave experienced by a sphere was derived. The present work extends the analysis of the radiation force to the case of a high-order Bessel beam (HOBB) of positive order m having an angular dependence on the phase phi.
The derivation for the general expression of the force is based on the formulation for the total acoustic scattering field of a HOBB by a sphere [F.G. Mitri, Acoustic scattering of a high-order Bessel beam by an elastic sphere, Annals of Physics 323 (2008) 2840-2850; F.G. Mitri, Equivalence of expressions for the acoustic scattering of a progressive high order Bessel beam by an elastic sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 56 (2009) 1100-1103] to derive the general expression for the radiation force function YJm,st(ka,beta,m)<0), which is the radiation force per unit characteristic energy density and unit cross-sectional surface. The radiation force function is expressed as a generalized partial wave series involving the half-cone angle beta of the wave-number components and the order m of the HOBB.
Numerical results for the radiation force function of a first and a second-order Bessel beam standing wave incident upon a rigid sphere immersed in non-viscous water are computed. The rigid sphere calculations for YJm,st(ka,beta,m)<0), show that the force is generally directed to a pressure node when m is a positive even integer number (i.e. YJm,st(ka,beta,m)<0), whereas the force is generally directed toward a pressure antinode when m is a positive odd integer number (i.e. YJm,st(ka,beta,m)<0).
An expression is derived for the radiation force on a rigid sphere placed along the axis of an ideal non-diffracting HOBB of acoustic standing (or stationary) waves propagating in an ideal fluid. The formulation includes results of a previous work done for a zero-order Bessel beam standing wave (m=0). The proposed theory is of particular interest essentially due to its inherent value as a canonical problem in particle manipulation using the acoustic radiation force of a HOBB standing wave on a sphere. It may also serve as the benchmark for comparison to other solutions obtained by strictly numerical or asymptotic approaches.
利用贝塞尔光束的声辐射力进行粒子操控是一个活跃的研究领域。在之前的一项研究中，[F.G. 米特里，《驻波和准驻波零阶贝塞尔光束镊子中球体上的声辐射力》，《物理学年鉴》323 (2008) 1604 - 1620] 推导出了球体所受零阶贝塞尔光束驻波辐射力的表达式。本工作将辐射力的分析扩展到正阶数(m)且相位(\phi)具有角度依赖性的高阶贝塞尔光束（HOBB）的情况。
力的一般表达式的推导基于球体对高阶贝塞尔光束的总声散射场的公式 [F.G. 米特里，《弹性球体对高阶贝塞尔光束的声散射》，《物理学年鉴》323 (2008) 2840 - 2850；F.G. 米特里，《弹性球体对正向高阶贝塞尔光束声散射表达式的等价性》，《IEEE 超声、铁电与频率控制汇刊》56 (2009) 1100 - 1103]，以推导出辐射力函数(YJm,st(ka,\beta,m)<0)的一般表达式，该函数是单位特征能量密度和单位横截面积的辐射力。辐射力函数表示为一个广义的分波级数，涉及波数分量的半锥角(\beta)和高阶贝塞尔光束的阶数(m)。
计算了入射到浸没在非粘性水中的刚性球体上的一阶和二阶贝塞尔光束驻波的辐射力函数的数值结果。刚性球体的(YJm,st(ka,\beta,m)<0)计算表明，当(m)为正偶数时，力通常指向压力节点（即(YJm,st(ka,\beta,m)<0)），而当(m)为正奇数时，力通常指向压力波腹（即(YJm,st(ka,\beta,m)<0)）。
推导出了沿在理想流体中传播的理想非衍射声驻波（或驻定波）高阶贝塞尔光束轴放置的刚性球体上的辐射力表达式。该公式包括了之前对零阶贝塞尔光束驻波（(m = 0)）所做工作的结果。所提出的理论特别有趣，主要是因为它作为使用高阶贝塞尔光束驻波对球体的声辐射力进行粒子操控中的一个典型问题具有内在价值。它也可以作为与通过严格数值或渐近方法获得的其他解进行比较的基准。
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