Abstract

An optically induced interparticle potential, applicable to particles of any shape, is derived in a formulation that accommodates the effects of beam structure. The theory allows the consideration of optical binding interactions in beams of spatially varying irradiance and polarization. Results of specific calculations are exhibited for spherical particles in linearly, circularly, and radially polarized Laguerre–Gaussian beams, leading to the identification of several possible optically induced particle arrangements. The patterning of these optically induced structures is shown to have an identical dependence on the optical wavenumber and spot size at the beam waist.

© 2008 Optical Society of America

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References

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  1. F. Depasse and J.-M. Vigoureux, J. Phys. D 27, 914 (1994).
    [CrossRef]
  2. T. Thirunamachandran, Mol. Phys. 40, 393 (1980).
    [CrossRef]
  3. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
    [CrossRef] [PubMed]
  4. M. Dienerowitz, M. Mazilu, P. J. Reece, T. F. Krauss, and K. Dholakia, Opt. Express 16, 4991 (2008).
    [CrossRef] [PubMed]
  5. M. Guillon and B. Stout, Phys. Rev. A 77, 023806 (2008).
    [CrossRef]
  6. R. F. Marchington, M. Mazilu, S. Kuriakose, V. Garcés-Chávez, P. J. Reece, T. F. Krauss, M. Gu, and K. Dholakia, Opt. Express 16, 3712 (2008).
    [CrossRef] [PubMed]
  7. D. L. Andrews and J. Rodríguez, Opt. Lett. 33, 1830 (2008).
    [CrossRef] [PubMed]
  8. L. C. Dávila Romero, J. Rodríguez, and D. L. Andrews, Proc. SPIE 6988, 6980L (2008).
  9. D. S. Bradshaw and D. L. Andrews, Opt. Lett. 30, 3039 (2005).
    [CrossRef] [PubMed]
  10. D. S. Bradshaw and D. L. Andrews, Phys. Rev. A 72, 033816 (2005).
    [CrossRef]
  11. L. Dávila Romero, S. Naguleswaran, G. E. Stedman, and D. L. Andrews, Nonlinear Opt. 23, 191 (2000).
  12. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, 1982).

2008 (5)

2005 (2)

D. S. Bradshaw and D. L. Andrews, Opt. Lett. 30, 3039 (2005).
[CrossRef] [PubMed]

D. S. Bradshaw and D. L. Andrews, Phys. Rev. A 72, 033816 (2005).
[CrossRef]

2000 (1)

L. Dávila Romero, S. Naguleswaran, G. E. Stedman, and D. L. Andrews, Nonlinear Opt. 23, 191 (2000).

1994 (1)

F. Depasse and J.-M. Vigoureux, J. Phys. D 27, 914 (1994).
[CrossRef]

1989 (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

1980 (1)

T. Thirunamachandran, Mol. Phys. 40, 393 (1980).
[CrossRef]

Andrews, D. L.

L. C. Dávila Romero, J. Rodríguez, and D. L. Andrews, Proc. SPIE 6988, 6980L (2008).

D. L. Andrews and J. Rodríguez, Opt. Lett. 33, 1830 (2008).
[CrossRef] [PubMed]

D. S. Bradshaw and D. L. Andrews, Opt. Lett. 30, 3039 (2005).
[CrossRef] [PubMed]

D. S. Bradshaw and D. L. Andrews, Phys. Rev. A 72, 033816 (2005).
[CrossRef]

L. Dávila Romero, S. Naguleswaran, G. E. Stedman, and D. L. Andrews, Nonlinear Opt. 23, 191 (2000).

Barron, L. D.

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, 1982).

Bradshaw, D. S.

D. S. Bradshaw and D. L. Andrews, Opt. Lett. 30, 3039 (2005).
[CrossRef] [PubMed]

D. S. Bradshaw and D. L. Andrews, Phys. Rev. A 72, 033816 (2005).
[CrossRef]

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

Dávila Romero, L.

L. Dávila Romero, S. Naguleswaran, G. E. Stedman, and D. L. Andrews, Nonlinear Opt. 23, 191 (2000).

Dávila Romero, L. C.

L. C. Dávila Romero, J. Rodríguez, and D. L. Andrews, Proc. SPIE 6988, 6980L (2008).

Depasse, F.

F. Depasse and J.-M. Vigoureux, J. Phys. D 27, 914 (1994).
[CrossRef]

Dholakia, K.

Dienerowitz, M.

Fournier, J.-M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

Garcés-Chávez, V.

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

Gu, M.

Guillon, M.

M. Guillon and B. Stout, Phys. Rev. A 77, 023806 (2008).
[CrossRef]

Krauss, T. F.

Kuriakose, S.

Marchington, R. F.

Mazilu, M.

Naguleswaran, S.

L. Dávila Romero, S. Naguleswaran, G. E. Stedman, and D. L. Andrews, Nonlinear Opt. 23, 191 (2000).

Reece, P. J.

Rodríguez, J.

D. L. Andrews and J. Rodríguez, Opt. Lett. 33, 1830 (2008).
[CrossRef] [PubMed]

L. C. Dávila Romero, J. Rodríguez, and D. L. Andrews, Proc. SPIE 6988, 6980L (2008).

Stedman, G. E.

L. Dávila Romero, S. Naguleswaran, G. E. Stedman, and D. L. Andrews, Nonlinear Opt. 23, 191 (2000).

Stout, B.

M. Guillon and B. Stout, Phys. Rev. A 77, 023806 (2008).
[CrossRef]

Thirunamachandran, T.

T. Thirunamachandran, Mol. Phys. 40, 393 (1980).
[CrossRef]

Vigoureux, J.-M.

F. Depasse and J.-M. Vigoureux, J. Phys. D 27, 914 (1994).
[CrossRef]

J. Phys. D (1)

F. Depasse and J.-M. Vigoureux, J. Phys. D 27, 914 (1994).
[CrossRef]

Mol. Phys. (1)

T. Thirunamachandran, Mol. Phys. 40, 393 (1980).
[CrossRef]

Nonlinear Opt. (1)

L. Dávila Romero, S. Naguleswaran, G. E. Stedman, and D. L. Andrews, Nonlinear Opt. 23, 191 (2000).

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (2)

D. S. Bradshaw and D. L. Andrews, Phys. Rev. A 72, 033816 (2005).
[CrossRef]

M. Guillon and B. Stout, Phys. Rev. A 77, 023806 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
[CrossRef] [PubMed]

Proc. SPIE (1)

L. C. Dávila Romero, J. Rodríguez, and D. L. Andrews, Proc. SPIE 6988, 6980L (2008).

Other (1)

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, 1982).

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Figures (3)

Fig. 1
Fig. 1

Transverse section of the waist of a LG beam with two particles trapped in two different rings.

Fig. 2
Fig. 2

Contour map of the optically induced pair potential for two particles trapped in the two rings at the waist of a linearly polarized LG beam with p = 2 , l = 1 , and for k ω 0 = ( a ) 10, (b) 20, (c) 30, and (d) 40. The maximum of irradiance where the particle A is present is at 0.47 k ω 0 from the beam center, and for the particle B it is at 1.51 k ω 0 . Angles θ A and θ B are as shown in Fig. 1. In the gray scale of the figure: (a) black signifies 1.06 × 10 4 , white 1.00 × 10 4 ; (b) black 2.43 × 10 5 , white 1.04 × 10 5 ; (c) black 6.22 × 10 6 , white 6.37 × 10 6 ; (d) black 2.47 × 10 6 , white 2.33 × 10 6 . Energy units are ( C 2 1 ) 2 α 0 ( A ) ( k , k ) α 0 ( B ) ( k , k ) k 5 4 π ε 0 .

Fig. 3
Fig. 3

Plot of the optically induced interparticle potential energy, Δ E , against θ B θ A for two particles trapped in the two annuli of an LG beam with p = 2 , l = 1 , and k ω 0 = 20 for the solid curve, k ω 0 = 30 for the dotted curve, and k ω 0 = 40 for the dashed curve. Angles θ A and θ B are as shown in Fig. 1. The maxima of irradiance where the particles are present are as shown in Fig. 2. Energy units are ( C 2 1 ) 2 α 0 ( A ) ( k , k ) α 0 ( B ) ( k , k ) k 5 4 π ε 0 . The graph applies equally to circularly and radially polarized beams.

Equations (6)

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μ i ( ξ ) ( t ) = μ i ( ξ ) + 1 2 α i j ( ξ ) ( E j ( R ξ ) e i k c t + i k R ξ + E ¯ j ( R ξ ) e i k c t i k R ξ ) + 1 4 β i j k ( ξ ) ( E ¯ j ( R ξ ) E k ( R ξ ) + E j ( R ξ ) E ¯ k ( R ξ ) ) ,
E k ( ξ ) ( r ) 1 2 α j i ( ξ ) ( E j ( R ξ ) V i k ( k , r ) e i ( k c t + k R ξ ) + E ¯ j ( R ξ ) V ¯ i k ( k , r ) e i ( k c t + k R ξ ) ) + ( μ i ( ξ ) + 1 4 β i j k ( ξ ) ( E ¯ j ( R ξ ) E k ( R ξ ) + E j ( R ξ ) E ¯ k ( R ξ ) ) ) V i k ( 0 , r ) ,
V i j ( k , r ) = e i k r 4 π ε 0 r 3 [ ( 1 i k r ) ( δ i j 3 r ̂ i r ̂ j ) k 2 r 2 ( δ i j r ̂ i r ̂ j ) ] .
Δ E = 1 2 Re { E ¯ k ( R A ) E l ( R B ) α k j ( A ) α l i ( B ) V i j ( k , R ) cos ( k R ) } + 1 2 V l k ( 0 , R ) ( Re { E ¯ i ( R A ) E j ( R A ) } β i j k ( A ) μ l ( B ) + Re { E ¯ i ( R B ) E j ( R B ) } β i j k ( B ) μ l ( A ) ) ,
E p l = C p l w 0 ( r ξ w 0 ) l L p l ( 2 r ξ 2 w 0 2 ) exp [ r ξ 2 w 0 2 ] exp ( i l θ ξ ) ,
Δ E = α 0 ( A ) α 0 ( B ) 4 π ε 0 R 3 i = x , y ( ( Re { E ¯ i ( R A ) E i ( R B ) } ( 1 3 ( R i R ) 2 ) ) ( cos k R + k R sin k R ) ( Re { E ¯ i ( R A ) E i ( R B ) } ( 1 ( R i R ) 2 ) ) k 2 R 2 cos k R ) ,

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