Abstract

The radiation force of circular Airy beams (CAB) on a dielectric Rayleigh particle is investigated in this paper. Our results show that the CAB can be used to trap the particle whose refractive index is larger than the ambient at different positions along the beam axis. Comparing with the Gaussian beam under the same conditions, the longitudinal and the transverse gradient force of CAB on the Rayleigh particle are increased, and the particle can be trapped more stable. Our analyses also demonstrate that the trapping properties of CAB can be modulated by controlling corresponding parameters of CAB.

© 2013 Optical Society of America

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2013 (1)

2012 (3)

2011 (6)

2010 (1)

2009 (1)

2008 (2)

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, (2008).

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

2007 (1)

2005 (1)

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature436(7049), 370–372 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (2)

Q. W. Zhan, “Radiation forces on a dielectric sphere produced by highly focused cylindrical vector beams,” J. Opt. A, Pure Appl. Opt.5(3), 229–232 (2003).
[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003).
[CrossRef] [PubMed]

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature419(6903), 145–147 (2002).
[CrossRef] [PubMed]

1998 (1)

P. Zemanek and C. J. Foot, “Atomic dipole trap formed by blue detuned strong Gaussian standing wave,” Opt. Commun.146(1-6), 119–123 (1998).
[CrossRef]

1997 (2)

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, “Elasticity and unfolding of single molecules of the giant muscle protein titin,” Nature387(6630), 308–312 (1997).
[CrossRef] [PubMed]

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J.72(3), 1335–1346 (1997).
[CrossRef] [PubMed]

1996 (1)

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]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

1992 (1)

1990 (1)

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead Movement by Single Kinesin Molecules Studied with Optical Tweezers,” Nature348(6299), 348–352 (1990).
[CrossRef] [PubMed]

1988 (1)

B. T. Draine, “The Discrete-Dipole Approximation and Its Application to Interstellar Graphite Grains,” Astrophys. J.333, 848–872 (1988).
[CrossRef]

1986 (1)

1972 (1)

1970 (1)

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.

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J.72(3), 1335–1346 (1997).
[CrossRef] [PubMed]

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead Movement by Single Kinesin Molecules Studied with Optical Tweezers,” Nature348(6299), 348–352 (1990).
[CrossRef] [PubMed]

Cai, Y. J.

Carter, W. H.

Chen, Z. G.

Chiou, P. Y.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature436(7049), 370–372 (2005).
[CrossRef] [PubMed]

Chremmos, I.

Christodoulides, D. N.

Chu, S.

Collins, S. A.

Cottrell, D. M.

Davis, J. A.

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, (2008).

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Dienerowitz, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, (2008).

Draine, B. T.

B. T. Draine, “The Discrete-Dipole Approximation and Its Application to Interstellar Graphite Grains,” Astrophys. J.333, 848–872 (1988).
[CrossRef]

Dziedzic, J. M.

Efremidis, N. K.

Eyyuboglu, H. T.

Foot, C. J.

P. Zemanek and C. J. Foot, “Atomic dipole trap formed by blue detuned strong Gaussian standing wave,” Opt. Commun.146(1-6), 119–123 (1998).
[CrossRef]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Gelles, J.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J.72(3), 1335–1346 (1997).
[CrossRef] [PubMed]

Goldstein, L. S. B.

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead Movement by Single Kinesin Molecules Studied with Optical Tweezers,” Nature348(6299), 348–352 (1990).
[CrossRef] [PubMed]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003).
[CrossRef] [PubMed]

Guizar-Sicairos, M.

Gutiérrez-Vega, J. C.

Harada, Y.

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]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Huang, K. K.

Jiang, Y. F.

Landick, R.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J.72(3), 1335–1346 (1997).
[CrossRef] [PubMed]

Leseberg, D.

Li, P.

Liu, S.

Liu, Z. R.

Lu, X. H.

Mazilu, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, (2008).

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

McGloin, D.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Mills, M. S.

Ohta, A. T.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature436(7049), 370–372 (2005).
[CrossRef] [PubMed]

Papazoglou, D. G.

Prakash, J.

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Sand, D.

Schnapp, B. J.

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead Movement by Single Kinesin Molecules Studied with Optical Tweezers,” Nature348(6299), 348–352 (1990).
[CrossRef] [PubMed]

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature419(6903), 145–147 (2002).
[CrossRef] [PubMed]

Simmons, R. M.

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, “Elasticity and unfolding of single molecules of the giant muscle protein titin,” Nature387(6630), 308–312 (1997).
[CrossRef] [PubMed]

Sleep, J. A.

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, “Elasticity and unfolding of single molecules of the giant muscle protein titin,” Nature387(6630), 308–312 (1997).
[CrossRef] [PubMed]

Trinick, J.

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, “Elasticity and unfolding of single molecules of the giant muscle protein titin,” Nature387(6630), 308–312 (1997).
[CrossRef] [PubMed]

Tskhovrebova, L.

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, “Elasticity and unfolding of single molecules of the giant muscle protein titin,” Nature387(6630), 308–312 (1997).
[CrossRef] [PubMed]

Tzortzakis, S.

Wang, L. G.

Wang, L. Q.

Wang, M.

Wang, M. D.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J.72(3), 1335–1346 (1997).
[CrossRef] [PubMed]

Wu, M. C.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature436(7049), 370–372 (2005).
[CrossRef] [PubMed]

Yin, H.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J.72(3), 1335–1346 (1997).
[CrossRef] [PubMed]

Zemanek, P.

P. Zemanek and C. J. Foot, “Atomic dipole trap formed by blue detuned strong Gaussian standing wave,” Opt. Commun.146(1-6), 119–123 (1998).
[CrossRef]

Zhan, Q. W.

Q. W. Zhan, “Radiation forces on a dielectric sphere produced by highly focused cylindrical vector beams,” J. Opt. A, Pure Appl. Opt.5(3), 229–232 (2003).
[CrossRef]

Zhang, P.

Zhang, Z.

Zhao, C. L.

Zhao, D. M.

Zhao, J.

Zhu, S. Y.

Appl. Opt. (1)

Astrophys. J. (1)

B. T. Draine, “The Discrete-Dipole Approximation and Its Application to Interstellar Graphite Grains,” Astrophys. J.333, 848–872 (1988).
[CrossRef]

Biophys. J. (1)

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J.72(3), 1335–1346 (1997).
[CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt. (1)

Q. W. Zhan, “Radiation forces on a dielectric sphere produced by highly focused cylindrical vector beams,” J. Opt. A, Pure Appl. Opt.5(3), 229–232 (2003).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Nat. Photonics (1)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

Nature (5)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature419(6903), 145–147 (2002).
[CrossRef] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003).
[CrossRef] [PubMed]

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature436(7049), 370–372 (2005).
[CrossRef] [PubMed]

S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead Movement by Single Kinesin Molecules Studied with Optical Tweezers,” Nature348(6299), 348–352 (1990).
[CrossRef] [PubMed]

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, “Elasticity and unfolding of single molecules of the giant muscle protein titin,” Nature387(6630), 308–312 (1997).
[CrossRef] [PubMed]

Opt. Commun. (2)

P. Zemanek and C. J. Foot, “Atomic dipole trap formed by blue detuned strong Gaussian standing wave,” Opt. Commun.146(1-6), 119–123 (1998).
[CrossRef]

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]

Opt. Express (5)

Opt. Lett. (9)

C. L. Zhao and Y. J. Cai, “Trapping two types of particles using a focused partially coherent elegant Laguerre-Gaussian beam,” Opt. Lett.36(12), 2251–2253 (2011).
[CrossRef] [PubMed]

L. G. Wang, C. L. Zhao, L. Q. Wang, X. H. Lu, and S. Y. Zhu, “Effect of spatial coherence on radiation forces acting on a Rayleigh dielectric sphere,” Opt. Lett.32(11), 1393–1395 (2007).
[CrossRef] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett.36(10), 1890–1892 (2011).
[CrossRef] [PubMed]

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett.38(14), 2416–2418 (2013).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. G. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett.36(15), 2883–2885 (2011).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a Single-Beam Gradient Force Optical Trap for Dielectric Particles,” Opt. Lett.11(5), 288–290 (1986).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35(23), 4045–4047 (2010).
[CrossRef] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett.36(10), 1842–1844 (2011).
[CrossRef] [PubMed]

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. G. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett.36(18), 3675–3677 (2011).
[CrossRef] [PubMed]

Optical manipulation of nanoparticles: a review (1)

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, (2008).

Phys. Rev. Lett. (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett.75(5), 826–829 (1995).
[CrossRef] [PubMed]

Other (3)

O. Vallée and M. Soares, Airy Functions and Applications to Physics, (Imperial College, 2004).

J. W. Goodman, Introduction to Fourier Optics, (Roberts & Company Publishers, 2005).

F. W. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, The NIST Handbook of Mathematical Functions, (Cambridge University Press, 2010).

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Figures (4)

Fig. 1
Fig. 1

Comparison about the intensity of the CAB in the beam center of the paraxial and the non-paraxial propagation results. (a) s = 5 μ m , (b) s = 1 μ m .

Fig. 2
Fig. 2

The distribution of the radiation force on the Rayleigh particle with np = 1.59. (a) The longitudinal gradient force; (b) the scattering force, (c) the sum of the gradient force and the scattering force, the inset figure shows the positions of za, zb and zc. (d) The transverse gradient force at za = 981 μ m ; (e) the transverse gradient force at zb = 1038 μ m , (f) the transverse gradient force of zc = 1076 μ m .

Fig. 3
Fig. 3

The distribution of the radiation force on the Rayleigh particle with np = 1.00. (a) The sum of the gradient force and the scattering force. (b) The transverse gradient force at zb = 1038 μ m .

Fig. 4
Fig. 4

The distributions of radiation forces with different parameters exerted on the Rayleigh particle with np = 1.59. (a)The longitudinal radiation forces with different a, while s = 5um, r0 = 50um; (b) the transverse gradient forces at the first equilibrium point in Fig. 4(a). (c) The longitudinal radiation forces with different r0, while a = 0.08, s = 5um; (d) the transverse gradient forces at the first equilibrium points in Fig. 4(c). (e) The longitudinal gradient forces with different s, while a = 0.08, r0 = 50um; (f) the transvers gradient forces at the first equilibrium points in Fig. 4(e).

Equations (16)

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E ( r , z = 0 ) = A i ( r 0 r s ) exp ( a r 0 r s ) ,
E ( r , φ , z ) = E x ( r , z ) x ^ + E z ( r , φ , z ) z ^ ,
E x ( r , z ) = 2 π 0 g ˜ ( k ) J 0 ( 2 π k r ) e 2 i π z k z k d k ,
g ˜ ( k ) = 2 π 0 E ( r , 0 ) J 0 ( 2 π k r ) r d r ,
E z ( r , φ , z ) = 0 2 π 0 k cos θ k z g ˜ ( k ) e i 2 π [ k z z + k r cos ( θ φ ) ] k d k d θ = 0 k 2 2 k z g ˜ ( k ) e i 2 π k z z ( 0 2 π e i 2 π k r cos ( θ φ ) + i θ d θ + 0 2 π e i 2 π k r cos ( θ φ ) i θ d θ ) d k = i 2 π 0 k 2 k z g ˜ ( k ) e i 2 π k z z J 1 ( 2 π k r ) d k cos φ ,
E ( r , z ) = 2 i π λ z exp ( i π r 2 2 λ z ) 0 A i ( r 0 r s ) exp ( a r 0 r s ) exp ( i π r 2 2 λ z ) J 0 ( 2 π r r λ z ) r d r ,
E ( 0 , z ) = 2 i π λ z A i ( r 0 r s ) exp ( a r 0 r s ) exp ( i π r 2 λ z ) r d r .
φ β ( y ) = 1 β e x 2 A i ( y x β ) d x = π β exp [ 1 4 β 3 ( y + 1 24 β 3 ) ] A i ( y β + 1 16 β 4 ) ,
1 β x e x 2 A i ( y x β ) d x = y φ β ( y ) + α 3 φ β ( y ) ,
E ( 0 , z ) = π exp ( P 1 ) [ A i ( P 2 ) ( 1 4 s 3 c 3 / 2 b c 1 / 2 ) A i ( P 2 ) s c 1 / 2 ] exp ( c b 2 + a r 0 s ) ,
P 1 = r 0 + b 4 c s 3 + 1 96 c 3 s 6 , P 2 = r 0 + b s + 1 16 c 2 s 4 .
α = 4 π R 3 ε p ε m ε p + 2 ε m ,
F g = 1 4 ε 0 ε m Re ( α ) | E 2 | ,
F s = ε 0 ε m 3 k 0 4 12 π | α 2 | | E 2 | ,
R = exp ( U / k B T ) 1 ,
U = 1 4 ε 0 ε m Re ( α ) Δ ( E 2 )

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