Abstract

When a Laguerre–Gaussian (LG) laser mode is used to trap nanoparticles, the spatial disposition of the particles about the beam axis is determined by a secondary mechanism that engages the input radiation with the interparticle potential. This analysis, based on the identification of a range-dependent laser-induced energy shift, elicits and details features that arise for spherical nanoparticles irradiated by a LG mode. Calculations of the absolute minima are performed for LG beams of variable topological charge, and the results are displayed graphically. It is shown that more complex ordered structures emerge on extension to three- and four-particle systems and that similar principles will apply to other kinds of radially structured optical mode.

© 2005 Optical Society of America

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References

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  2. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
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    [CrossRef]
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    [CrossRef]

2005

D. L. Andrews and D. S. Bradshaw, Opt. Lett. 30, 783 (2005).
[CrossRef] [PubMed]

D. S. Bradshaw and D. L. Andrews, in Proc. SPIE 5736, 87 (2005).
[CrossRef]

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

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

2002

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, J. Opt. B: Quantum Semiclassical Opt. 4, S66 (2002).
[CrossRef]

2001

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature (London) 412, 313 (2001).
[CrossRef]

1998

R. Passante, E. A. Power, and T. Thirunamachandran, Phys. Rev. A 249, 77 (1998).

1997

1990

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

1989

D. P. Craig and T. Thirunamachandran, Chem. Phys. 135, 37 (1989).
[CrossRef]

Allen, L.

Andrews, D. L.

D. S. Bradshaw and D. L. Andrews, in Proc. SPIE 5736, 87 (2005).
[CrossRef]

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

D. L. Andrews and D. S. Bradshaw, Opt. Lett. 30, 783 (2005).
[CrossRef] [PubMed]

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, J. Opt. B: Quantum Semiclassical Opt. 4, S66 (2002).
[CrossRef]

Babiker, M.

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, J. Opt. B: Quantum Semiclassical Opt. 4, S66 (2002).
[CrossRef]

Bradshaw, D. S.

D. L. Andrews and D. S. Bradshaw, Opt. Lett. 30, 783 (2005).
[CrossRef] [PubMed]

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

D. S. Bradshaw and D. L. Andrews, in Proc. SPIE 5736, 87 (2005).
[CrossRef]

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

Carruthers, A. E.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Craig, D. P.

D. P. Craig and T. Thirunamachandran, Chem. Phys. 135, 37 (1989).
[CrossRef]

Dávila Romero, L. C.

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, J. Opt. B: Quantum Semiclassical Opt. 4, S66 (2002).
[CrossRef]

Dholakia, K.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[CrossRef] [PubMed]

Fournier, J.-M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

Golovchenko, J. A.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature (London) 412, 313 (2001).
[CrossRef]

McGloin, D.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

Padgett, M. J.

Passante, R.

R. Passante, E. A. Power, and T. Thirunamachandran, Phys. Rev. A 249, 77 (1998).

Power, E. A.

R. Passante, E. A. Power, and T. Thirunamachandran, Phys. Rev. A 249, 77 (1998).

Simpson, N. B.

Tatarkova, S. A.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Thirunamachandran, T.

R. Passante, E. A. Power, and T. Thirunamachandran, Phys. Rev. A 249, 77 (1998).

D. P. Craig and T. Thirunamachandran, Chem. Phys. 135, 37 (1989).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature (London) 412, 313 (2001).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature (London) 412, 313 (2001).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature (London) 412, 313 (2001).
[CrossRef]

Chem. Phys.

D. P. Craig and T. Thirunamachandran, Chem. Phys. 135, 37 (1989).
[CrossRef]

Contemp. Phys.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt.

L. C. Dávila Romero, D. L. Andrews, and M. Babiker, J. Opt. B: Quantum Semiclassical Opt. 4, S66 (2002).
[CrossRef]

Nature (London)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature (London) 412, 313 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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

R. Passante, E. A. Power, and T. Thirunamachandran, Phys. Rev. A 249, 77 (1998).

Phys. Rev. Lett.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Phys. World

M. J. Padgett and L. Allen, Phys. World 10, 35 (1997).

Proc. SPIE

D. S. Bradshaw and D. L. Andrews, in Proc. SPIE 5736, 87 (2005).
[CrossRef]

Science

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Science 249, 749 (1990).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Typical Feynman diagrams (each with 23 further time-ordered permutations) for calculation of the laser-induced interaction energy shift: 0 denotes the ground-state level, and α and β are the excited levels for particles A and B, respectively.

Fig. 2
Fig. 2

Geometry of a spherical nanoparticle pair in a LG with l = 1 , p = 0 .

Fig. 3
Fig. 3

Plot of Δ E AB 0 versus Δ ψ for a nanoparticle pair in a LG beam with (a) l = 5 and, (b) l = 10 .

Fig. 4
Fig. 4

Contour graph of Δ E ABC 0 versus Δ ψ 1 (x axis) and Δ ψ 2 (y axis) for three nanoparticles in a LG beam with (a) l = 4 , (b) l = 10 , (c) l = 20 , (d) l = 20 (close up). Lighter shading denotes higher values of Δ E ABC 0 .

Tables (1)

Tables Icon

Table 1 Absolute Minima (in Degrees) of Δ E AB 0 for Different l

Equations (2)

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Δ E AB = ( I f l p 2 α 2 4 π ϵ 0 2 c A l p ) [ ( 1 3 sin 2 ϕ ) ( cos k R R 3 + k sin k R R 2 ) k 2 cos 2 ϕ cos k R R ] × cos ( l Δ ψ ) ,
Δ E AB 0 = [ I f l p 2 α 2 ( 1 3 sin 2 ϕ ) 8 2 π ϵ 0 2 r 3 c A l p ] cos ( l Δ ψ ) ( η cos Δ ψ ) 3 2 .

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