Phase shifts from scattering are used to analyze and engineer acoustic radiation forces. With the aid of phase shifts, analytical results for acoustic radiation forces can be simplified into compact and physically meaningful expressions, which can be used to develop a simplified procedure for the engineering of the radiation force. The desired radiation force can be fulfilled by a specific set of phase shifts up to a certain order, and then the required phase shifts can be fulfilled by engineering object and beam parameters. As an example, the phase shift approach is used to engineer the inner-to-outer radius ratio and the outer radius of a spherical shell to show how to use the phase shift method for the design of acoustic radiation forces. The example here is a force that is desired to pull particles against the propagation of a Bessel beam. A small paraxial parameter to pull a spherical shell is satisfied by in-phase scattering of monopole, dipole, quadrupole, octupole, and beyond. The example presented here is relatively simple yet reveals the advantages of the phase shift approach. The phase shift method can provide a simplified route for the design of acoustic tweezers using either traveling beams or standing waves.

1.
P. J.
Westervelt
, “
The theory of steady forces caused by sound waves
,”
J. Acoust. Soc. Am.
23
,
312
315
(
1951
).
2.
P. J.
Westervelt
, “
Acoustical radiation pressure
,”
J. Acoust. Soc. Am.
29
,
26
29
(
1957
).
3.
H.
Olsen
,
H.
Wergeland
, and
P. J.
Westervelt
, “
Acoustic radiation force
,”
J. Acoust. Soc. Am.
30
(
7
),
633
634
(
1958
).
4.
H.
Olsen
,
W.
Romberg
, and
H.
Wergeland
, “
Radiation force on bodies in a sound field
,”
J. Acoust. Soc. Am.
30
(
1
),
69
76
(
1958
).
5.
T.
Hasegawa
, “
Comparison of two solutions for acoustic radiation pressure on a sphere
,”
J. Acoust. Soc. Am.
61
(
6
),
1445
1448
(
1977
).
6.
T.
Hasegawa
and
Y.
Watanabe
, “
Acoustic radiation pressure on an absorbing sphere
,”
J. Acoust. Soc. Am.
63
(
6
),
1733
1737
(
1978
).
7.
X.
Chen
and
R. E.
Apfel
, “
Radiation force on a spherical object in an axisymmetric wave field and its application to the calibration of high-frequency transducers
,”
J. Acoust. Soc. Am.
99
(
2
),
713
724
(
1996
).
8.
P. L.
Marston
, “
Axial radiation force of a Bessel beam on a sphere and direction reversal of the force
,”
J. Acoust. Soc. Am.
120
(
6
),
3518
3524
(
2006
).
9.
P. L.
Marston
, “
Acoustic beam scattering and excitation of sphere resonance: Bessel beam example
,”
J. Acoust. Soc. Am.
122
(
1
),
247
252
(
2007
).
10.
P. L.
Marston
, “
Negative axial radiation forces on solid spheres and shells in a Bessel beam
,”
J. Acoust. Soc. Am.
122
,
3162
3165
(
2007
).
11.
D. B.
Thiessen
,
L. K.
Zhang
, and
P. L.
Marston
, “
Radiation force on spheres in helicoidal bessel beams modeled using finite elements
,”
J. Acoust. Soc. Am.
125
(
1
),
2552
(
2009
).
12.
L. K.
Zhang
and
P. L.
Marston
, “
Geometrical interpretation of negative radiation forces of acoustical Bessel beams on spheres
,”
Phys. Rev. E
84
,
035601
(
2011
).
13.
L. K.
Zhang
and
P. L.
Marston
, “
Axial radiation force exerted by general non-diffracting beams
,”
J. Acoust. Soc. Am.
131
(
4
),
EL329
EL335
(
2012
).
14.
L. K.
Zhang
and
P. L.
Marston
, “
Optical theorem for acoustic non-diffracting beams and application to radiation force and torque
,”
Biomed. Opt. Express
4
(
9
),
1610
1617
(
2013
).
15.
G. T.
Silva
, “
An expression for the radiation force exerted by an acoustic beam with arbitrary wavefront (L)
,”
J. Acoust. Soc. Am.
130
(
6
),
3541
3544
(
2011
).
16.
D.
Baresch
,
J. L.
Thomas
, and
R.
Marchiano
, “
Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere
,”
J. Acoust. Soc. Am.
133
(
1
),
25
36
(
2013
).
17.
O. A.
Sapozhnikov
and
M. R.
Bailey
, “
Radiation force of an arbitrary acoustic beam on an elastic sphere in a fluid
,”
J. Acoust. Soc. Am.
133
(
2
),
661
676
(
2013
).
18.
L. K.
Zhang
and
P. L.
Marston
, “
Acoustic radiation force expressed using complex phase shifts and momentum-transfer cross sections
,”
J. Acoust. Soc. Am.
140
(
2
),
EL178
EL183
(
2016
).
19.
P. L.
Marston
and
L. K.
Zhang
, “
Relationship of scattering phase shifts to special radiation force conditions for spheres in axisymmetric wave-fields
,”
J. Acoust. Soc. Am.
141
(
5
),
3042
3049
(
2017
).
20.
P. L.
Marston
, “
Phase-shift expansions for approximate radiation forces on solid spheres in inviscid-acoustic standing waves
,”
J. Acoust. Soc. Am.
142
(
2
),
3358
3361
(
2017
).
21.
L. K.
Zhang
, “
Reversals of orbital angular momentum transfer and radiation torque
,”
Phys. Rev. Appl.
10
,
034039
(
2018
).
22.
P. L.
Marston
, “
Phase-shift derivation of expansions for material and frequency dependence of progressive-wave radiation forces and backscattering by spheres
,”
J. Acoust. Soc. Am.
145
(
2
),
EL39
EL44
(
2019
).
23.
Z.
Gong
,
P. L.
Marston
, and
W.
Li
, “
T-matrix evaluation of three-dimensional acoustic radiation forces on nonspherical objects in Bessel beams with arbitrary order and location
,”
Phys. Rev. E
99
,
063004
(
2019
).
24.
X. D.
Fan
and
L. K.
Zhang
, “
Trapping force of acoustical Bessel beams on a sphere and stable tractor beams
,”
Phys. Rev. Appl.
11
,
014055
(
2019
).
25.
L.
Meng
,
F.
Cai
,
F.
Li
,
W.
Zhou
,
L.
Niu
, and
H.
Zheng
, “
Acoustic tweezers
,”
J. Phys. D Appl. Phys.
52
(
27
),
273001
(
2019
).
26.
M.
Baudoin
and
J.-L.
Thomas
, “
Acoustic tweezers for particle and fluid micromanipulation
,”
Annu. Rev. Fluid Mech.
52
(
1
),
205
234
(
2020
).
27.
L. K.
Zhang
, “
From acoustic radiation pressure to three-dimensional acoustic radiation forces
,”
J. Acoust. Soc. Am.
144
(
1
),
443
447
(
2018
).
28.
P. L.
Marston
and
L. K.
Zhang
, “
Unphysical consequences of negative absorbed power in linear passive scattering: Implications for radiation force and torque
,”
J. Acoust. Soc. Am.
139
(
5
),
3139
3144
(
2016
).
29.
M.
Rajabi
and
A.
Mojahed
, “
Acoustic manipulation of active spherical carriers: Generation of negative radiation force
,”
Ann. Phys.
372
,
182
200
(
2016
).
30.
H.-Q.
Yu
,
J.
Yao
,
D.-J.
Wu
,
X.-W.
Wu
, and
X.-J.
Liu
, “
Negative acoustic radiation force induced on an elastic sphere by laser irradiation
,”
Phys. Rev. E
98
,
053105
(
2018
).
31.
Y.
Meng
,
X.
Li
,
Z.
Liang
,
J.
Ng
, and
J.
Li
, “
Acoustic pulling with a single incident plane wave
,”
Phys. Rev. Appl.
14
,
014089
(
2020
).
32.
P.
Martin
, “
Quadratic quantities in acoustics: Scattering cross-section and radiation force
,”
Wave Motion
86
,
63
78
(
2019
).
33.
A. A.
Gorlach
,
M. A.
Gorlach
,
A. V.
Lavrinenko
, and
A.
Novitsky
, “
Matter-wave tractor beams
,”
Phys. Rev. Lett.
118
,
180401
(
2017
).
34.
L. P.
Gor'kov
, “
On the forces acting on a small particle in an acoustical field in an ideal fluid
,”
Sov. Phys. Dokl.
6
,
773
775
(
1962
), available at http://mi.mathnet.ru/eng/dan/v140/i1/p88.
35.
T.
Hasegawa
,
Y.
Hino
,
A.
Annou
,
H.
Noda
,
M.
Kato
, and
N.
Inoue
, “
Acoustic radiation pressure acting on spherical and cylindrical shells
,”
J. Acoust. Soc. Am.
93
(
1
),
154
161
(
1993
).
36.
P. L.
Marston
, “
Scattering and radiation force dependence on properties of empty elastic spherical shells: Low-frequency phase-shift derivation
,”
J. Acoust. Soc. Am.
146
(
2
),
EL145
EL150
(
2019
).
37.
P. V.
Zinin
,
J. S.
Allen
, and
V. M.
Levin
, “
Mechanical resonances of bacteria cells
,”
Phys. Rev. E
72
,
061907
(
2005
).
38.
Y.-Y.
Wang
,
J.
Yao
,
X.-W.
Wu
,
D.-J.
Wu
, and
X.-J.
Liu
, “
Influences of the geometry and acoustic parameter on acoustic radiation forces on three-layered nucleate cells
,”
J. Appl. Phys.
122
(
9
),
094902
(
2017
).
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