Abstract

Carbon nanotubes are the focus of intense research interest because of their unique properties and applications potential. We present a study based on quantum electrodynamics concerning the optical force between a pair of nanotubes under laser irradiance. To identify separate effects associated with the pair orientation and laser beam geometry, two different systems are analyzed. For each, an analytical expression for the laser-induced optical force is determined, and the corresponding magnitude is estimated.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Cao, Nanostructures and Nanomaterials:?Syn - thesis, Properties and Applications (Imperial College Press, London, 2004), p. 238.
  2. J. Plewa, E. Tanner, D. M. Mueth, and D. G. Grier, Opt. Express 12, 1978 (2004), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  3. S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, Nano Lett. 4, 1415 (2004).
    [CrossRef]
  4. J. E. Molloy, K. Dholakia, and M. J. Padgett, J. Mod. Opt. 50, 1501 (2003).
  5. A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853 (1997).
    [CrossRef]
  6. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
    [CrossRef] [PubMed]
  7. F. Depasse and J.-M. Vigoureux, J. Phys. D 27, 914 (1994).
    [CrossRef]
  8. P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
    [CrossRef]
  9. D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover, Mineola, N.Y., 1998), pp. 152–163.
  10. P. Allcock, R. D. Jenkins, and D. L. Andrews, Phys. Rev. A 61, 023812 (2000).
    [CrossRef]
  11. G. J. Daniels, R. D. Jenkins, D. S. Bradshaw, and D. L. Andrews, J. Chem. Phys. 119, 2264 (2003).
    [CrossRef]
  12. G. Y. Guo, K. C. Chu, D.-S. Wang, and C.-G. Duan, Comput. Mater. Sci. 30, 269 (2004).
    [CrossRef]
  13. D. L. Andrews and M. J. Harlow, Phys. Rev. A 29, 2796 (1984).
    [CrossRef]

2004

J. Plewa, E. Tanner, D. M. Mueth, and D. G. Grier, Opt. Express 12, 1978 (2004), http://www.opticsexpress.org.
[CrossRef] [PubMed]

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, Nano Lett. 4, 1415 (2004).
[CrossRef]

G. Y. Guo, K. C. Chu, D.-S. Wang, and C.-G. Duan, Comput. Mater. Sci. 30, 269 (2004).
[CrossRef]

2003

J. E. Molloy, K. Dholakia, and M. J. Padgett, J. Mod. Opt. 50, 1501 (2003).

G. J. Daniels, R. D. Jenkins, D. S. Bradshaw, and D. L. Andrews, J. Chem. Phys. 119, 2264 (2003).
[CrossRef]

2001

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
[CrossRef]

2000

P. Allcock, R. D. Jenkins, and D. L. Andrews, Phys. Rev. A 61, 023812 (2000).
[CrossRef]

1997

A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853 (1997).
[CrossRef]

1994

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

1989

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

1984

D. L. Andrews and M. J. Harlow, Phys. Rev. A 29, 2796 (1984).
[CrossRef]

Allcock, P.

P. Allcock, R. D. Jenkins, and D. L. Andrews, Phys. Rev. A 61, 023812 (2000).
[CrossRef]

Andrews, D. L.

G. J. Daniels, R. D. Jenkins, D. S. Bradshaw, and D. L. Andrews, J. Chem. Phys. 119, 2264 (2003).
[CrossRef]

P. Allcock, R. D. Jenkins, and D. L. Andrews, Phys. Rev. A 61, 023812 (2000).
[CrossRef]

D. L. Andrews and M. J. Harlow, Phys. Rev. A 29, 2796 (1984).
[CrossRef]

Ashkin, A.

A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853 (1997).
[CrossRef]

Bradshaw, D. S.

G. J. Daniels, R. D. Jenkins, D. S. Bradshaw, and D. L. Andrews, J. Chem. Phys. 119, 2264 (2003).
[CrossRef]

Burns, M. M.

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

Cai, C. W.

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, Nano Lett. 4, 1415 (2004).
[CrossRef]

Cao, G.

G. Cao, Nanostructures and Nanomaterials:?Syn - thesis, Properties and Applications (Imperial College Press, London, 2004), p. 238.

Chaumet, P. C.

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
[CrossRef]

Chu, K. C.

G. Y. Guo, K. C. Chu, D.-S. Wang, and C.-G. Duan, Comput. Mater. Sci. 30, 269 (2004).
[CrossRef]

Craig, D. P.

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover, Mineola, N.Y., 1998), pp. 152–163.

Daniels, G. J.

G. J. Daniels, R. D. Jenkins, D. S. Bradshaw, and D. L. Andrews, J. Chem. Phys. 119, 2264 (2003).
[CrossRef]

Depasse, F.

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

Dholakia, K.

J. E. Molloy, K. Dholakia, and M. J. Padgett, J. Mod. Opt. 50, 1501 (2003).

Duan, C.-G.

G. Y. Guo, K. C. Chu, D.-S. Wang, and C.-G. Duan, Comput. Mater. Sci. 30, 269 (2004).
[CrossRef]

Fournier, J.-M.

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

Golovchenko, J. A.

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

Grier, D. G.

Guo, G. Y.

G. Y. Guo, K. C. Chu, D.-S. Wang, and C.-G. Duan, Comput. Mater. Sci. 30, 269 (2004).
[CrossRef]

Harlow, M. J.

D. L. Andrews and M. J. Harlow, Phys. Rev. A 29, 2796 (1984).
[CrossRef]

Jenkins, R. D.

G. J. Daniels, R. D. Jenkins, D. S. Bradshaw, and D. L. Andrews, J. Chem. Phys. 119, 2264 (2003).
[CrossRef]

P. Allcock, R. D. Jenkins, and D. L. Andrews, Phys. Rev. A 61, 023812 (2000).
[CrossRef]

Lopez, H. A.

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, Nano Lett. 4, 1415 (2004).
[CrossRef]

Molloy, J. E.

J. E. Molloy, K. Dholakia, and M. J. Padgett, J. Mod. Opt. 50, 1501 (2003).

Mueth, D. M.

Nieto-Vesperinas, M.

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
[CrossRef]

Padgett, M. J.

J. E. Molloy, K. Dholakia, and M. J. Padgett, J. Mod. Opt. 50, 1501 (2003).

Plewa, J.

Tan, S.

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, Nano Lett. 4, 1415 (2004).
[CrossRef]

Tanner, E.

Thirunamachandran, T.

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover, Mineola, N.Y., 1998), pp. 152–163.

Vigoureux, J.-M.

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

Wang, D.-S.

G. Y. Guo, K. C. Chu, D.-S. Wang, and C.-G. Duan, Comput. Mater. Sci. 30, 269 (2004).
[CrossRef]

Zhang, Y.

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, Nano Lett. 4, 1415 (2004).
[CrossRef]

Comput. Mater. Sci.

G. Y. Guo, K. C. Chu, D.-S. Wang, and C.-G. Duan, Comput. Mater. Sci. 30, 269 (2004).
[CrossRef]

J. Chem. Phys.

G. J. Daniels, R. D. Jenkins, D. S. Bradshaw, and D. L. Andrews, J. Chem. Phys. 119, 2264 (2003).
[CrossRef]

J. Mod. Opt.

J. E. Molloy, K. Dholakia, and M. J. Padgett, J. Mod. Opt. 50, 1501 (2003).

J. Phys. D

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

Nano Lett.

S. Tan, H. A. Lopez, C. W. Cai, and Y. Zhang, Nano Lett. 4, 1415 (2004).
[CrossRef]

Opt. Express

Phys. Rev. A

D. L. Andrews and M. J. Harlow, Phys. Rev. A 29, 2796 (1984).
[CrossRef]

P. Allcock, R. D. Jenkins, and D. L. Andrews, Phys. Rev. A 61, 023812 (2000).
[CrossRef]

Phys. Rev. B

P. C. Chaumet and M. Nieto-Vesperinas, Phys. Rev. B 64, 035422 (2001).
[CrossRef]

Phys. Rev. Lett.

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

Proc. Natl. Acad. Sci. U.S.A.

A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853 (1997).
[CrossRef]

Other

D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics (Dover, Mineola, N.Y., 1998), pp. 152–163.

G. Cao, Nanostructures and Nanomaterials:?Syn - thesis, Properties and Applications (Imperial College Press, London, 2004), p. 238.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Feynman diagrams (each with 23 further permutations) for calculation of the laser-induced interaction energy: 0 denotes the ground state, and α and β are excited states for nanotubes A and B, respectively.

Fig. 2
Fig. 2

Geometry of a parallel nanotube system irradiated in a fixed direction.

Fig. 3
Fig. 3

Geometry of a nanotube pair with fixed orientation.

Equations (10)

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

Δ E ind = Re [ t , s , r i H int t t H int s s H int r r H int i ( E i E t ) ( E i E s ) ( E i E r ) ] .
Δ E ind = Re [ ( n c k ε 0 V ) e i ( 1 ) α i j A V j k ( k , R ) α k l B e l ( 2 ) exp ( i k R ) ] ,
Δ E ind = ( I 4 π ε 0 2 c ) [ ( α 2 sin 2 ϕ sin 2 θ + α 2 cos 2 ϕ ) ( cos k R R 3 + k sin k R R 2 k 2 cos k R R ) 2 α 2 sin 2 ϕ cos 2 θ ( cos k R R 3 + k sin k R R 2 ) ] cos ( k R ) ,
F z = ( I 4 π ε 0 2 c R 4 ) ( [ α 2 sin 2 ϕ ( 1 3 cos 2 θ ) + α 2 cos 2 ϕ ] { 3 R ̂ z cos k R cos ( k R ) + k R [ 3 R ̂ z sin k R cos ( k R ) + k ̂ z cos k R sin ( k R ) ] k 2 R 2 [ R ̂ z cos k R cos ( k R ) k ̂ z sin k R sin ( k R ) ] } ( α 2 sin 2 ϕ sin 2 θ + α 2 cos 2 ϕ ) { k 2 R 2 R ̂ z cos k R cos ( k R ) + k 3 R 3 [ R ̂ z sin k R cos ( k R ) + k ̂ z cos k R sin ( k R ) ] } ) .
F z 0 = ( 3 I R ̂ z 4 π ε 0 2 c R 4 ) [ α 2 sin 2 ϕ ( 1 3 cos 2 θ ) + α 2 cos 2 ϕ ] .
Δ E ind = ( I ε 0 c ) Re [ 1 3 j 0 ( k R ) α i j A V j k α k i B 3 2 j 2 ( k R ) ( 1 3 R ̂ i α i j A V j k α k l B R ̂ l + 1 9 α i j A V j k α k i B ) ] .
j 0 ( k R ) = sin k R k R ,
j 2 ( k R ) = ( 1 k R + 3 k 3 R 3 ) sin k R 3 cos k R k 2 R 2 .
F z = ( I k 3 R ̂ z 8 π ε 0 2 c ) [ cos 2 k R sin 2 k R k R 2 { ( 1 η cos 2 ϕ A ) [ α 2 cos 2 θ ( 1 η cos 2 ϕ B ) + α α sin 2 θ ] + α α sin 2 θ ( 1 η cos 2 ϕ B ) + α 2 cos 2 θ } sin k R cos k R k 2 R 3 ( 6 { ( 1 η cos 2 ϕ A ) [ α 2 cos 2 θ ( 1 η cos 2 ϕ B ) + α α sin 2 θ ] + α α sin 2 θ ( 1 η cos 2 ϕ B ) + α 2 cos 2 θ } 8 α 2 η 2 sin ϕ A sin ϕ B cos ϕ A cos ϕ B cos θ ) + sin 2 k R cos 2 k R k 3 R 4 ( 6 { ( 1 η cos 2 ϕ A ) [ α 2 cos 2 θ ( 1 η cos 2 ϕ B ) + α α sin 2 θ ] + α α sin 2 θ ( 1 η cos 2 ϕ B ) + α 2 cos 2 θ } 14 α 2 η 2 sin ϕ A sin ϕ B cos ϕ A cos ϕ B cos θ + 4 α 2 ( 1 η sin 2 ϕ A ) ( 1 η sin 2 ϕ B ) ) + sin k R cos k R k 4 R 5 ( 16 { ( 1 η cos 2 ϕ A ) [ α 2 cos 2 θ ( 1 η cos 2 ϕ B ) + α α sin 2 θ ] + α α sin 2 θ ( 1 η cos 2 ϕ B ) + α 2 cos 2 θ } 48 α 2 η 2 sin ϕ A sin ϕ B cos ϕ A cos ϕ B cos θ + 32 α 2 ( 1 η sin 2 ϕ A ) ( 1 η sin 2 ϕ B ) ) + ( cos 2 k R sin 2 k R k 5 R 6 sin k R cos k R k 6 R 7 ) ( 6 { ( 1 η cos 2 ϕ A ) [ α 2 cos 2 θ ( 1 η cos 2 ϕ B ) + α α sin 2 θ ] + α α sin 2 θ ( 1 η cos 2 ϕ B ) + α 2 cos 2 θ } 24 α 2 η 2 sin ϕ A sin ϕ B cos ϕ A cos ϕ B cos θ + 24 α 2 ( 1 η sin 2 ϕ A ) ( 1 η sin 2 ϕ B ) ) ] ,
F z 0 = ( I R ̂ z 8 π ε 0 2 c R 4 ) ( 4 { ( 1 η cos 2 ϕ A ) [ α 2 cos 2 θ ( 1 η cos 2 ϕ B ) + α α sin 2 θ ] + α α sin 2 θ ( 1 η cos 2 ϕ B ) + α 2 cos 2 θ } 10 α 2 η 2 sin ϕ A sin ϕ B cos ϕ A cos ϕ B cos θ + 4 α 2 ( 1 η sin 2 ϕ A ) ( 1 η sin 2 ϕ B ) ) .

Metrics