Abstract

The surface integral equation (SIE) method is used for the computational study of radiation torque on arbitrarily shaped homogeneous particles. The Multilevel Fast Multipole Algorithm (MLFMA) is employed to reduce memory requirements and improve the capability of SIE. The resultant matrix equations are solved iteratively to obtain equivalent electric and magnetic currents. Then, radiation torque is computed using the vector flux of the pseudotensor over a spherical surface tightly enclosing the particle. We use, therefore, the analytical electromagnetic field expression for incident waves in the near region, instead of the far-field approximation. This avoids the error which may be caused when describing the incident beam. The numerical results of three kinds of non-spherical particles are presented to illustrate the validity and capability of the developed method. It is shown that our method can be applied to predict, in the rigorous sense, the torque from a beam of any shape on a particle of complex configuration with a size parameter as large as 650. The radiation torques on large ellipsoids are exemplified to show the performance of the method and to study the influence that different aspect ratios have on the results. Then, the code is used for the calculation of radiation torque on objects of complex shape including a biconcave cell-like particle and a motor with a non-smooth surface.

© 2015 Optical Society of America

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References

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2015 (2)

Martin Łiler, Luká Chvátal, Petr Jákl, Stephen Simpson, Pavel Zemánek, Oto Brzobohatý, and Alejandro V. Arzola., “Complex rotational dynamics of multiple spheroidal particles in a circularly polarized, dual beam trap,” Opt. Express 23, 7273–7287 (2015).
[Crossref] [PubMed]

Y. Q. Wu, M. L. Yang, X. Q. Sheng, and K. F. Ren., “Computation of scattering matrix elements of large and complex shaped absorbing particles with multilevel fast multipole algorithm,” J. Quant. Spectrosc. Radiat. Transfer 156, 88–96 (2015).
[Crossref]

2014 (3)

M. L. Yang, K. F. Ren, Y. Q. Wu, and X. Q. Sheng., “Computation of stress on the surface of a soft homogeneous arbitrarily shaped particle,” Phys. Rev. E 89(4), 043310 (2014).
[Crossref]

J. C. Loudet, B. M. Mihiretie, and B. Pouligny., “Optically driven oscillations of ellipsoidal particles. part ii: Ray-optics calculations,” Eur. Phys. J. E 37125–139 (2014).
[Crossref]

B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny., “Optically driven oscillations of ellipsoid particles. part i: Experimental observations,” Eur. Phys. J. E 37, 124–140 (2014).
[Crossref]

2013 (2)

B. Mihiretie, J. C. Loudet, and B. Pouligny., “Optical levitation and long-working-distance trapping: From spherical up to high aspect ratio ellipsoidal particles,” J. Quant. Spectrosc. Radiat. Transf. 126, 61–68 (2013).
[Crossref]

M. L. Yang, K. F. Ren, M. J. Gou, and X. Q. Sheng., “Computation of radiation pressure force on arbitrary shaped homogenous particles by multilevel fast multipole algorithm,” Opt. Lett. 38(11), 1784–1786 (2013).
[Crossref] [PubMed]

2012 (2)

C. B. Chang, W. X. Huang, K. H. Lee, and H. J. Sung., “Optical levitation of a non-spherical particle in a loosely focused gaussian beam,” Opt. Express 20(21), 24068–24084 (2012).
[Crossref] [PubMed]

B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny., “Radiation pressure makes ellipsoidal particles tumble,” Europhys. Lett. 100(4), 48005 (2012).
[Crossref]

2011 (3)

2010 (2)

2009 (2)

Ö. Ergül and L. Gürel., “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propagat. 57(1), 176–187 (2009).
[Crossref]

S. H. Simpson and S. Hanna., “Rotation of absorbing spheres in LaguerrecGaussian beams,” J. Opt. Soc. Am. A 26(1), 173–183 (2009).
[Crossref]

2008 (1)

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea., “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A 78(1), 013843 (2008).
[Crossref]

2007 (5)

D. Bonessi, K. Bonin, and T. Walker., “Optical forces on particles of arbitrary shape and size,” J. Opt. A: Pure Appl. Opt. 9(8), S228 (2007).
[Crossref]

P. C. Chaumet and C. Billaudeau., “Coupled dipole method to compute optical torque: Application to a micro-propeller,” J. Appl. Phys. 101(2), 023106 (2007).
[Crossref]

S. H. Simpson and S. Hanna., “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24(2), 430–443 (2007).
[Crossref]

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan., “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75(2), 026613 (2007).
[Crossref]

A. van der Horst, An. I. Campbell, L. K. van Vugt, D. A. Vanmaekelbergh, M. Dogterom, and A. van Blaaderen., “Manipulating metal-oxide nanowires using counter-propagating optical line tweezers,” Opt. Express 15(18), 11629–11639 (2007).
[Crossref] [PubMed]

2006 (3)

2005 (3)

2004 (1)

2003 (4)

W. L. Collett, C. A. Ventrice, and S. M. Mahajan., “Electromagnetic wave technique to determine radiation torque on micromachines driven by light,” Appl. Phys. Lett. 82(16), 2730–2732 (2003).
[Crossref]

Z. D. Cheng, T. G. Mason, and P. M. Chaikin., “Periodic oscillation of a colloidal disk near a wall in an optical trap,” Phys. Rev. E 68(5), 051404 (2003).
[Crossref]

J. C. Weingartner and B. T. Draine., “Radiative torques on interstellar grains III. dynamics with thermal relaxation,” Astrophys. J. 589(1), 289 (2003).
[Crossref]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg., “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79, 1005–1017 (2003).
[Crossref]

2001 (5)

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop., “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142(1), 468–471 (2001).
[Crossref]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg., “Calculation and optical measurement of laser trapping forces on non-spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 70(4), 627–637 (2001).
[Crossref]

A. G. Hoekstra, M. Frijlink, L. B. F. M. Waters, and P. M. A. Sloot., “Radiation forces in the discrete-dipole approximation,” J. Opt. Soc. Am. A 18(8), 1944–1953 (2001).
[Crossref]

M. E. J. Friese and H. Rubinsztein-Dunlop., “Optically driven micromachine elements,” Appl. Phys. Lett. 78(4), 547–549 (2001).
[Crossref]

M. I. Mishchenko., “Radiation force caused by scattering, absorption, and emission of light by nonspherical particles,” J. Quant. Spectrosc. Radiat. Transf. 70(4–6), 811–816 (2001).
[Crossref]

1998 (5)

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu., “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propagat. 46(11), 1718–1726 (1998).
[Crossref]

H. Kimura and I. Mann., “Radiation pressure cross section for fluffy aggregates,” J. Quant. Spectrosc. Radiat. Transfer 60(3), 425–438 (1998).
[Crossref]

H. Polaert, G. Gréhan, and G. Gouesbet., “Improved standard beams with application to reverse radiation pressure,” Appl. Opt. 37(12), 2435–2440 (1998).
[Crossref]

H. Polaert, G. Gréhan, and G. Gouesbet., “Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam,” Opt. Commun. 155(1–3), 169–179 (1998).
[Crossref]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop., “Optical alignment and spinning of laser-trapped microscopic particles,” Natrue 394(6691), 348–350 (1998).
[Crossref]

1997 (1)

B. T. Draine and J. C. Weingartner., “Radiative torques on interstellar grains II. grain alignment,” Astrophys. J. 480(2), 633 (1997).
[Crossref]

1996 (4)

1995 (1)

J. M. Song and W. C. Chew., “Multilevel fast multipole algorithm for solving combined field integral equations of electromagnetic scattering,” Micro. Opt. Tech. Let. 10(1), 14–19 (1995).
[Crossref]

1994 (2)

K. F. Ren, G. Grehan, and G. Gouesbet., “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun 108(4–6), 343–354 (1994).
[Crossref]

K. Svoboda and S. M. Block., “Biological applications of optical forces,” Annu. Rev. Bioph. Biom. 23(1), 247–285 (1994).
[Crossref]

1992 (1)

A. Ashkin., “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[Crossref] [PubMed]

1989 (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub., “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66(10), 4594–4602 (1989).
[Crossref]

J. P. Barton and D.R. Alexander., “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66(7), 2800–2802 (1989).
[Crossref]

1988 (1)

1987 (1)

A. Ashkin and J. M. Dziedzic., “Optical trapping and manipulation of viruses and bacteria,” Science 235(4795), 1517–1520 (1987).
[Crossref] [PubMed]

1986 (1)

1985 (1)

1982 (1)

S. M. Rao, D. R. Wilton, and A. W. Glisson., “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propagat. 30(3), 409–418 (1982).
[Crossref]

1979 (2)

L. W. Davis., “Theory of electromagnetic beams,” Phys. Rev. A 19(3), 1177 (1979).
[Crossref]

J. R. Mautz and R. F. Harrington., “Electromagnetic scattering from a homogeneous material body of revolution,” Arch. Elektr. Uebertrag. 33, 71–80 (1979).

1970 (1)

A. Ashkin., “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156 (1970).
[Crossref]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub., “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66(10), 4594–4602 (1989).
[Crossref]

Alexander., D.R.

J. P. Barton and D.R. Alexander., “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66(7), 2800–2802 (1989).
[Crossref]

Arzola., Alejandro V.

Asakura., T.

Y. Harada and T. Asakura., “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5–6), 529–541 (1996).
[Crossref]

Ashkin, A.

Ashkin., A.

A. Ashkin., “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[Crossref] [PubMed]

A. Ashkin., “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156 (1970).
[Crossref]

Barton, J. P.

J. P. Barton and D.R. Alexander., “Fifth-order corrected electromagnetic field components for fundamental Gaussian beam,” J. Appl. Phys. 66(7), 2800–2802 (1989).
[Crossref]

J. P. Barton, D. R. Alexander, and S. A. Schaub., “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66(10), 4594–4602 (1989).
[Crossref]

Billaudeau., C.

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B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny., “Optically driven oscillations of ellipsoid particles. part i: Experimental observations,” Eur. Phys. J. E 37, 124–140 (2014).
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M. L. Yang, K. F. Ren, M. J. Gou, and X. Q. Sheng., “Computation of radiation pressure force on arbitrary shaped homogenous particles by multilevel fast multipole algorithm,” Opt. Lett. 38(11), 1784–1786 (2013).
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Y. Q. Wu, M. L. Yang, X. Q. Sheng, and K. F. Ren., “Computation of scattering matrix elements of large and complex shaped absorbing particles with multilevel fast multipole algorithm,” J. Quant. Spectrosc. Radiat. Transfer 156, 88–96 (2015).
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T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg., “Multipole expansion of strongly focussed laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79, 1005–1017 (2003).
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M. E. J. Friese and H. Rubinsztein-Dunlop., “Optically driven micromachine elements,” Appl. Phys. Lett. 78(4), 547–549 (2001).
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M. L. Yang, K. F. Ren, Y. Q. Wu, and X. Q. Sheng., “Computation of stress on the surface of a soft homogeneous arbitrarily shaped particle,” Phys. Rev. E 89(4), 043310 (2014).
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M. L. Yang, K. F. Ren, M. J. Gou, and X. Q. Sheng., “Computation of radiation pressure force on arbitrary shaped homogenous particles by multilevel fast multipole algorithm,” Opt. Lett. 38(11), 1784–1786 (2013).
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B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny., “Optically driven oscillations of ellipsoid particles. part i: Experimental observations,” Eur. Phys. J. E 37, 124–140 (2014).
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B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny., “Radiation pressure makes ellipsoidal particles tumble,” Europhys. Lett. 100(4), 48005 (2012).
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X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu., “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propagat. 46(11), 1718–1726 (1998).
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W. L. Collett, C. A. Ventrice, and S. M. Mahajan., “Electromagnetic wave technique to determine radiation torque on micromachines driven by light,” Appl. Phys. Lett. 82(16), 2730–2732 (2003).
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S. M. Rao, D. R. Wilton, and A. W. Glisson., “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propagat. 30(3), 409–418 (1982).
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Y. Q. Wu, M. L. Yang, X. Q. Sheng, and K. F. Ren., “Computation of scattering matrix elements of large and complex shaped absorbing particles with multilevel fast multipole algorithm,” J. Quant. Spectrosc. Radiat. Transfer 156, 88–96 (2015).
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Figures (12)

Fig. 1
Fig. 1

Schematic of arbitrarily shaped homogeneous particle illuminated by a shaped beam and the definition of the Euler angles.

Fig. 2
Fig. 2

Geometry of a triaxial ellipsoid.

Fig. 3
Fig. 3

Comparison of the radiation torque on two prolate particles (m = 1.573 + 6.0 × 10−4i) of aspect ratios κ2 = 1.01 and κ2 = 1.10 computed using our approach. The wavelength and the beam waist radius of the Gaussian beam are λ = 0.785 μm and w0 = 1.0 μm respectively. The centre of the particle coincides with the beam centre. The spheroids have the same volume as a sphere of radius r = 1.0 μm (Fig. 3 in [18]).

Fig. 4
Fig. 4

Radiation torque as a function of incident angle β on prolate spheroids (κ1 = 1.0) with different aspect ratios κ2. The polystyrene particle (m = 1.59) is submerged in water (m = 1.33) and illuminated by a Gaussian beam (λ = 0.5145 μm, w0 = 1.3 μm). All the prolate spheroids have the same volume as a sphere with a radius of 4.7622 μm.

Fig. 5
Fig. 5

Radiation torque as a function of incident angle β on oblate spheroids (κ1 = 1.0) with different aspect ratios κ2. The polystyrene particle (m = 1.59) is submerged in water (m = 1.33) and illuminated by a Gaussian beam (λ = 0.5145 μm, w0 = 1.3 μm). All the oblate spheroids have the same volume as a sphere with a radius of 4.7622 μm.

Fig. 6
Fig. 6

Sketch of the incident beam rotation direction.

Fig. 7
Fig. 7

Radiation torque on a spheroidal polystyrene particle (κ1 = 1.0, κ2 = 4.0, m = 1.59) in water (m = 1.33) illuminated by a Gaussian beam (λ = 0.5145 μm, w0 = 1.3 μm). The incident Gaussian beam rotates in two different manners. The particle has the same volume as a sphere with a radius of 4.7622 μm.

Fig. 8
Fig. 8

Radiation torque on a spheroidal bubble (κ1 = 1.0, κ2 = 4.0, m = 1.0) in water (m = 1.33) illuminated by a Gaussian beam (λ = 0.5145 μm, w0 = 1.3 μm). All the other parameters are the same as those in Fig. 7.

Fig. 9
Fig. 9

Radiation torque as a function of the incident angle, β, on an ellipsoid with aspect ratios κ1 = 3.0 and κ2 = 4.5. The particle is made of polystyrene(m = 1.59) and is submerged in water (m = 1.33) whilst being illuminated by a focused Gaussian beam (λ = 0.5145 μm, w0 = 1.3 μm). The Euler angles, α and γ, of the incident wave are set to 45° and 0° respectively.

Fig. 10
Fig. 10

Comparison of the radiation torque on the biconcave, cell-like particle in water. The waist radius of the Gaussian beam is w0 = 2 μm. The diameter of the particle is d = 8.419 μm (xy plane), with the maximum and the minimum thickness being hM = 1.765 μm and hm = 0.718 μm.

Fig. 11
Fig. 11

Geometry of the regular motor.

Fig. 12
Fig. 12

Torque versus a varying offset in y evaluated for a motor (m = 1.58) in water (m = 1.33). The incident beam is set to λ = 1.07 μm, w0 = 3.6 μm and kept at a constant distance z = 10 μm from centre of the motor in its direction of propagation. The motor is 2 μm in height (x – axis), with diameter 10 μm (yz – plane).

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

EFIE-O : E 1 Z 1 L 1 ( J ) + K 1 ( M ) = E i
MFIE-O : H 1 Z 1 1 L 1 ( M ) K 1 ( J ) = H i
EFIE-I : E 2 Z 2 L 2 ( J ) + K 2 ( M ) = 0
MFIE-I : H 2 Z 2 1 L 2 ( M ) K 2 ( J ) = 0
L l { X } ( r ) = j k l S [ X ( r ) + 1 k l 2 ( X ( r ) ) ] G l ( r , r ) d r
K l { X } ( r ) = S X ( r ) × G l ( r , r ) d r
G ( r , r ) = exp ( j k l | r r | ) 4 π | r r |
{ Z 1 1 t ^ ( EFIE-O ) + Z 2 1 t ^ ( EFIE-I ) Z 1 t ^ ( MFIE-O ) + Z 2 t ^ ( MFIE-I )
J = i = 1 N s g i J i M = i = 1 N s g i M i
g i , L l ( g j ) = k l 2 ( 4 π ) 2 V 1 l T l ( k ^ r ^ m m ) V l d 2 k ^
g i , L l ( g j ) = k l 2 ( 4 π ) 2 V 2 l T l ( k ^ r ^ m m ) V l d 2 k ^
V 1 l = S e j k l r im ( I k ^ k ^ ) g i d S V 2 l = S e j k l r im ( k ^ × g i ) d S V l = S e j k l r j m g j d S T l = n l = 0 L ( j ) n l ( 2 n l + 1 ) h n l ( 2 ) ( k l r m m ) P n l ( k ^ r ^ m m )
M = S v ( T ( r ) × r ) n ^ d s
T ( r ) = 1 2 Re [ ε 1 E ( r ) E * ( r ) + μ 1 H ( r ) H * ( r ) 1 2 ( ε 1 | E ( r ) | 2 + μ 1 | H ( r ) | 2 ) I ]
E ( r ) = E s ( r ) + E i ( r )
H ( r ) = H s ( r ) + H i ( r )
E s = Z 1 L 1 ( J ) K 1 ( M )
H s = 1 / Z 1 L 1 ( M ) K 1 ( J )
M = 1 2 0 2 π 0 π Re [ ( ε 1 E r E θ * + μ 1 H r H θ * ) e ϕ ( ε 1 E r E ϕ * + μ 1 H r H ϕ * ) e θ ] r s 3 sin θ d θ d ϕ
N L = k 1 r s + 3 ln ( k 1 r s + π )
P = 1 2 π w 0 2 I 0 ( 1 + s 2 + 1.5 s 4 )
r ( θ A ) = a sin q θ A + b

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