Abstract

We report a physical explanation for the phenomenon wherein the backscattering of light by dielectric particles of sizes between 100 and 1nm is enhanced by 7–11 orders of magnitude. The phenomenon involves complex composite interactions between a dielectric microsphere and a nanoparticle positioned in close proximity to the microsphere. We provide both analytical and perturbation analyses that show that the enhanced backscattering intensity of a nanoparticle is proportional to the third power of its size parameter. Potential applications of this phenomenon include visible-light detection, characterization, and manipulation of particles as small as a few nanometers.

© 2006 Optical Society of America

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References

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  1. S. Nie and S. R. Emory, Science 275, 1102 (1997).
    [CrossRef] [PubMed]
  2. G. Wu, R. H. Datar, K. M. Hansen, T. Thundat, R. J. Cote, and A. Majumdar, Nat. Biotechnol. 19, 856 (2001).
    [CrossRef] [PubMed]
  3. B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, Appl. Phys. Lett. 85, 4854 (2004).
    [CrossRef]
  4. W. E. Moerner, Science 265, 46 (1994).
    [CrossRef] [PubMed]
  5. F.-R. F. Fan and A. J. Bard, Science 267, 871 (1995).
    [CrossRef] [PubMed]
  6. Z. Chen, A. Taflove, and V. Backman, Opt. Express 12, 1214 (2004).
    [CrossRef] [PubMed]
  7. X. Li, Z. Chen, A. Taflove, and V. Backman, Opt. Express 13, 526 (2005).
    [CrossRef] [PubMed]
  8. R. K. Chang and T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, 1982).
  9. Y.-L. Xu, Appl. Opt. 34, 4573 (1995).
    [CrossRef] [PubMed]

2005 (1)

2004 (2)

Z. Chen, A. Taflove, and V. Backman, Opt. Express 12, 1214 (2004).
[CrossRef] [PubMed]

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, Appl. Phys. Lett. 85, 4854 (2004).
[CrossRef]

2001 (1)

G. Wu, R. H. Datar, K. M. Hansen, T. Thundat, R. J. Cote, and A. Majumdar, Nat. Biotechnol. 19, 856 (2001).
[CrossRef] [PubMed]

1997 (1)

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

1995 (2)

F.-R. F. Fan and A. J. Bard, Science 267, 871 (1995).
[CrossRef] [PubMed]

Y.-L. Xu, Appl. Opt. 34, 4573 (1995).
[CrossRef] [PubMed]

1994 (1)

W. E. Moerner, Science 265, 46 (1994).
[CrossRef] [PubMed]

Almeida, V.

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, Appl. Phys. Lett. 85, 4854 (2004).
[CrossRef]

Backman, V.

Bard, A. J.

F.-R. F. Fan and A. J. Bard, Science 267, 871 (1995).
[CrossRef] [PubMed]

Chang, R. K.

R. K. Chang and T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, 1982).

Chen, Z.

Cote, R. J.

G. Wu, R. H. Datar, K. M. Hansen, T. Thundat, R. J. Cote, and A. Majumdar, Nat. Biotechnol. 19, 856 (2001).
[CrossRef] [PubMed]

Datar, R. H.

G. Wu, R. H. Datar, K. M. Hansen, T. Thundat, R. J. Cote, and A. Majumdar, Nat. Biotechnol. 19, 856 (2001).
[CrossRef] [PubMed]

Emory, S. R.

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

Fan, F.-R. F.

F.-R. F. Fan and A. J. Bard, Science 267, 871 (1995).
[CrossRef] [PubMed]

Furtak, T. E.

R. K. Chang and T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, 1982).

Hansen, K. M.

G. Wu, R. H. Datar, K. M. Hansen, T. Thundat, R. J. Cote, and A. Majumdar, Nat. Biotechnol. 19, 856 (2001).
[CrossRef] [PubMed]

Li, X.

Lipson, M.

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, Appl. Phys. Lett. 85, 4854 (2004).
[CrossRef]

Majumdar, A.

G. Wu, R. H. Datar, K. M. Hansen, T. Thundat, R. J. Cote, and A. Majumdar, Nat. Biotechnol. 19, 856 (2001).
[CrossRef] [PubMed]

Manolatou, C.

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, Appl. Phys. Lett. 85, 4854 (2004).
[CrossRef]

Moerner, W. E.

W. E. Moerner, Science 265, 46 (1994).
[CrossRef] [PubMed]

Nie, S.

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

Preble, S.

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, Appl. Phys. Lett. 85, 4854 (2004).
[CrossRef]

Schmidt, B.

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, Appl. Phys. Lett. 85, 4854 (2004).
[CrossRef]

Taflove, A.

Thundat, T.

G. Wu, R. H. Datar, K. M. Hansen, T. Thundat, R. J. Cote, and A. Majumdar, Nat. Biotechnol. 19, 856 (2001).
[CrossRef] [PubMed]

Wu, G.

G. Wu, R. H. Datar, K. M. Hansen, T. Thundat, R. J. Cote, and A. Majumdar, Nat. Biotechnol. 19, 856 (2001).
[CrossRef] [PubMed]

Xu, Y.-L.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, Appl. Phys. Lett. 85, 4854 (2004).
[CrossRef]

Nat. Biotechnol. (1)

G. Wu, R. H. Datar, K. M. Hansen, T. Thundat, R. J. Cote, and A. Majumdar, Nat. Biotechnol. 19, 856 (2001).
[CrossRef] [PubMed]

Opt. Express (2)

Science (3)

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

W. E. Moerner, Science 265, 46 (1994).
[CrossRef] [PubMed]

F.-R. F. Fan and A. J. Bard, Science 267, 871 (1995).
[CrossRef] [PubMed]

Other (1)

R. K. Chang and T. E. Furtak, Surface Enhanced Raman Scattering (Plenum, 1982).

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Figures (3)

Fig. 1
Fig. 1

Photonic nanojet emerging at the shadow-side surface (blue circle) of a dielectric microsphere. The electric field intensity (normalized to the incident intensity) is visualized on the meridian plane.

Fig. 2
Fig. 2

(a) Comparison of the superenhanced backscattering intensity of a nanosphere (solid line) with the lens focusing effect of the microsphere (dashed–dotted line) and the Rayleigh scattering intensity (dashed line) as a function of the size parameter. (b) The backscattering enhancement factor. Logarithmic scales are used in both (a) and (b).

Fig. 3
Fig. 3

(Color online) Comparison of the superenhanced backscattering intensity of a nanosphere calculated by using a perturbation analysis with that calculated by using the GMM theory, as a function of the size parameter.

Equations (7)

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a m n M = a n M [ p m n M ν = 1 μ = ν ν ( a μ ν N A m n μ ν + b μ ν N B m n μ ν ) ] ,
b m n M = b n M [ q m n M ν = 1 μ = ν ν ( a μ ν N B m n μ ν + b μ ν N A m n μ ν ) ] ,
a m n N ( I ̃ jet I 0 ) 1 2 a n N p m n N , b m n N ( I ̃ jet I 0 ) 1 2 b n M q m n M ,
δ a m n M = a n M ( I ̃ jet I 0 ) 1 2 a 1 N μ = 1 1 p μ 1 N A m n μ 1 ,
δ b m n M = b n M ( I ̃ jet I 0 ) 1 2 a 1 N μ = 1 1 p μ 1 N B m n μ 1 ,
S ( 180 ° ) 2 = S M 2 + δ S M 2 .
δ S M 2 ( 2 3 ) [ ( m 2 1 ) ( m 2 + 2 ) ] ( I ̃ jet I 0 ) 1 2 F M ( k d ) x 3 ,

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