Sub-wavelength focusing meta-lens

Tapashree Roy; Edward T. F. Rogers; Nikolay I. Zheludev

doi:10.1364/OE.21.007577

Sub-wavelength focusing meta-lens

Tapashree Roy, Edward T. F. Rogers, and Nikolay I. Zheludev

Optics Express
Vol. 21,
Issue 6,
pp. 7577-7582
(2013)
•https://doi.org/10.1364/OE.21.007577

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Tapashree Roy, Edward T. F. Rogers, and Nikolay I. Zheludev, "Sub-wavelength focusing meta-lens," Opt. Express 21, 7577-7582 (2013)

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Abstract

We show that a planar plasmonic metamaterial with spatially variable meta-atom parameters can focus transmitted light into sub-wavelength hot-spots located beyond the near-field of the metamaterial. By nano-structuring a gold film we created an array of meta-lenses generating foci of 160 nm (0.2λ) in diameter when illuminated by a wavelength of 800 nm. We attribute the occurrence of sub-wavelength hotspots beyond the near field to the phenomenon of superoscillation.

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References

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Publication

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]
E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]
M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. Math. Gen. 39(22), 6965–6977 (2006).
[Crossref]
F. M. Huang, N. Zheludev, Y. Chen, and F. Javier Garcia de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007).
[Crossref]
B. Walther, C. Helgert, C. Rockstuhl, and T. Pertsch, “Diffractive optical elements based on plasmonic metamaterials,” Appl. Phys. Lett. 98(19), 191101 (2011).
[Crossref]
B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E. B. Kley, F. Lederer, A. Tünnermann, and T. Pertsch, “Spatial and spectral light shaping with metamaterials,” Adv. Mater. 24(47), 6300–6304 (2012).
[Crossref] [PubMed]
N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]
F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]
N. I. Zheludev, “What diffraction limit?” Nat. Mater. 7(6), 420–422 (2008).
[Crossref] [PubMed]
X. Wang, J. Fu, X. Liu, and L.-M. Tong, “Subwavelength focusing by a micro/nanofiber array,” J. Opt. Soc. Am. A 26(8), 1827–1833 (2009).
[Crossref] [PubMed]
R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102(20), 207402 (2009).
[Crossref] [PubMed]
D. Choi, Y. Lim, S. Roh, I.-M. Lee, J. Jung, and B. Lee, “Optical beam focusing with a metal slit array arranged along a semicircular surface and its optimization with a genetic algorithm,” Appl. Opt. 49(7), A30–A35 (2010).
[Crossref] [PubMed]
M. H. Wu and G. M. Whitesides, “Fabrication of arrays of two-dimensional micropatterns using microspheres as lenses for projection photolithography,” Appl. Phys. Lett. 78(16), 2273 (2001).
[Crossref]
E. Plum, K. Tanaka, W. T. Chen, V. A. Fedotov, D. P. Tsai, and N. I. Zheludev, “A combinatorial approach to metamaterials discovery,” J. Opt. 13(5), 055102 (2011).
[Crossref]
H. F. Talbot, “Facts relating to optical science. no. IV,” Philosophical Magazine Series 3 9(56), 401–407 (1836).
[Crossref]
P. Zhou and J. H. Burge, “Analysis of wavefront propagation using the Talbot effect,” Appl. Opt. 49(28), 5351–5359 (2010).
[Crossref] [PubMed]

2012 (3)

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012).
[Crossref] [PubMed]

B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E. B. Kley, F. Lederer, A. Tünnermann, and T. Pertsch, “Spatial and spectral light shaping with metamaterials,” Adv. Mater. 24(47), 6300–6304 (2012).
[Crossref] [PubMed]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref] [PubMed]

2011 (3)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

E. Plum, K. Tanaka, W. T. Chen, V. A. Fedotov, D. P. Tsai, and N. I. Zheludev, “A combinatorial approach to metamaterials discovery,” J. Opt. 13(5), 055102 (2011).
[Crossref]

B. Walther, C. Helgert, C. Rockstuhl, and T. Pertsch, “Diffractive optical elements based on plasmonic metamaterials,” Appl. Phys. Lett. 98(19), 191101 (2011).
[Crossref]

2010 (2)

P. Zhou and J. H. Burge, “Analysis of wavefront propagation using the Talbot effect,” Appl. Opt. 49(28), 5351–5359 (2010).
[Crossref] [PubMed]

D. Choi, Y. Lim, S. Roh, I.-M. Lee, J. Jung, and B. Lee, “Optical beam focusing with a metal slit array arranged along a semicircular surface and its optimization with a genetic algorithm,” Appl. Opt. 49(7), A30–A35 (2010).
[Crossref] [PubMed]

2009 (2)

X. Wang, J. Fu, X. Liu, and L.-M. Tong, “Subwavelength focusing by a micro/nanofiber array,” J. Opt. Soc. Am. A 26(8), 1827–1833 (2009).
[Crossref] [PubMed]

R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102(20), 207402 (2009).
[Crossref] [PubMed]

2008 (1)

N. I. Zheludev, “What diffraction limit?” Nat. Mater. 7(6), 420–422 (2008).
[Crossref] [PubMed]

2007 (1)

F. M. Huang, N. Zheludev, Y. Chen, and F. Javier Garcia de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007).
[Crossref]

2006 (1)

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. Math. Gen. 39(22), 6965–6977 (2006).
[Crossref]

2001 (1)

M. H. Wu and G. M. Whitesides, “Fabrication of arrays of two-dimensional micropatterns using microspheres as lenses for projection photolithography,” Appl. Phys. Lett. 78(16), 2273 (2001).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1836 (1)

H. F. Talbot, “Facts relating to optical science. no. IV,” Philosophical Magazine Series 3 9(56), 401–407 (1836).
[Crossref]

Aieta, F.

Berry, M. V.

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. Math. Gen. 39(22), 6965–6977 (2006).
[Crossref]

Blanchard, R.

Burge, J. H.

P. Zhou and J. H. Burge, “Analysis of wavefront propagation using the Talbot effect,” Appl. Opt. 49(28), 5351–5359 (2010).
[Crossref] [PubMed]

Capasso, F.

Chad, J. E.

Chen, W. T.

E. Plum, K. Tanaka, W. T. Chen, V. A. Fedotov, D. P. Tsai, and N. I. Zheludev, “A combinatorial approach to metamaterials discovery,” J. Opt. 13(5), 055102 (2011).
[Crossref]

Chen, Y.

F. M. Huang, N. Zheludev, Y. Chen, and F. Javier Garcia de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007).
[Crossref]

Choi, D.

Dennis, M. R.

Eilenberger, F.

Fedotov, V. A.

E. Plum, K. Tanaka, W. T. Chen, V. A. Fedotov, D. P. Tsai, and N. I. Zheludev, “A combinatorial approach to metamaterials discovery,” J. Opt. 13(5), 055102 (2011).
[Crossref]

Fu, J.

X. Wang, J. Fu, X. Liu, and L.-M. Tong, “Subwavelength focusing by a micro/nanofiber array,” J. Opt. Soc. Am. A 26(8), 1827–1833 (2009).
[Crossref] [PubMed]

Gaburro, Z.

Genevet, P.

Gordon, R.

R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102(20), 207402 (2009).
[Crossref] [PubMed]

Helgert, C.

B. Walther, C. Helgert, C. Rockstuhl, and T. Pertsch, “Diffractive optical elements based on plasmonic metamaterials,” Appl. Phys. Lett. 98(19), 191101 (2011).
[Crossref]

Huang, F. M.

F. M. Huang, N. Zheludev, Y. Chen, and F. Javier Garcia de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007).
[Crossref]

Javier Garcia de Abajo, F.

F. M. Huang, N. Zheludev, Y. Chen, and F. Javier Garcia de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007).
[Crossref]

Jung, J.

Kats, M. A.

Kley, E. B.

Lederer, F.

Lee, B.

Lee, I.-M.

Lim, Y.

Lindberg, J.

Liu, X.

X. Wang, J. Fu, X. Liu, and L.-M. Tong, “Subwavelength focusing by a micro/nanofiber array,” J. Opt. Soc. Am. A 26(8), 1827–1833 (2009).
[Crossref] [PubMed]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Pertsch, T.

B. Walther, C. Helgert, C. Rockstuhl, and T. Pertsch, “Diffractive optical elements based on plasmonic metamaterials,” Appl. Phys. Lett. 98(19), 191101 (2011).
[Crossref]

Plum, E.

E. Plum, K. Tanaka, W. T. Chen, V. A. Fedotov, D. P. Tsai, and N. I. Zheludev, “A combinatorial approach to metamaterials discovery,” J. Opt. 13(5), 055102 (2011).
[Crossref]

Popescu, S.

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. Math. Gen. 39(22), 6965–6977 (2006).
[Crossref]

Rockstuhl, C.

B. Walther, C. Helgert, C. Rockstuhl, and T. Pertsch, “Diffractive optical elements based on plasmonic metamaterials,” Appl. Phys. Lett. 98(19), 191101 (2011).
[Crossref]

Rogers, E. T. F.

Roh, S.

Roy, T.

Savo, S.

Setzpfandt, F.

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science. no. IV,” Philosophical Magazine Series 3 9(56), 401–407 (1836).
[Crossref]

Tanaka, K.

E. Plum, K. Tanaka, W. T. Chen, V. A. Fedotov, D. P. Tsai, and N. I. Zheludev, “A combinatorial approach to metamaterials discovery,” J. Opt. 13(5), 055102 (2011).
[Crossref]

Tetienne, J. P.

Tong, L.-M.

X. Wang, J. Fu, X. Liu, and L.-M. Tong, “Subwavelength focusing by a micro/nanofiber array,” J. Opt. Soc. Am. A 26(8), 1827–1833 (2009).
[Crossref] [PubMed]

Tsai, D. P.

E. Plum, K. Tanaka, W. T. Chen, V. A. Fedotov, D. P. Tsai, and N. I. Zheludev, “A combinatorial approach to metamaterials discovery,” J. Opt. 13(5), 055102 (2011).
[Crossref]

Tünnermann, A.

Walther, B.

B. Walther, C. Helgert, C. Rockstuhl, and T. Pertsch, “Diffractive optical elements based on plasmonic metamaterials,” Appl. Phys. Lett. 98(19), 191101 (2011).
[Crossref]

Wang, X.

X. Wang, J. Fu, X. Liu, and L.-M. Tong, “Subwavelength focusing by a micro/nanofiber array,” J. Opt. Soc. Am. A 26(8), 1827–1833 (2009).
[Crossref] [PubMed]

Whitesides, G. M.

Wu, M. H.

Yu, N.

Zheludev, N.

F. M. Huang, N. Zheludev, Y. Chen, and F. Javier Garcia de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007).
[Crossref]

Zheludev, N. I.

E. Plum, K. Tanaka, W. T. Chen, V. A. Fedotov, D. P. Tsai, and N. I. Zheludev, “A combinatorial approach to metamaterials discovery,” J. Opt. 13(5), 055102 (2011).
[Crossref]

N. I. Zheludev, “What diffraction limit?” Nat. Mater. 7(6), 420–422 (2008).
[Crossref] [PubMed]

Zhou, P.

P. Zhou and J. H. Burge, “Analysis of wavefront propagation using the Talbot effect,” Appl. Opt. 49(28), 5351–5359 (2010).
[Crossref] [PubMed]

Adv. Mater. (1)

Appl. Opt. (2)

P. Zhou and J. H. Burge, “Analysis of wavefront propagation using the Talbot effect,” Appl. Opt. 49(28), 5351–5359 (2010).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

F. M. Huang, N. Zheludev, Y. Chen, and F. Javier Garcia de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90(9), 091119 (2007).
[Crossref]

B. Walther, C. Helgert, C. Rockstuhl, and T. Pertsch, “Diffractive optical elements based on plasmonic metamaterials,” Appl. Phys. Lett. 98(19), 191101 (2011).
[Crossref]

J. Opt. (1)

E. Plum, K. Tanaka, W. T. Chen, V. A. Fedotov, D. P. Tsai, and N. I. Zheludev, “A combinatorial approach to metamaterials discovery,” J. Opt. 13(5), 055102 (2011).
[Crossref]

J. Opt. Soc. Am. A (1)

X. Wang, J. Fu, X. Liu, and L.-M. Tong, “Subwavelength focusing by a micro/nanofiber array,” J. Opt. Soc. Am. A 26(8), 1827–1833 (2009).
[Crossref] [PubMed]

J. Phys. Math. Gen. (1)

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. Math. Gen. 39(22), 6965–6977 (2006).
[Crossref]

Nano Lett. (1)

Nat. Mater. (2)

N. I. Zheludev, “What diffraction limit?” Nat. Mater. 7(6), 420–422 (2008).
[Crossref] [PubMed]

Philosophical Magazine Series 3 (1)

H. F. Talbot, “Facts relating to optical science. no. IV,” Philosophical Magazine Series 3 9(56), 401–407 (1836).
[Crossref]

Phys. Rev. Lett. (2)

R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102(20), 207402 (2009).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Science (1)

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Fig. 1

Comparison of design and performance of (a) an hypothetical continuous superoscillatory mask, and (b) superoscillatory meta-lens generator, both producing arbitrarily small hot spots at post-evanescent distances from the surface.

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Fig. 2

Regular metamaterial vs. meta-lens array: (a) Section of an infinite planar array of ring meta-atoms. (b) Phase and (c) intensity, over 3 x 3 meta-atoms, at 2λ from the surface. (d) Phase and (e) intensity in the propagation direction over the 3 x 3 meta-atoms. (f) Section of an infinite meta-lens array. (g) Curved phase front and (h) focused intensity profile over a meta-lens unit, at 2λ from the surface. Note that phase wrapping occurs in (g). (i) Phase profile like that of a converging lens and (j) intensity showing a focal spot in the propagation direction over a meta-lens unit.

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Fig. 3

SEM image of the combinatorial meta-lens sample: (a) Matrix of nine samples with varying inter-ring spacing and ring radii. (b) Sample A3 consisting of 11x11 meta-lens units; a single unit is marked with red box.

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Fig. 4

Experimental focusing with meta-lens A3: (a) Intensity distribution on the surface of the meta-lens array; (right) over a meta-lens unit. (b) Simulated (top) and experimental (bottom) intensity plots over one meta-lens unit showing repeated formation of focal spots along the propagation direction with Talbot distance z_T. (c) FWHM of a spot along the propagation distance. The focal spot is below diffraction limit (dashed line). (d) Zoom of (b) showing low intensity region over which focal spot is smaller than the diffraction limit.

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Fig. 5

Long-range performance of a superoscillatory meta-device: (a) Experimentally measured intensity and (b) FWHM from a sample formed by 30 by 30 meta-lenses. Hot-spots measuring ~0.2λ at 11.7 μm from the lens with Talbot distance of 3.8 μm are observed.

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Abstract

References

2012 (3)

2011 (3)

2010 (2)

2009 (2)

2008 (1)

2007 (1)

2006 (1)

2001 (1)

2000 (1)

1836 (1)

Aieta, F.

Berry, M. V.

Blanchard, R.

Burge, J. H.

Capasso, F.

Chad, J. E.

Chen, W. T.

Chen, Y.

Choi, D.

Dennis, M. R.

Eilenberger, F.

Fedotov, V. A.

Fu, J.

Gaburro, Z.

Genevet, P.

Gordon, R.

Helgert, C.

Huang, F. M.

Javier Garcia de Abajo, F.

Jung, J.

Kats, M. A.

Kley, E. B.

Lederer, F.

Lee, B.

Lee, I.-M.

Lim, Y.

Lindberg, J.

Liu, X.

Pendry, J. B.

Pertsch, T.

Plum, E.

Popescu, S.

Rockstuhl, C.

Rogers, E. T. F.

Roh, S.

Roy, T.

Savo, S.

Setzpfandt, F.

Talbot, H. F.

Tanaka, K.

Tetienne, J. P.

Tong, L.-M.

Tsai, D. P.

Tünnermann, A.

Walther, B.

Wang, X.

Whitesides, G. M.

Wu, M. H.

Yu, N.

Zheludev, N.

Zheludev, N. I.

Zhou, P.

Adv. Mater. (1)

Appl. Opt. (2)

Appl. Phys. Lett. (3)

J. Opt. (1)

J. Opt. Soc. Am. A (1)

J. Phys. Math. Gen. (1)

Nano Lett. (1)

Nat. Mater. (2)

Philosophical Magazine Series 3 (1)

Phys. Rev. Lett. (2)

Science (1)

Cited By

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