Abstract

A full-wave numerical method based on the surface integral equation for computing radiation pressure force (RPF) exerted by a shaped light beam on arbitrary shaped homogenous particles is presented. The multilevel fast multipole algorithm is employed to reduce memory requirement and to improve its capability. The resultant matrix equation is solved by using an iterative solver to obtain equivalent electric and magnetic currents. Then RPF is computed by vector flux of the Maxwell’s stress tensor over a spherical surface tightly enclosing the particle. So the analytical expressions for electromagnetic fields of incident beam in near region are used. Some numerical results are performed to illustrate the validity and capability of the developed method. Good agreements between our method and the Lorenz–Mie theory for spherical and small spheroidal particle are found while our method has powerful capability for computing RPF of any shaped beam on a relatively large particle of complex shape. Tests for ellipsoidal and red blood cell-like particles illuminated by Gaussian beam have shown that the size of the particle can be as large as 50–100 wavelengths, respectively, for the relative refractive of 1.33 and 1.1.

© 2013 Optical Society of America

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2012 (1)

B. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, Europhys. Lett. 100, 48005 (2012).
[CrossRef]

2011 (2)

2007 (2)

F. Borghese, P. Denti, R. Saija, and M. A. Iat, Opt. Express 15, 11984 (2007).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, Phys. Rev. E 75, 026613 (2007).
[CrossRef]

2005 (2)

J. Q. Lu, P. Yang, and X.-H. Hu, J. Biomed. Opt. 10, 024022 (2005).
[CrossRef]

R. S. Brock, X.-H. Hu, P. Yang, and J. Q. Lu, Opt. Express 13, 5279 (2005).
[CrossRef]

2004 (1)

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[CrossRef]

2001 (1)

M. I. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 70, 811 (2001).
[CrossRef]

1998 (2)

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, IEEE Trans. Antennas Propag. 46, 1718 (1998).
[CrossRef]

K. F. Ren, G. Gouesbet, and G. Grehan, Appl. Opt. 37, 4218 (1998).
[CrossRef]

1996 (1)

1994 (3)

K. F. Ren, G. Grehan, and G. Gouesbet, Opt. Commun. 108, 343 (1994).
[CrossRef]

B. T. Draine and P. J. Flatau, J. Opt. Soc. Am. A 11, 1491 (1994).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, J. Opt. 25, 165 (1994).
[CrossRef]

1993 (1)

R. Coifman, V. Rokhlin, and S. Wandzura, IEEE Antennas Propag. Mag. 35(3), 7 (1993).
[CrossRef]

1989 (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

1988 (1)

1986 (1)

1982 (1)

S. M. Rao, D. R. Wilton, and A. W. Glisson, IEEE Trans. Antennas Propag. 30, 409 (1982).
[CrossRef]

1976 (1)

G. Roosen and C. Imbert, Phys. Lett. 59A, 6 (1976).

Alexander, D. R.

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

Ashkin, A.

Barton, J. P.

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[CrossRef]

Borghese, F.

Brock, R. S.

Cai, X.

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, Phys. Rev. E 75, 026613 (2007).
[CrossRef]

Chang, S.

Chew, W. C.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, IEEE Trans. Antennas Propag. 46, 1718 (1998).
[CrossRef]

Chu, S.

Coifman, R.

R. Coifman, V. Rokhlin, and S. Wandzura, IEEE Antennas Propag. Mag. 35(3), 7 (1993).
[CrossRef]

Denti, P.

Draine, B. T.

Dziedzic, J. M.

Flatau, P. J.

Girasole, T.

Glisson, A. W.

S. M. Rao, D. R. Wilton, and A. W. Glisson, IEEE Trans. Antennas Propag. 30, 409 (1982).
[CrossRef]

Gouesbet, G.

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, Phys. Rev. E 75, 026613 (2007).
[CrossRef]

K. F. Ren, G. Gouesbet, and G. Grehan, Appl. Opt. 37, 4218 (1998).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, Appl. Opt. 35, 2702 (1996).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, Opt. Commun. 108, 343 (1994).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, J. Opt. 25, 165 (1994).
[CrossRef]

Grehan, G.

K. F. Ren, G. Gouesbet, and G. Grehan, Appl. Opt. 37, 4218 (1998).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, Appl. Opt. 35, 2702 (1996).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, Opt. Commun. 108, 343 (1994).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, J. Opt. 25, 165 (1994).
[CrossRef]

Gréhan, G.

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, Phys. Rev. E 75, 026613 (2007).
[CrossRef]

Hanna, S.

S. H. Simpson and S. Hanna, Phys. Rev. A 84, 053808 (2011).
[CrossRef]

Hu, X.-H.

J. Q. Lu, P. Yang, and X.-H. Hu, J. Biomed. Opt. 10, 024022 (2005).
[CrossRef]

R. S. Brock, X.-H. Hu, P. Yang, and J. Q. Lu, Opt. Express 13, 5279 (2005).
[CrossRef]

Iat, M. A.

Imbert, C.

G. Roosen and C. Imbert, Phys. Lett. 59A, 6 (1976).

Jin, J. M.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, IEEE Trans. Antennas Propag. 46, 1718 (1998).
[CrossRef]

Lee, S. S.

Loudet, J. C.

B. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, Europhys. Lett. 100, 48005 (2012).
[CrossRef]

Lu, C. C.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, IEEE Trans. Antennas Propag. 46, 1718 (1998).
[CrossRef]

Lu, J. Q.

R. S. Brock, X.-H. Hu, P. Yang, and J. Q. Lu, Opt. Express 13, 5279 (2005).
[CrossRef]

J. Q. Lu, P. Yang, and X.-H. Hu, J. Biomed. Opt. 10, 024022 (2005).
[CrossRef]

Mihiretie, B.

B. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, Europhys. Lett. 100, 48005 (2012).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 70, 811 (2001).
[CrossRef]

Neuman, K. C.

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[CrossRef]

Onofri, F.

Pouligny, B.

B. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, Europhys. Lett. 100, 48005 (2012).
[CrossRef]

Rao, S. M.

S. M. Rao, D. R. Wilton, and A. W. Glisson, IEEE Trans. Antennas Propag. 30, 409 (1982).
[CrossRef]

Ren, K. F.

K. F. Ren, F. Onofri, C. Rozé, and T. Girasole, Opt. Lett. 36, 370 (2011).
[CrossRef]

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, Phys. Rev. E 75, 026613 (2007).
[CrossRef]

K. F. Ren, G. Gouesbet, and G. Grehan, Appl. Opt. 37, 4218 (1998).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, Appl. Opt. 35, 2702 (1996).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, Opt. Commun. 108, 343 (1994).
[CrossRef]

K. F. Ren, G. Grehan, and G. Gouesbet, J. Opt. 25, 165 (1994).
[CrossRef]

Rokhlin, V.

R. Coifman, V. Rokhlin, and S. Wandzura, IEEE Antennas Propag. Mag. 35(3), 7 (1993).
[CrossRef]

Roosen, G.

G. Roosen and C. Imbert, Phys. Lett. 59A, 6 (1976).

Rozé, C.

Saija, R.

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

Sheng, X. Q.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, IEEE Trans. Antennas Propag. 46, 1718 (1998).
[CrossRef]

Simpson, S. H.

S. H. Simpson and S. Hanna, Phys. Rev. A 84, 053808 (2011).
[CrossRef]

Snabre, P.

B. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, Europhys. Lett. 100, 48005 (2012).
[CrossRef]

Song, J. M.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, IEEE Trans. Antennas Propag. 46, 1718 (1998).
[CrossRef]

Wandzura, S.

R. Coifman, V. Rokhlin, and S. Wandzura, IEEE Antennas Propag. Mag. 35(3), 7 (1993).
[CrossRef]

Wilton, D. R.

S. M. Rao, D. R. Wilton, and A. W. Glisson, IEEE Trans. Antennas Propag. 30, 409 (1982).
[CrossRef]

Xu, F.

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, Phys. Rev. E 75, 026613 (2007).
[CrossRef]

Yang, P.

J. Q. Lu, P. Yang, and X.-H. Hu, J. Biomed. Opt. 10, 024022 (2005).
[CrossRef]

R. S. Brock, X.-H. Hu, P. Yang, and J. Q. Lu, Opt. Express 13, 5279 (2005).
[CrossRef]

Appl. Opt. (2)

Europhys. Lett. (1)

B. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, Europhys. Lett. 100, 48005 (2012).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

R. Coifman, V. Rokhlin, and S. Wandzura, IEEE Antennas Propag. Mag. 35(3), 7 (1993).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, IEEE Trans. Antennas Propag. 46, 1718 (1998).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, IEEE Trans. Antennas Propag. 30, 409 (1982).
[CrossRef]

J. Appl. Phys. (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 66, 4594 (1989).
[CrossRef]

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

J. Biomed. Opt. (1)

J. Q. Lu, P. Yang, and X.-H. Hu, J. Biomed. Opt. 10, 024022 (2005).
[CrossRef]

J. Opt. (1)

K. F. Ren, G. Grehan, and G. Gouesbet, J. Opt. 25, 165 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

M. I. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 70, 811 (2001).
[CrossRef]

Opt. Commun. (1)

K. F. Ren, G. Grehan, and G. Gouesbet, Opt. Commun. 108, 343 (1994).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Lett. (1)

G. Roosen and C. Imbert, Phys. Lett. 59A, 6 (1976).

Phys. Rev. A (1)

S. H. Simpson and S. Hanna, Phys. Rev. A 84, 053808 (2011).
[CrossRef]

Phys. Rev. E (1)

F. Xu, K. F. Ren, G. Gouesbet, X. Cai, and G. Gréhan, Phys. Rev. E 75, 026613 (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Definition of the beam and particle coordinate systems as well as the parameters used in MLFMA.

Fig. 2.
Fig. 2.

Comparison of the longitudinal RPCS of a Gaussian beam (λ=0.5145μm and w0=2λ) on a prolate slightly volatile silicone oil particle (m=1.5) computed by our approach and by GLMT [7]. The transversal radius of the particle is b=1μm while the radius a along z axis varies.

Fig. 3.
Fig. 3.

RPF on a spheroidal particle (a=b=3μm, c=12μm) of polystyrene (m=1.59) in water (m=1.33) illuminated by a Gaussian beam (λ=0.5145μm, w0=1.3μm). The incident beam rotates around the bottom extremity of the particle.

Fig. 4.
Fig. 4.

RPF on a biconcave cell-like particle (m=1.4) in water (m=1.33) versus beam center position along y axis for two wavelengths. The waist radius of the Gaussian beam is w0=2μm. The diameter of the cell-like particle is d=8.419μm (xy plane), the maximum and the minimum thickness are hM=1.765μm and hm=0.718μm.

Equations (12)

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

EFIE-O:E1Z1L1(J)+K1(M)=Ei,
MFIE-O:H1Z11L1(M)K1(J)=Hi,
EFIE-I:E2Z2L2(J)+K2(M)=0,
MFIE-I:H2Z21L2(M)K2(J)=0,
Ll(X)=jkl[X+1kl2(·X)]Gldτ,
Kl(X)=X×Gldτ
Gl(r,r)=exp(jkl|rr|)4π|rr|.
Z11t^·(EFIE-O)+Z21t^·(EFIE-I)Z1t^·(MFIE-O)+Z2t^·(MFIE-I).
Es=Z1L1(J)K1(M),
Hs=1/Z1Ll(M)K1(J).
F=ΣT(r)·n^dS,
T(r)=12[ϵ1E(r)E*(r)+μ1H(r)H*(r)12(ϵ1|E(r)|2+μ1|H(r)|2)I].

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