Abstract

We demonstrate that a nonvanishing interaction force exists between pairs of induced dipoles in a random, statistically stationary electromagnetic field. This new type of optical binding force leads to long-range interaction between dipolar particles even when placed in spatially incoherent fields. We also discuss several unique features of the dipole–dipole interaction in spatially incoherent Gaussian fields.

© 2013 Optical Society of America

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  1. P. Chaumet and M. Nieto-Vesperinas, Opt. Lett. 25, 1065 (2000).
    [CrossRef]
  2. T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, J. Phys. B 43, 102001 (2010).
    [CrossRef]
  3. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (University, 1995).
  4. J. Ellis and A. Dogariu, Phys. Rev. Lett. 95, 203905 (2005).
    [CrossRef]
  5. J. M. Auñón and M. Nieto-Vesperinas, J. Opt. Soc. Am. A 29, 1389 (2012).
    [CrossRef]
  6. L. G. Wang, C. L. Zhao, L. Q. Wang, X. H. Lu, and S. Y. Zhu, Opt. Lett. 32, 1393 (2007).
    [CrossRef]
  7. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989).
    [CrossRef]
  8. K. Dholakia and P. Zemánek, Rev. Mod. Phys. 82, 1767 (2010).
    [CrossRef]
  9. J. Rodríguez and D. L. Andrews, Opt. Commun. 282, 2267 (2009).
    [CrossRef]
  10. M. Mazilu, A. P. Rudhall, E. Wright, and K. Dholakia, J. Phys. Condens. Matter 24, 464117 (2012).
    [CrossRef]
  11. M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Philos. Trans. R. Soc. 362, 719 (2004).
    [CrossRef]
  12. L. C. D. Romero, J. Rodríguez, and D. L. Andrews, Opt. Commun. 281, 865 (2008).
    [CrossRef]
  13. F. Depasse and J.-M. Vigoureux, J. Phys. D 27, 914 (1994).
    [CrossRef]
  14. B. Eckhardt, U. Dorr, U. Kuhl, and H.-J. Stockmann, Europhys. Lett. 46, 134 (1999).
    [CrossRef]
  15. M. Berry, J. Phys. A 10, 2083 (1977).
    [CrossRef]
  16. B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
    [CrossRef]
  17. I. Freund and N. Shvartsrnan, Phys. Rev. E 51, 3770 (1995).
    [CrossRef]
  18. T. Thirunamachandran, Mol. Phys. 40, 393 (1980).
    [CrossRef]
  19. D. O’Dell, S. Giovanazzi, G. Kurizki, and V. M. Akulin, Phys. Rev. Lett. 84, 5687 (2000).
    [CrossRef]
  20. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
  21. K. M. Douglass, S. Sukhov, and A. Dogariu, Nat. Photonics 6, 834 (2012).
    [CrossRef]
  22. A. T. Black, J. K. Thompson, and V. Vuletić, J. Phys. B 38, S605 (2005).
    [CrossRef]
  23. V. Démery, Phys. Rev. E 87, 052105 (2013).
    [CrossRef]

2013

V. Démery, Phys. Rev. E 87, 052105 (2013).
[CrossRef]

2012

K. M. Douglass, S. Sukhov, and A. Dogariu, Nat. Photonics 6, 834 (2012).
[CrossRef]

J. M. Auñón and M. Nieto-Vesperinas, J. Opt. Soc. Am. A 29, 1389 (2012).
[CrossRef]

M. Mazilu, A. P. Rudhall, E. Wright, and K. Dholakia, J. Phys. Condens. Matter 24, 464117 (2012).
[CrossRef]

2010

K. Dholakia and P. Zemánek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, J. Phys. B 43, 102001 (2010).
[CrossRef]

2009

J. Rodríguez and D. L. Andrews, Opt. Commun. 282, 2267 (2009).
[CrossRef]

2008

L. C. D. Romero, J. Rodríguez, and D. L. Andrews, Opt. Commun. 281, 865 (2008).
[CrossRef]

2007

2005

J. Ellis and A. Dogariu, Phys. Rev. Lett. 95, 203905 (2005).
[CrossRef]

A. T. Black, J. K. Thompson, and V. Vuletić, J. Phys. B 38, S605 (2005).
[CrossRef]

2004

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Philos. Trans. R. Soc. 362, 719 (2004).
[CrossRef]

2000

P. Chaumet and M. Nieto-Vesperinas, Opt. Lett. 25, 1065 (2000).
[CrossRef]

D. O’Dell, S. Giovanazzi, G. Kurizki, and V. M. Akulin, Phys. Rev. Lett. 84, 5687 (2000).
[CrossRef]

1999

B. Eckhardt, U. Dorr, U. Kuhl, and H.-J. Stockmann, Europhys. Lett. 46, 134 (1999).
[CrossRef]

1995

I. Freund and N. Shvartsrnan, Phys. Rev. E 51, 3770 (1995).
[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]

1986

B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
[CrossRef]

1980

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

1977

M. Berry, J. Phys. A 10, 2083 (1977).
[CrossRef]

Akulin, V. M.

D. O’Dell, S. Giovanazzi, G. Kurizki, and V. M. Akulin, Phys. Rev. Lett. 84, 5687 (2000).
[CrossRef]

Andrews, D. L.

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, J. Phys. B 43, 102001 (2010).
[CrossRef]

J. Rodríguez and D. L. Andrews, Opt. Commun. 282, 2267 (2009).
[CrossRef]

L. C. D. Romero, J. Rodríguez, and D. L. Andrews, Opt. Commun. 281, 865 (2008).
[CrossRef]

Auñón, J. M.

Berry, M.

M. Berry, J. Phys. A 10, 2083 (1977).
[CrossRef]

Black, A. T.

A. T. Black, J. K. Thompson, and V. Vuletić, J. Phys. B 38, S605 (2005).
[CrossRef]

Burns, M. M.

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

Chaumet, P.

Chaumet, P. C.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Philos. Trans. R. Soc. 362, 719 (2004).
[CrossRef]

Cižmár, T.

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, J. Phys. B 43, 102001 (2010).
[CrossRef]

Démery, V.

V. Démery, Phys. Rev. E 87, 052105 (2013).
[CrossRef]

Depasse, F.

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

Dholakia, K.

M. Mazilu, A. P. Rudhall, E. Wright, and K. Dholakia, J. Phys. Condens. Matter 24, 464117 (2012).
[CrossRef]

K. Dholakia and P. Zemánek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, J. Phys. B 43, 102001 (2010).
[CrossRef]

Dogariu, A.

K. M. Douglass, S. Sukhov, and A. Dogariu, Nat. Photonics 6, 834 (2012).
[CrossRef]

J. Ellis and A. Dogariu, Phys. Rev. Lett. 95, 203905 (2005).
[CrossRef]

Dorr, U.

B. Eckhardt, U. Dorr, U. Kuhl, and H.-J. Stockmann, Europhys. Lett. 46, 134 (1999).
[CrossRef]

Douglass, K. M.

K. M. Douglass, S. Sukhov, and A. Dogariu, Nat. Photonics 6, 834 (2012).
[CrossRef]

Eckhardt, B.

B. Eckhardt, U. Dorr, U. Kuhl, and H.-J. Stockmann, Europhys. Lett. 46, 134 (1999).
[CrossRef]

Ellis, J.

J. Ellis and A. Dogariu, Phys. Rev. Lett. 95, 203905 (2005).
[CrossRef]

Fournier, J.-M.

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

Freund, I.

I. Freund and N. Shvartsrnan, Phys. Rev. E 51, 3770 (1995).
[CrossRef]

Giovanazzi, S.

D. O’Dell, S. Giovanazzi, G. Kurizki, and V. M. Akulin, Phys. Rev. Lett. 84, 5687 (2000).
[CrossRef]

Golovchenko, J. A.

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

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Kuhl, U.

B. Eckhardt, U. Dorr, U. Kuhl, and H.-J. Stockmann, Europhys. Lett. 46, 134 (1999).
[CrossRef]

Kurizki, G.

D. O’Dell, S. Giovanazzi, G. Kurizki, and V. M. Akulin, Phys. Rev. Lett. 84, 5687 (2000).
[CrossRef]

Lu, X. H.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (University, 1995).

Mazilu, M.

M. Mazilu, A. P. Rudhall, E. Wright, and K. Dholakia, J. Phys. Condens. Matter 24, 464117 (2012).
[CrossRef]

Nieto-Vesperinas, M.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

O’Dell, D.

D. O’Dell, S. Giovanazzi, G. Kurizki, and V. M. Akulin, Phys. Rev. Lett. 84, 5687 (2000).
[CrossRef]

Rahmani, A.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Philos. Trans. R. Soc. 362, 719 (2004).
[CrossRef]

Rodríguez, J.

J. Rodríguez and D. L. Andrews, Opt. Commun. 282, 2267 (2009).
[CrossRef]

L. C. D. Romero, J. Rodríguez, and D. L. Andrews, Opt. Commun. 281, 865 (2008).
[CrossRef]

Romero, L. C. D.

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, J. Phys. B 43, 102001 (2010).
[CrossRef]

L. C. D. Romero, J. Rodríguez, and D. L. Andrews, Opt. Commun. 281, 865 (2008).
[CrossRef]

Rudhall, A. P.

M. Mazilu, A. P. Rudhall, E. Wright, and K. Dholakia, J. Phys. Condens. Matter 24, 464117 (2012).
[CrossRef]

Shapiro, B.

B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
[CrossRef]

Shvartsrnan, N.

I. Freund and N. Shvartsrnan, Phys. Rev. E 51, 3770 (1995).
[CrossRef]

Stockmann, H.-J.

B. Eckhardt, U. Dorr, U. Kuhl, and H.-J. Stockmann, Europhys. Lett. 46, 134 (1999).
[CrossRef]

Sukhov, S.

K. M. Douglass, S. Sukhov, and A. Dogariu, Nat. Photonics 6, 834 (2012).
[CrossRef]

Thirunamachandran, T.

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

Thompson, J. K.

A. T. Black, J. K. Thompson, and V. Vuletić, J. Phys. B 38, S605 (2005).
[CrossRef]

Vigoureux, J.-M.

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

Vuletic, V.

A. T. Black, J. K. Thompson, and V. Vuletić, J. Phys. B 38, S605 (2005).
[CrossRef]

Wang, L. G.

Wang, L. Q.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (University, 1995).

Wright, E.

M. Mazilu, A. P. Rudhall, E. Wright, and K. Dholakia, J. Phys. Condens. Matter 24, 464117 (2012).
[CrossRef]

Zemánek, P.

K. Dholakia and P. Zemánek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

Zhao, C. L.

Zhu, S. Y.

Europhys. Lett.

B. Eckhardt, U. Dorr, U. Kuhl, and H.-J. Stockmann, Europhys. Lett. 46, 134 (1999).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. A

M. Berry, J. Phys. A 10, 2083 (1977).
[CrossRef]

J. Phys. B

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, J. Phys. B 43, 102001 (2010).
[CrossRef]

A. T. Black, J. K. Thompson, and V. Vuletić, J. Phys. B 38, S605 (2005).
[CrossRef]

J. Phys. Condens. Matter

M. Mazilu, A. P. Rudhall, E. Wright, and K. Dholakia, J. Phys. Condens. Matter 24, 464117 (2012).
[CrossRef]

J. Phys. D

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

Mol. Phys.

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

Nat. Photonics

K. M. Douglass, S. Sukhov, and A. Dogariu, Nat. Photonics 6, 834 (2012).
[CrossRef]

Opt. Commun.

J. Rodríguez and D. L. Andrews, Opt. Commun. 282, 2267 (2009).
[CrossRef]

L. C. D. Romero, J. Rodríguez, and D. L. Andrews, Opt. Commun. 281, 865 (2008).
[CrossRef]

Opt. Lett.

Philos. Trans. R. Soc.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Philos. Trans. R. Soc. 362, 719 (2004).
[CrossRef]

Phys. Rev. E

I. Freund and N. Shvartsrnan, Phys. Rev. E 51, 3770 (1995).
[CrossRef]

V. Démery, Phys. Rev. E 87, 052105 (2013).
[CrossRef]

Phys. Rev. Lett.

D. O’Dell, S. Giovanazzi, G. Kurizki, and V. M. Akulin, Phys. Rev. Lett. 84, 5687 (2000).
[CrossRef]

B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
[CrossRef]

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

J. Ellis and A. Dogariu, Phys. Rev. Lett. 95, 203905 (2005).
[CrossRef]

Rev. Mod. Phys.

K. Dholakia and P. Zemánek, Rev. Mod. Phys. 82, 1767 (2010).
[CrossRef]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (University, 1995).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

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Equations (13)

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F¯(r)=12Re[α*(r)E*(r)·()E(r)].
{Eγ(r1)=Eγ(r1)+G¯¯αEγ(r2)Eγ(r2)=Eγ(r2)+G¯¯αEγ(r1),
Eγ(r2)=(I¯¯G¯¯2α2)1[Eγ(r2)+G¯¯αEγ(r1)].
Fx(r)=12Re(α*E*γ(r)Eγ(r)xγ),
|Eu(r1)|2γ=|Eu(r2)|2γ=13|E|2γ=13I,
Eu*(r1)Eu(r2)γ=13Iμu(|r1r2|)=13Iμu(R).
μ(ξ)=32(sinξξsinξξcosξξ3),μ(ξ)=3sinξξcosξξ3.
νu(x)(R)=iEu2m|Eum|2kxmkexp(ikxmR)γ,
νu(x)(R)=kμu(R)R.
νx(x)(R)=3(3kRcos(kR)+(3+(kR)2)sin(kR))(kR)4,νy(x)(R)=3kR(3+(kR)2)cos(kR)+(32(kR)2)sin(kR)2(kR)4
Fx(R)=16Iu=x,y,z{kRe(Gu*α*21(Gu*α*)2)νu(x)(R)+|α|2Re(GuR)[μu(R)(1+|Guα|2)+2Re(Guα)]|1Gu2α2|2}.
Fx(R)16Iα2k4f(kR),f(ξ)=3[ξ(188ξ2+ξ4)cos(2ξ)+(9+16ξ23ξ4)sin(2ξ)]ξ7.
U=16Iα2Re(u=x,y,zμuGu).

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