Abstract

Light emitted by an atomic source of radiation appears to travel along a straight line (ray) from the location of the source to the observer in the far field. However, when the energy flow pattern of the radiation is resolved with an accuracy better than an optical wavelength, it turns out that the field lines are usually curved. We consider electric dipole radiation, a prime example of which is the radiation emitted by an atom during an electronic transition, and we show that the field lines of energy flow are in general curves. Near the location of the dipole, the field lines exhibit a vortex structure, and in the far field they approach a straight line. The spatial extension of the vortex in the optical near field is of nanoscale dimension. Due to the rotation of the field lines near the source, the asymptotic limit of a field line is not exactly in the radially outward direction and as a consequence, the image in the far field is slightly shifted. This sub-wavelength displacement of the image of the source should be amenable to experimental observation with contemporary nanoscale-precision techniques.

© 2009 Chinese Optics Letters

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  1. M. Born and E. Wolf, Principles of Optics (6th edn.) (Pergamon, Oxford, 1980) Chap.3.
  2. H. F. Arnoldus and J. T. Foley, Opt. Commun. 231, 115 (2004).
  3. H. F. Arnoldus, Opt. Commun. 252, 253 (2005).
  4. W. Braunbek and G. Laukien, Optik (in German) 9, 174 (1952).
  5. H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, and H. Blok, Opt. Express 11, 371 (2003).
  6. H. F. Schouten, T. D. Visser, D. Lenstra, and H. Blok, Phys. Rev. E 67, 036608 (2003).
  7. M. Vasnetsov and K. Staliunas, (eds.) Optical Vortices, Horizons in World Physics, Vol.228 (Nova Science, New York, 1999).
  8. A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).
  9. V. A. Pas'ko, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 198, 49 (2001).
  10. K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).
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2008 (1)

2007 (1)

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

2005 (1)

H. F. Arnoldus, Opt. Commun. 252, 253 (2005).

2004 (1)

H. F. Arnoldus and J. T. Foley, Opt. Commun. 231, 115 (2004).

2003 (2)

H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, and H. Blok, Opt. Express 11, 371 (2003).

H. F. Schouten, T. D. Visser, D. Lenstra, and H. Blok, Phys. Rev. E 67, 036608 (2003).

2001 (2)

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).

V. A. Pas'ko, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 198, 49 (2001).

1952 (1)

W. Braunbek and G. Laukien, Optik (in German) 9, 174 (1952).

Arnoldus, H. F.

H. F. Arnoldus, Opt. Commun. 252, 253 (2005).

H. F. Arnoldus and J. T. Foley, Opt. Commun. 231, 115 (2004).

Blok, H.

H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, and H. Blok, Opt. Express 11, 371 (2003).

H. F. Schouten, T. D. Visser, D. Lenstra, and H. Blok, Phys. Rev. E 67, 036608 (2003).

Braunbek, W.

W. Braunbek and G. Laukien, Optik (in German) 9, 174 (1952).

Choi, S. B.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Choi, W. J.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Fadeeva, T. A.

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).

Foley, J. T.

H. F. Arnoldus and J. T. Foley, Opt. Commun. 231, 115 (2004).

Gbur, G.

Hori, H.

Inoue, T.

Kihm, H. W.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Kihm, J. E.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Kim, D. S.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Kim, H.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Kim, J.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Kitahara, K.

Laukien, G.

W. Braunbek and G. Laukien, Optik (in German) 9, 174 (1952).

Lee, B.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Lee, K. G.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Lenstra, D.

H. F. Schouten, T. D. Visser, D. Lenstra, and H. Blok, Phys. Rev. E 67, 036608 (2003).

H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, and H. Blok, Opt. Express 11, 371 (2003).

Lienau, C.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Ohdaira, Y.

Park, D. J.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Park, Q. H.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Pas'ko, V. A.

V. A. Pas'ko, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 198, 49 (2001).

Ropers, C.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Schouten, H. F.

H. F. Schouten, T. D. Visser, D. Lenstra, and H. Blok, Phys. Rev. E 67, 036608 (2003).

H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, and H. Blok, Opt. Express 11, 371 (2003).

Shvedov, V. G.

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).

Soskin, M. S.

V. A. Pas'ko, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 198, 49 (2001).

Vasnetsov, M. V.

V. A. Pas'ko, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 198, 49 (2001).

Visser, T. D.

H. F. Schouten, T. D. Visser, D. Lenstra, and H. Blok, Phys. Rev. E 67, 036608 (2003).

H. F. Schouten, T. D. Visser, G. Gbur, D. Lenstra, and H. Blok, Opt. Express 11, 371 (2003).

Volyar, A. V.

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).

Woo, D. H.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Yoon, Y. C.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Nature Photon. (1)

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, Nature Photon. 1, 53 (2007).

Opt. Commun. (3)

H. F. Arnoldus and J. T. Foley, Opt. Commun. 231, 115 (2004).

H. F. Arnoldus, Opt. Commun. 252, 253 (2005).

V. A. Pas'ko, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 198, 49 (2001).

Opt. Express (2)

Opt. Spectrosc. (1)

A. V. Volyar, V. G. Shvedov, and T. A. Fadeeva, Opt. Spectrosc. 90, 93 (2001).

Optik (in German) (1)

W. Braunbek and G. Laukien, Optik (in German) 9, 174 (1952).

Phys. Rev. E (1)

H. F. Schouten, T. D. Visser, D. Lenstra, and H. Blok, Phys. Rev. E 67, 036608 (2003).

Other (4)

M. Vasnetsov and K. Staliunas, (eds.) Optical Vortices, Horizons in World Physics, Vol.228 (Nova Science, New York, 1999).

M. Born and E. Wolf, Principles of Optics (6th edn.) (Pergamon, Oxford, 1980) Chap.3.

I. V. Lindell, Methods for Electromagnetic Field Analysis (Oxford University Press, Oxford, 1992) sec.1.4.

J. D. Jackson, Classical Electrodynamics (3rd edn.) (Wiley, New York, 1999) p.411.

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