Abstract

In this paper, we have considered the optical forces acting on submicron particles induced by arbitrary-order full Poincaré (FP) beams. Different from the traditional scalar beams, the optical forces of the FP beams include three contributions: the scattering, gradient, and curl forces. The last contribution is due to both the vectorial properties of the FP beams’ polarization and the rotating phase structure of the FP beams. We analytically derive all components of the optical forces of the FP beams acting on Rayleigh particles. The numerical results show that the optical curl force is very significant to the absorbing Rayleigh particles, and it has the same order with the scattering force. The total vortex force fields and their trapping effects of different order FP beams on the absorbing dielectric and metallic Rayleigh particles are discussed in detail. Our results may stimulate further investigations on the trapping effect of various vector-vortex beams on submicron or nanometer sized objects.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (2)

2011 (5)

W. Han, W. Cheng, and Q. Zhan, “Flattop focusing with full Poincaré beams under low numerical aperture illumination,” Opt. Lett.36(9), 1605–1607 (2011).
[CrossRef] [PubMed]

L.-G. Wang and H.-S. Chai, “Revisit on dynamic radiation forces induced by pulsed Gaussian beams,” Opt. Express19(15), 14389–14402 (2011).
[CrossRef] [PubMed]

I. Iglesias and J. J. Sáenz, “Scattering forces in the focal volume of high numerical aperture microscope objectives,” Opt. Commun.284(10-11), 2430–2436 (2011).
[CrossRef]

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics5(9), 531–534 (2011).
[CrossRef]

J. J. Sáenz, “Optical forces: Laser tractor beams,” Nat. Photonics5(9), 514–515 (2011).
[CrossRef]

2010 (4)

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett.104(10), 103601 (2010).
[CrossRef] [PubMed]

X.-L. Wang, J. Chen, Y. Li, J. Ding, C.-S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

A. M. Beckley, T. G. Brown, and M. A. Alonso, “Full Poincaré beams,” Opt. Express18(10), 10777–10785 (2010).
[CrossRef] [PubMed]

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express18(10), 10828–10833 (2010).
[CrossRef] [PubMed]

2009 (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon.1(1), 1–57 (2009).
[CrossRef]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102(11), 113602 (2009).
[CrossRef] [PubMed]

2008 (2)

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B93(1), 139–143 (2008).
[CrossRef]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett.33(2), 122–124 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (1)

V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B73(7), 075416 (2006).
[CrossRef]

2003 (1)

2000 (1)

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]

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)

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
[CrossRef]

Albaladejo, S.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102(11), 113602 (2009).
[CrossRef] [PubMed]

Alonso, M. A.

Arias-González, J. R.

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.

Beckley, A. M.

Bjorkholm, J. E.

Brown, T. G.

Chai, H.-S.

Chan, C. T.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics5(9), 531–534 (2011).
[CrossRef]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett.104(10), 103601 (2010).
[CrossRef] [PubMed]

Chaumet, P. C.

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics5(9), 531–534 (2011).
[CrossRef]

X.-L. Wang, J. Chen, Y. Li, J. Ding, C.-S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

Cheng, W.

Chu, S.

Ding, J.

X.-L. Wang, J. Chen, Y. Li, J. Ding, C.-S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

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.

Guo, C.-S.

X.-L. Wang, J. Chen, Y. Li, J. Ding, C.-S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

Han, W.

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]

Heckenberg, N. R.

Iglesias, I.

I. Iglesias and J. J. Sáenz, “Light spin forces in optical traps: comment on “Trapping metallic Rayleigh particles with radial polarization”,” Opt. Express20(3), 2832–2834 (2012).
[CrossRef] [PubMed]

I. Iglesias and J. J. Sáenz, “Scattering forces in the focal volume of high numerical aperture microscope objectives,” Opt. Commun.284(10-11), 2430–2436 (2011).
[CrossRef]

Kawauchi, H.

Kozawa, Y.

Laroche, M.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102(11), 113602 (2009).
[CrossRef] [PubMed]

Laroche, T.

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B93(1), 139–143 (2008).
[CrossRef]

Li, Y.

X.-L. Wang, J. Chen, Y. Li, J. Ding, C.-S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

Lin, Z.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics5(9), 531–534 (2011).
[CrossRef]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett.104(10), 103601 (2010).
[CrossRef] [PubMed]

Marqués, M. I.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102(11), 113602 (2009).
[CrossRef] [PubMed]

Ng, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics5(9), 531–534 (2011).
[CrossRef]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett.104(10), 103601 (2010).
[CrossRef] [PubMed]

Nieminen, T. A.

Nieto-Vesperinas, M.

Novitsky, A. V.

Novitsky, D. V.

Ratner, M. A.

V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B73(7), 075416 (2006).
[CrossRef]

Rubinsztein-Dunlop, H.

Sáenz, J. J.

I. Iglesias and J. J. Sáenz, “Light spin forces in optical traps: comment on “Trapping metallic Rayleigh particles with radial polarization”,” Opt. Express20(3), 2832–2834 (2012).
[CrossRef] [PubMed]

I. Iglesias and J. J. Sáenz, “Scattering forces in the focal volume of high numerical aperture microscope objectives,” Opt. Commun.284(10-11), 2430–2436 (2011).
[CrossRef]

J. J. Sáenz, “Optical forces: Laser tractor beams,” Nat. Photonics5(9), 514–515 (2011).
[CrossRef]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102(11), 113602 (2009).
[CrossRef] [PubMed]

Sato, S.

Vial, A.

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B93(1), 139–143 (2008).
[CrossRef]

Wang, H.-T.

X.-L. Wang, J. Chen, Y. Li, J. Ding, C.-S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

Wang, L.-G.

Wang, X.-L.

X.-L. Wang, J. Chen, Y. Li, J. Ding, C.-S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

Wong, V.

V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B73(7), 075416 (2006).
[CrossRef]

Yan, S.

S. Yan and B. Yao, “Radiation forces of a highly focused radially polarized beam on spherical particles,” Phys. Rev. A76(5), 053836 (2007).
[CrossRef]

Yao, B.

S. Yan and B. Yao, “Radiation forces of a highly focused radially polarized beam on spherical particles,” Phys. Rev. A76(5), 053836 (2007).
[CrossRef]

Yonezawa, K.

Zhan, Q.

Adv. Opt. Photon. (1)

Appl. Phys. B (1)

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B93(1), 139–143 (2008).
[CrossRef]

Astrophys. J. (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J.333, 848–872 (1988).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nat. Photonics (2)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, “Optical pulling force,” Nat. Photonics5(9), 531–534 (2011).
[CrossRef]

J. J. Sáenz, “Optical forces: Laser tractor beams,” Nat. Photonics5(9), 514–515 (2011).
[CrossRef]

Opt. Commun. (2)

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]

I. Iglesias and J. J. Sáenz, “Scattering forces in the focal volume of high numerical aperture microscope objectives,” Opt. Commun.284(10-11), 2430–2436 (2011).
[CrossRef]

Opt. Express (5)

Opt. Lett. (5)

Phys. Rev. A (1)

S. Yan and B. Yao, “Radiation forces of a highly focused radially polarized beam on spherical particles,” Phys. Rev. A76(5), 053836 (2007).
[CrossRef]

Phys. Rev. B (1)

V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B73(7), 075416 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett.102(11), 113602 (2009).
[CrossRef] [PubMed]

X.-L. Wang, J. Chen, Y. Li, J. Ding, C.-S. Guo, and H.-T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett.24(4), 156–159 (1970).
[CrossRef]

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett.104(10), 103601 (2010).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

(a) Schematic for a FP beam passing through the beam waist region (or the focusing region). (b) Distributions of intensities and polarizations of FP beams with different order m at the beam waist’s plane (z = 0). The states of light polarization are denoted by the different ellipses.

Fig. 2
Fig. 2

The magnitude and direction distributions of (a) the gradient force, (b) the curl force, (c) the scattering force, and (d) total force in the plane of z=0 for the FP beam with m=1 and γ=π/4 . Other parameters are a=50 nm and ε p =2.56 (no absorption).

Fig. 3
Fig. 3

The magnitude and direction distributions of (a) the gradient force, (b) the curl force, (c) the scattering force, and (d) total force in the plane of z=0 for the FP beam with m=1 and γ=π/4 . Other parameters are a=50 nm and ε m =2.56+i2.56 (with absorption).

Fig. 4
Fig. 4

The magnitude and direction distributions of (a) the gradient force, (b) the curl force, (c) the scattering force, and (d) total force in the plane of z=0 for a linear-polarized Gaussian beam. Other parameters are the same as in Fig. 3.

Fig. 5
Fig. 5

The magnitude and direction distributions of (a) the gradient force, (b) the curl force, (c) the scattering force, and (d) total force in the plane of z=0 for a linear-polarized LG01 beam. Other parameters are the same as in Fig. 3.

Fig. 6
Fig. 6

Distributions of (a-c) the beam intensities and the states of polarization (different ellipses), and the magnitude and direction distributions of (d-f) the sum of the curl and scattering forces, and (g-i) the total transverse force at different planes: (a), (d), and (g) for z=0.5 Z R , (b), (e), and (h) for z=0 , and (c), (f), and (i) for z=0.5 Z R . Other parameters are the same as in Fig. 3.

Fig. 7
Fig. 7

Distributions of (a-c) the beam intensities and the states of polarization (different ellipses), and the magnitude and direction distributions of (d-f) the sum of the curl and scattering forces, and (g-i) the total transverse force at the different planes: (a), (d), and (g) for z=0.5 Z R , (b), (e), and (h) for z=0 , and (c), (f), and (i) for z=0.5 Z R , with m=3 and γ0.356π . Other parameters are the same as in Fig. 3.

Fig. 8
Fig. 8

Distributions of the z component of the total force acting on the small particle ( a=10 nm) under different absorptions (a) ε m =2.56 , (b) ε m =2.56+0.01i , and (c) ε m =2.56+0.05i , for the FP beam with m=1 and γ=0.25π .

Fig. 9
Fig. 9

Dependence of (a) F c max / F g max , (b) F s max / F g max , and (c) | F c + F s | max / F g max on the absorption factor Im[ ε p ] for the cases of the different particle’s sizes, under the radiation of the FP beam with m=1 and γ=0.25π .

Fig. 10
Fig. 10

Dependence of (a) F c max / F g max , (b) F s max / F g max , and (c) ( F c + F s ) max / F g max on the order value m with a=50 nm and ε p =2.56+2.56i . Other parameters are γ=0.25π for m=1 , γ=π/3 for m=2 , γ=0.356π for Re[ ε p ] , λ= for m=4 , and γ=0.373π for m=5 .

Fig. 11
Fig. 11

Distributions of the total transverse optical forces (in the unit of pN) of the second-order FP beam acting on (a-c) the Al nano-particle and (d-f) the Au nano-particle at different positions: (a) and (d) for z=0.5 Z R , (b) and (e) for z=0 , and (c) and (f) for z=0.5 Z R . Other parameters are m=2 and γ=π/3 .

Equations (19)

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E m (r,φ,z)=cosγ LG 00 (r,φ,z) x ^ +sinγ LG 0m (r,φ,z) y ^
LG 00 (r,φ,z)= 2 π 1 w(z) exp[ ik r 2 2Q(z) ]exp[ i(kzϕ) ],
LG 0m (r,φ,z)= 2 πm! 1 w(z) ( 2 r w(z) ) m exp[ ik r 2 2Q(z) ] ×exp[ i(kzϕ) ]exp[ im(φϕ) ],
E m (r,φ,z)= 2 π 1 w(z) exp[ ik r 2 2Q(z) ]exp[ i(kzϕ) ]cosγ ×{ x ^ + y ^ tanγ 1 m! ( 2 r w(z) ) m exp[ im(φϕ) ] }.
E m (r,φ,z)= E 0 ( 1 Ωexp[ iδ ] ),
F = 1 4 Re(α) | E | 2 + k 2 Im( α )Re( E * × B )+ 1 2 Im(α)Im[( E * ) E ],
α= α 0 1i α 0 k 3 /(6π ε 0 )
α 0 =4π ε 0 a 3 ( ε p / ε m )1 ( ε p / ε m )+2
F g,x = Re[α] I 0 2 P ε 0 c x w 2 (z) { 1+ Ω 2 [ 1 m w 2 (z) 2( x 2 + y 2 ) ] },
F g,y = Re[α] I 0 2 P ε 0 c y w 2 (z) { 1+ Ω 2 [ 1 m w 2 (z) 2( x 2 + y 2 ) ] },
F g,z = Re[α] I 0 2 P 2 ε 0 c z ( z 2 + Z R 2 ) [ 2( x 2 + y 2 ) w 2 (z) ( Ω 2 +1 ) Ω 2 (m+1)1 ],
F s,x = Im[α]P 2 ε 0 c ε m I 0 Ω{ kr z 2 + Z R 2 [ zΩcosφzsinφcos(m(ϕφ)) + Z R sinφsin(m(ϕφ)) ] m r Ωsinφ },
F s,y = Im[α]P 2 ε 0 c ε m I 0 { kr z 2 + Z R 2 [ zsinφ+zΩcosφcos(m(ϕφ)) Z R Ωcosφsin(m(ϕφ)) ] + m r Ωsin[m(ϕφ)+φ] },
F s,z = Im[α]P 2 ε 0 c ε m I 0 { k(1+ Ω 2 )[ 1 r 2 ( z 2 Z R 2 ) 2 ( z 2 + Z R 2 ) 2 ] Z R z 2 + Z R 2 (m Ω 2 + Ω 2 +1) },
F c,x = Im[α]P I 0 kr 2 ε 0 c( z 2 + Z R 2 ) { zcosφ+Ωsinφ( zcos[m(ϕφ)] Z R sin[m(ϕφ)] ) },
F c,y = Im[α]P I 0 Ω 2 ε 0 c { krz ( z 2 + Z R 2 ) ( Ωsinφ+cosφcos[m(ϕφ)] ) + kr Z R ( z 2 + Z R 2 ) cosφsin[m(ϕφ)] m r sin[m(ϕφ)+φ]+ m r Ωcosφ },
F x = F g,x + F s,x + F c,x ,
F y = F g,y + F s,y + F c,y ,
F z = F g,z + F s,z .

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