Abstract

By focusing light with a sphere several wavelengths in diameter, we can obtain a photonic nanojet [Opt. Express 13, 526 (2005) ]: if light is focused on the surface of the sphere, the width of the beam stays smaller than the wavelength along a distance of propagation of approximately two wavelengths and reaches a high intensity. We use the rigorous Mie theory to analyze the basic properties of the photonic jet in the general three-dimensional polarized case. This fast algorithm allows us to determine the influence of the radius and the refractive index of the sphere on the photonic jet. The polarization response is also studied. We observe that high-intensity concentrations and subwavelength focusing are two different effects. Their basic properties are analyzed, and explanations are proposed.

© 2005 Optical Society of America

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References

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  1. Z. Chen and A. Taflove, Opt. Express 12, 1214 (2004).
    [CrossRef] [PubMed]
  2. X. Li, Z. Chen, A. Taflove, and V. Backman, Opt. Express 13, 526 (2005).
    [CrossRef] [PubMed]
  3. G. Mie, Ann. Phys. 25, 377 (1908).
    [CrossRef]
  4. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), p. 115.
  5. B. Peterson and S. Strom, Phys. Rev. D 8, 3661 (1973).
    [CrossRef]
  6. W. T. Welford, Aberration of Optical Systems (Hilger, 1986), p. 38.
  7. F. de Fornel, Evanescent Waves (Springer, 2000).
  8. D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, (1984).
    [CrossRef]
  9. R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
    [CrossRef]
  10. E. Betzig and J. K. Trautman, Science 257, 189 (1992).
    [CrossRef] [PubMed]
  11. S. M. Mansfield and G. S. Kino, Appl. Phys. Lett. 57, 2615 (1990).
    [CrossRef]
  12. B. B. Goldberg, S. B. Ippolito, L. Novotny, Z. Liu, and M. S. Unlu, IEEE J. Sel. Top. Quantum Electron. 8, 1051 (2002).
    [CrossRef]
  13. M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1980).
  14. H. J. Munzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer, and J. Boneberg, J. Microsc. 202, 129 (2001).
    [CrossRef]
  15. M.-B. Lee, M. Kourogi, T. Yatsui, K. Tsutsui, N. Atoda, and M. Ohtsu, Appl. Opt. 38, 3566 (1999).
    [CrossRef]
  16. E. Betzig, Opt. Lett. 20, 237 (1995).
    [CrossRef] [PubMed]

2005 (1)

2004 (1)

2002 (1)

B. B. Goldberg, S. B. Ippolito, L. Novotny, Z. Liu, and M. S. Unlu, IEEE J. Sel. Top. Quantum Electron. 8, 1051 (2002).
[CrossRef]

2001 (1)

H. J. Munzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer, and J. Boneberg, J. Microsc. 202, 129 (2001).
[CrossRef]

1999 (1)

1995 (1)

1992 (1)

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

1990 (1)

S. M. Mansfield and G. S. Kino, Appl. Phys. Lett. 57, 2615 (1990).
[CrossRef]

1989 (1)

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

1984 (1)

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, (1984).
[CrossRef]

1973 (1)

B. Peterson and S. Strom, Phys. Rev. D 8, 3661 (1973).
[CrossRef]

1908 (1)

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Atoda, N.

Backman, V.

Bertsch, M.

H. J. Munzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer, and J. Boneberg, J. Microsc. 202, 129 (2001).
[CrossRef]

Betzig, E.

E. Betzig, Opt. Lett. 20, 237 (1995).
[CrossRef] [PubMed]

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Boneberg, J.

H. J. Munzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer, and J. Boneberg, J. Microsc. 202, 129 (2001).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1980).

Chen, Z.

de Fornel, F.

F. de Fornel, Evanescent Waves (Springer, 2000).

Denk, W.

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, (1984).
[CrossRef]

Ferrell, T. L.

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

Goldberg, B. B.

B. B. Goldberg, S. B. Ippolito, L. Novotny, Z. Liu, and M. S. Unlu, IEEE J. Sel. Top. Quantum Electron. 8, 1051 (2002).
[CrossRef]

Ippolito, S. B.

B. B. Goldberg, S. B. Ippolito, L. Novotny, Z. Liu, and M. S. Unlu, IEEE J. Sel. Top. Quantum Electron. 8, 1051 (2002).
[CrossRef]

Kino, G. S.

S. M. Mansfield and G. S. Kino, Appl. Phys. Lett. 57, 2615 (1990).
[CrossRef]

Kourogi, M.

Lanz, M.

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, (1984).
[CrossRef]

Lee, M.-B.

Leiderer, P.

H. J. Munzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer, and J. Boneberg, J. Microsc. 202, 129 (2001).
[CrossRef]

Li, X.

Liu, Z.

B. B. Goldberg, S. B. Ippolito, L. Novotny, Z. Liu, and M. S. Unlu, IEEE J. Sel. Top. Quantum Electron. 8, 1051 (2002).
[CrossRef]

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, Appl. Phys. Lett. 57, 2615 (1990).
[CrossRef]

Mie, G.

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Mosbacher, M.

H. J. Munzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer, and J. Boneberg, J. Microsc. 202, 129 (2001).
[CrossRef]

Munzer, H. J.

H. J. Munzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer, and J. Boneberg, J. Microsc. 202, 129 (2001).
[CrossRef]

Novotny, L.

B. B. Goldberg, S. B. Ippolito, L. Novotny, Z. Liu, and M. S. Unlu, IEEE J. Sel. Top. Quantum Electron. 8, 1051 (2002).
[CrossRef]

Ohtsu, M.

Peterson, B.

B. Peterson and S. Strom, Phys. Rev. D 8, 3661 (1973).
[CrossRef]

Pohl, D. W.

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, (1984).
[CrossRef]

Reddick, R. C.

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

Strom, S.

B. Peterson and S. Strom, Phys. Rev. D 8, 3661 (1973).
[CrossRef]

Taflove, A.

Trautman, J. K.

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Tsutsui, K.

Unlu, M. S.

B. B. Goldberg, S. B. Ippolito, L. Novotny, Z. Liu, and M. S. Unlu, IEEE J. Sel. Top. Quantum Electron. 8, 1051 (2002).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), p. 115.

Warmack, R. J.

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

Welford, W. T.

W. T. Welford, Aberration of Optical Systems (Hilger, 1986), p. 38.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1980).

Yatsui, T.

Zimmermann, J.

H. J. Munzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer, and J. Boneberg, J. Microsc. 202, 129 (2001).
[CrossRef]

Ann. Phys. (1)

G. Mie, Ann. Phys. 25, 377 (1908).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. M. Mansfield and G. S. Kino, Appl. Phys. Lett. 57, 2615 (1990).
[CrossRef]

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, (1984).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

B. B. Goldberg, S. B. Ippolito, L. Novotny, Z. Liu, and M. S. Unlu, IEEE J. Sel. Top. Quantum Electron. 8, 1051 (2002).
[CrossRef]

J. Microsc. (1)

H. J. Munzer, M. Mosbacher, M. Bertsch, J. Zimmermann, P. Leiderer, and J. Boneberg, J. Microsc. 202, 129 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

Phys. Rev. D (1)

B. Peterson and S. Strom, Phys. Rev. D 8, 3661 (1973).
[CrossRef]

Science (1)

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Other (4)

W. T. Welford, Aberration of Optical Systems (Hilger, 1986), p. 38.

F. de Fornel, Evanescent Waves (Springer, 2000).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), p. 115.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Pergamon, 1980).

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Figures (4)

Fig. 1
Fig. 1

Geometrical description of the microsphere.

Fig. 2
Fig. 2

Intensity of the total electric field for a sphere with R = 5 λ and n = 1.63 in two orthogonal planes. Calculations have been made with L = 45 orders, and the incident plane wave is ( E x , H y , k z ) .

Fig. 3
Fig. 3

Electric field intensity for a sphere with R = 5 λ and n = 1.3 , a sub-λ FWHM is observed. Calculations have been made with 45 orders, and the incident plane wave is ( E x , H y , k z ) .

Fig. 4
Fig. 4

Distance along z where the FWHM stays smaller than the wavelength and the intensity is greater than half- maximum for two sphere radii. The curves are regular only for a small index because for a larger index the global intensity maximum, which is close to the sphere, jumps from a local maximum of the stationary case to another value.

Equations (1)

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E ( r ) = l = 0 L a l ψ TE , l ( r ) + l = 0 L b l ψ TM , l ( r ) .

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