Abstract

It is theoretically shown that by superimposing diffraction-free solutions of the Helmholtz equation, one can construct localized diffraction-free beams that pass through predetermined points on subwavelength distances. These beams are based on the phenomenon of superoscillations and thus do not contain any evanescent waves. The effect of an aperture and noise is examined in specific examples where truncated beams with λ/3 subwavelength features can propagate into the far field.

© 2011 Optical Society of America

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  1. L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006).
  2. L. Novotny, D. W. Pohl, and B. Hecht, Opt. Lett. 20, 970(1995).
    [CrossRef] [PubMed]
  3. S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, Opt. Express 17, 23920 (2009).
    [CrossRef]
  4. A. Salandrino and D. N. Christodoulides, Opt. Lett. 36, 487 (2011).
    [CrossRef] [PubMed]
  5. M. V. Berry and S. Popescu, J. Phys. A. 39, 6965 (2006).
    [CrossRef]
  6. M. V. Berry and M. R. Dennis, J. Phys. A 42, 022003(2009).
    [CrossRef]
  7. P. J. S. G. Ferreira and A. Kempf, IEEE Trans. Signal Process. 54, 3732 (2006).
    [CrossRef]
  8. M. R. Dennis, A. C. Hamilton, and J. Courtial, Opt. Lett. 33, 2976 (2008).
    [CrossRef] [PubMed]
  9. J. Turunen, A. Vasara, and A. T. Friberg, J. Opt. Soc. Am. A 8, 282 (1991).
    [CrossRef]
  10. F. M. Huang, Y. Chen, F. J. G. De Abajo, and N. I. Zheludev, J. Opt. A 9, S285 (2007).
    [CrossRef]
  11. F. M. Huang and N. I. Zheludev, Nano Lett. 9, 1249(2009).
    [CrossRef] [PubMed]
  12. M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, Opt. Express 19, 933 (2011).
    [CrossRef] [PubMed]
  13. J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, Appl. Phys. Lett. 98, 181109(2011).
    [CrossRef]
  14. A. M. H. Wong and G. V. Eleftheriades, IEEE Antennas Wirel. Propag. Lett. 9, 315 (2010).
    [CrossRef]
  15. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  16. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  17. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493 (2000).
    [CrossRef]
  18. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef] [PubMed]
  19. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  20. M. V. Berry, in Coherence and Quantum Optics, N.P.Bigelow, J.H.Ebery, and C.R.Stroud, eds. (Optical Society of America, 2008), Vol. IX, p. 37.
  21. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

2011 (3)

2010 (1)

A. M. H. Wong and G. V. Eleftheriades, IEEE Antennas Wirel. Propag. Lett. 9, 315 (2010).
[CrossRef]

2009 (3)

M. V. Berry and M. R. Dennis, J. Phys. A 42, 022003(2009).
[CrossRef]

F. M. Huang and N. I. Zheludev, Nano Lett. 9, 1249(2009).
[CrossRef] [PubMed]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, Opt. Express 17, 23920 (2009).
[CrossRef]

2008 (1)

2007 (3)

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

F. M. Huang, Y. Chen, F. J. G. De Abajo, and N. I. Zheludev, J. Opt. A 9, S285 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

2006 (2)

M. V. Berry and S. Popescu, J. Phys. A. 39, 6965 (2006).
[CrossRef]

P. J. S. G. Ferreira and A. Kempf, IEEE Trans. Signal Process. 54, 3732 (2006).
[CrossRef]

2000 (1)

1995 (1)

1991 (1)

1987 (2)

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Baumgartl, J.

M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, Opt. Express 19, 933 (2011).
[CrossRef] [PubMed]

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, Appl. Phys. Lett. 98, 181109(2011).
[CrossRef]

Berry, M. V.

M. V. Berry and M. R. Dennis, J. Phys. A 42, 022003(2009).
[CrossRef]

M. V. Berry and S. Popescu, J. Phys. A. 39, 6965 (2006).
[CrossRef]

M. V. Berry, in Coherence and Quantum Optics, N.P.Bigelow, J.H.Ebery, and C.R.Stroud, eds. (Optical Society of America, 2008), Vol. IX, p. 37.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chávez-Cerda, S.

Chen, Y.

F. M. Huang, Y. Chen, F. J. G. De Abajo, and N. I. Zheludev, J. Opt. A 9, S285 (2007).
[CrossRef]

Christodoulides, D. N.

Courtial, J.

De Abajo, F. J. G.

F. M. Huang, Y. Chen, F. J. G. De Abajo, and N. I. Zheludev, J. Opt. A 9, S285 (2007).
[CrossRef]

Dennis, M. R.

Dholakia, K.

M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, Opt. Express 19, 933 (2011).
[CrossRef] [PubMed]

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, Appl. Phys. Lett. 98, 181109(2011).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Durnin, J.

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eldar, Y. C.

Eleftheriades, G. V.

A. M. H. Wong and G. V. Eleftheriades, IEEE Antennas Wirel. Propag. Lett. 9, 315 (2010).
[CrossRef]

Ferreira, P. J. S. G.

P. J. S. G. Ferreira and A. Kempf, IEEE Trans. Signal Process. 54, 3732 (2006).
[CrossRef]

Friberg, A. T.

Gazit, S.

Gutiérrez-Vega, J. C.

Hamilton, A. C.

Hecht, B.

L. Novotny, D. W. Pohl, and B. Hecht, Opt. Lett. 20, 970(1995).
[CrossRef] [PubMed]

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

Huang, F. M.

F. M. Huang and N. I. Zheludev, Nano Lett. 9, 1249(2009).
[CrossRef] [PubMed]

F. M. Huang, Y. Chen, F. J. G. De Abajo, and N. I. Zheludev, J. Opt. A 9, S285 (2007).
[CrossRef]

Iturbe-Castillo, M. D.

Kempf, A.

P. J. S. G. Ferreira and A. Kempf, IEEE Trans. Signal Process. 54, 3732 (2006).
[CrossRef]

Kosmeier, S.

M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, Opt. Express 19, 933 (2011).
[CrossRef] [PubMed]

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, Appl. Phys. Lett. 98, 181109(2011).
[CrossRef]

Mazilu, M.

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, Appl. Phys. Lett. 98, 181109(2011).
[CrossRef]

M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia, Opt. Express 19, 933 (2011).
[CrossRef] [PubMed]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Novotny, L.

L. Novotny, D. W. Pohl, and B. Hecht, Opt. Lett. 20, 970(1995).
[CrossRef] [PubMed]

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

Pohl, D. W.

Popescu, S.

M. V. Berry and S. Popescu, J. Phys. A. 39, 6965 (2006).
[CrossRef]

Rogers, E. T. F.

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, Appl. Phys. Lett. 98, 181109(2011).
[CrossRef]

Salandrino, A.

Segev, M.

Siviloglou, G. A.

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Szameit, A.

Turunen, J.

Vasara, A.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Wong, A. M. H.

A. M. H. Wong and G. V. Eleftheriades, IEEE Antennas Wirel. Propag. Lett. 9, 315 (2010).
[CrossRef]

Zheludev, N. I.

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, Appl. Phys. Lett. 98, 181109(2011).
[CrossRef]

F. M. Huang and N. I. Zheludev, Nano Lett. 9, 1249(2009).
[CrossRef] [PubMed]

F. M. Huang, Y. Chen, F. J. G. De Abajo, and N. I. Zheludev, J. Opt. A 9, S285 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

J. Baumgartl, S. Kosmeier, M. Mazilu, E. T. F. Rogers, N. I. Zheludev, and K. Dholakia, Appl. Phys. Lett. 98, 181109(2011).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett. (1)

A. M. H. Wong and G. V. Eleftheriades, IEEE Antennas Wirel. Propag. Lett. 9, 315 (2010).
[CrossRef]

IEEE Trans. Signal Process. (1)

P. J. S. G. Ferreira and A. Kempf, IEEE Trans. Signal Process. 54, 3732 (2006).
[CrossRef]

J. Opt. A (1)

F. M. Huang, Y. Chen, F. J. G. De Abajo, and N. I. Zheludev, J. Opt. A 9, S285 (2007).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. A (1)

M. V. Berry and M. R. Dennis, J. Phys. A 42, 022003(2009).
[CrossRef]

J. Phys. A. (1)

M. V. Berry and S. Popescu, J. Phys. A. 39, 6965 (2006).
[CrossRef]

Nano Lett. (1)

F. M. Huang and N. I. Zheludev, Nano Lett. 9, 1249(2009).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. Lett. (2)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Other (3)

M. V. Berry, in Coherence and Quantum Optics, N.P.Bigelow, J.H.Ebery, and C.R.Stroud, eds. (Optical Society of America, 2008), Vol. IX, p. 37.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

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

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Figures (4)

Fig. 1
Fig. 1

Schematic diagrams of three dif ferent patterns (a), (b), and (c) of predetermined points (red dots) in the x y plane. The distances between the dots are subwavelength.

Fig. 2
Fig. 2

Transverse intensity profiles of the resulted diffractionless beams that are based on the patterns depicted in Figs. 1a, 1b, 1c, respectively.

Fig. 3
Fig. 3

(a) Intensity transverse profile, (b) y-cut of the | U | in (a), (c) phase of the field in (a), and (d) y-cut of the 2 ρ / ρ of the field in (a). The red squares in (b) and the black in (c), denote the location of the superoscillatory regions. The red (upper) line in (d) is the y-cut of | U | around the superoscillatory region located at x 5 μm .

Fig. 4
Fig. 4

Normalized | U | (solid red lines) of the truncated beam at y=0 for (a) Fig. 2a as an input after z = 250 μm , and (b) Fig. 3a as an input after z = 150 μm , and under the presence of noise. The jagged blue lines represent the fields at the input, and the green squares the superoscillatory regions.

Equations (3)

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2 U z 2 + 2 U x 2 + 2 U y 2 + k 0 2 U = 0 ,
g ( x , y ) = m = 1 N c m f m 1 ( x , y ) ,
c = M 1 G ,

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