Abstract

The diffraction limit sets the smallest achievable linewidth at half the wavelength. With a subwavelength plasmonic lens allowing one to reduce the diffraction via an asymmetry and to generate and squeeze the wave functions, an incident light is focused by the aperture to a single line with its width smaller than the limited value in the intermediate zone. The focused fields are capable of propagating in free space. This light focusing process, besides being of academic interest, is expected to open up a wide range of application possibilities.

© 2010 Optical Society of America

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F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, Appl. Phys. Lett. 83, 4500 (2003).
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H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

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J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
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R. Hillenbrand and F. Keilmann, Phys. Rev. Lett. 85, 3029 (2000).
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B. Knoll and F. Keilmann, Nature 399, 134 (1999).
[CrossRef]

J. B. Pendry, Science 285, 1687 (1999).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
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K. R. Chen, Bull. Am. Phys. Soc. 52, 202 (2007).

K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

Chu, W. H.

K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

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K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

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W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
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K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

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F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, Appl. Phys. Lett. 83, 4500 (2003).
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H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
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T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61, 44 (2008).
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T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
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A. Grbic, L. Jiang, and R. Merlin, Science 320, 511(2008).
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R. Hillenbrand and F. Keilmann, Phys. Rev. Lett. 85, 3029 (2000).
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K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

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K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

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K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

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J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

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A. Grbic, L. Jiang, and R. Merlin, Science 320, 511(2008).
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R. Hillenbrand and F. Keilmann, Phys. Rev. Lett. 85, 3029 (2000).
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B. Knoll and F. Keilmann, Nature 399, 134 (1999).
[CrossRef]

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B. Knoll and F. Keilmann, Nature 399, 134 (1999).
[CrossRef]

Korobkin, D.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef] [PubMed]

Lalanne, P.

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef] [PubMed]

Lee, H.

Z. W. Liu, H. Lee, C. Sun, and X. Zhang, Science 315, 1686(2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534(2005).
[CrossRef] [PubMed]

Lezec, H. J.

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Lin, C. Y.

K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Liu, C. P.

K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

Liu, H. T.

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef] [PubMed]

Liu, Z.

X. Zhang and Z. Liu, Nat. Mater. 7, 435 (2008).
[CrossRef] [PubMed]

Liu, Z. W.

Z. W. Liu, H. Lee, C. Sun, and X. Zhang, Science 315, 1686(2007).
[CrossRef] [PubMed]

Lo, Y. L.

K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

Markley, L.

L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef] [PubMed]

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Melville, D. O. S.

Merlin, R.

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511(2008).
[CrossRef] [PubMed]

R. Merlin, Science 317, 927 (2007).
[CrossRef] [PubMed]

Moyer, P. J.

M. A. Paesler and P. J. Moyer, Near-Field Optics: Theory, Instrumentation, and Applications (Wiley, 1996).

Paesler, M. A.

M. A. Paesler and P. J. Moyer, Near-Field Optics: Theory, Instrumentation, and Applications (Wiley, 1996).

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1998).

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

J. B. Pendry, Science 285, 1687 (1999).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[CrossRef]

Sambles, R.

W. Barnes and R. Sambles, Science 305, 785 (2004).
[CrossRef] [PubMed]

Shvets, G.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef] [PubMed]

Sun, C.

Z. W. Liu, H. Lee, C. Sun, and X. Zhang, Science 315, 1686(2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534(2005).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method(Artech, 2005).

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef] [PubMed]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Urzhumov, Y.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef] [PubMed]

Wang, Y.

L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 2005).

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Wong, A. M. H.

L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef] [PubMed]

Zhang, X.

X. Zhang and Z. Liu, Nat. Mater. 7, 435 (2008).
[CrossRef] [PubMed]

Z. W. Liu, H. Lee, C. Sun, and X. Zhang, Science 315, 1686(2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534(2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

F. J. Garcia-Vidal, L. Martin-Moreno, H. J. Lezec, and T. W. Ebbesen, Appl. Phys. Lett. 83, 4500 (2003).
[CrossRef]

Bull. Am. Phys. Soc. (1)

K. R. Chen, Bull. Am. Phys. Soc. 52, 202 (2007).

Nat. Mater. (1)

X. Zhang and Z. Liu, Nat. Mater. 7, 435 (2008).
[CrossRef] [PubMed]

Nature (4)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

H. T. Liu and P. Lalanne, Nature 452, 728 (2008).
[CrossRef] [PubMed]

B. Knoll and F. Keilmann, Nature 399, 134 (1999).
[CrossRef]

Opt. Express (1)

Phys. Rev. (2)

R. H. Ritchie, Phys. Rev. 106, 874 (1957).
[CrossRef]

H. A. Bethe, Phys. Rev. 66, 163 (1944).
[CrossRef]

Phys. Rev. Lett. (3)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef] [PubMed]

R. Hillenbrand and F. Keilmann, Phys. Rev. Lett. 85, 3029 (2000).
[CrossRef] [PubMed]

Phys. Today (1)

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61, 44 (2008).
[CrossRef]

Science (9)

J. B. Pendry, Science 285, 1687 (1999).
[CrossRef]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534(2005).
[CrossRef] [PubMed]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, Science 313, 1595 (2006).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef] [PubMed]

W. Barnes and R. Sambles, Science 305, 785 (2004).
[CrossRef] [PubMed]

Z. W. Liu, H. Lee, C. Sun, and X. Zhang, Science 315, 1686(2007).
[CrossRef] [PubMed]

R. Merlin, Science 317, 927 (2007).
[CrossRef] [PubMed]

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511(2008).
[CrossRef] [PubMed]

Other (10)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

M. Born and E. Wolf, Principles of Optics (Pergamon, 2005).

F. J. Duarte, Tunable Laser Optics (Academic, 2003).

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[CrossRef]

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K. R. Chen, W. H. Chu, H. C. Fang, C. P. Liu, C. H. Huang, H. C. Chui, C. H. Chuang, Y. L. Lo, C. Y. Lin, S. J. Chang, F. Y. Hung, H. H. Hwuang, and A. Y.-G. Fuh, arXiv:0901.1731v1.

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Supplementary Material (2)

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Figures (3)

Fig. 1
Fig. 1

Aperture structure, approach, and simulation result. (a) Schematic diagram of the approach, aperture structure, and the paths of the light transmitted, bent, and focused. (b) Schematic structure of the aperture on a silver film used in the FDTD simulation. The depth, width, and distance in between the periodical grooves at the incident side are 80, 200, and 200 nm , respectively; the slit width is 80 nm ; both the width and depth of grooves at the exit side are 80 nm ; the distance between the slit and the exit groove is 160 nm ; the film thickness is 280 nm ; the thickness and the width of the central strip are 200 nm and 320 nm , respectively. To clarify the possible near-field involvement, the central metal width of 320 nm and the exit width of 480 nm are larger than λ / 2 , 316.5 nm . (c) Snapshot of the H z field at t = t f + 0.12 , where t f is defined in Fig. 2. (d) y profile of the H z [in (c)] and E x fields and the estimated curves of the profile peaks, normalized to the peak at y = 1.175 , as a function proportional to y 1 / 2 (brown long dashed curve and dashed curve) and to y 1 , y 2 , and y 3 (orange long dashed curve, purple dashed curve, green dotted curve) for the fields being the far, mid, and near fields, respectively, according to a dipole source model [15].

Fig. 2
Fig. 2

Profiles and width of the focused light. (a) FWHM versus normalized r profiles of the time-averaged H z field energy (red solid curve) and the snapshot of the H z field energy (blue squares), where r is the y distance from the metal surface. (b) Profiles of the focused H z field energy at the focused time t = t f (red solid curve), t f + 0.12 (blue dashed curve), and t f + 0.29 (green dotted curve).

Fig. 3
Fig. 3

Poynting vector contours and the field profiles. (a) Time-averaged contours of the Poynting vector (i.e., the energy flow) in the y direction. (b) Temporal profiles of the magnetic field H z (red solid curve), the electric field E x (blue dashed curve), and the current J x (green dotted curve) at x = 0 of the central metal surface. (c) x profiles of peak E x (blue dashed curve) and Z H z (red solid curve) fields at t = t f + 0.12 , where | Z | = 0.832 and the phase is three cells or 0.0237 λ . (d) r profiles of the E x field at t = t f (light blue short dashed curve), t = t f + 0.13 (blue dashed curve), and t f + 0.29 (purple short dashed curve and dashed curve) when the FWHM of the H z energy is still smaller than λ / 2 , as well as the Z H z field (red solid curve, the estimated propagating E x field, where | Z | = 0.840 ), the near E x field (dark green dotted curve, the difference of the overall and propagating fields), and the near- E x field for the case of an almost perfect electric conductor (light green dotted curve and short dashed curve).

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