Abstract

We designed and implemented a gradient index metasurface for in-plane focusing of confined terahertz (THz) surface waves. We measured the spatial propagation of the surface waves by two-dimensional mapping of the complex electric field using a THz near-field spectroscope. The surface waves were focused to a diameter of 500 μm after a focal length of approximately 2 mm. In the focus, we measured a field amplitude enhancement of a factor of 3.

© 2013 Optical Society of America

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  1. T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
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  2. J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, Opt. Express 16, 1786 (2008).
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  3. H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
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    [CrossRef]
  5. C. Rau, G. Torosyan, R. Beigang, and K. Nerkararyan, Appl. Phys. Lett. 86, 211119 (2005).
    [CrossRef]
  6. T. H. Isaac, W. L. Barnes, and E. Hendry, Appl. Phys. Lett. 93, 241115 (2008).
    [CrossRef]
  7. M. Theuer, R. Beigang, and D. Grischkowsky, Appl. Phys. Lett. 97, 071106 (2010).
    [CrossRef]
  8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef]
  9. M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, Opt. Express 17, 18184 (2009).
    [CrossRef]
  10. B. Reinhard, O. Paul, R. Beigang, and M. Rahm, Opt. Lett. 35, 1320 (2010).
    [CrossRef]
  11. Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
    [CrossRef]
  12. E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).
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    [CrossRef]
  14. N. C. J. van der Valk and P. C. M. Planken, Appl. Phys. Lett. 81, 1558 (2002).
    [CrossRef]
  15. J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
    [CrossRef]

2012 (1)

B. Reinhard, K. M. Schmitt, V. Wollrab, J. Neu, R. Beigang, and M. Rahm, Appl. Phys. Lett. 100, 221101 (2012).
[CrossRef]

2011 (1)

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

2010 (4)

M. Theuer, R. Beigang, and D. Grischkowsky, Appl. Phys. Lett. 97, 071106 (2010).
[CrossRef]

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

B. Reinhard, O. Paul, R. Beigang, and M. Rahm, Opt. Lett. 35, 1320 (2010).
[CrossRef]

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
[CrossRef]

2009 (1)

2008 (3)

2007 (1)

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

2005 (1)

C. Rau, G. Torosyan, R. Beigang, and K. Nerkararyan, Appl. Phys. Lett. 86, 211119 (2005).
[CrossRef]

2003 (1)

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

2002 (1)

N. C. J. van der Valk and P. C. M. Planken, Appl. Phys. Lett. 81, 1558 (2002).
[CrossRef]

Agrafiotis, S.

Andreev, G. O.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

Averitt, R.

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

Averitt, R. D.

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Barnes, W. L.

T. H. Isaac, W. L. Barnes, and E. Hendry, Appl. Phys. Lett. 93, 241115 (2008).
[CrossRef]

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

Basov, D. N.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

Beigang, R.

B. Reinhard, K. M. Schmitt, V. Wollrab, J. Neu, R. Beigang, and M. Rahm, Appl. Phys. Lett. 100, 221101 (2012).
[CrossRef]

M. Theuer, R. Beigang, and D. Grischkowsky, Appl. Phys. Lett. 97, 071106 (2010).
[CrossRef]

B. Reinhard, O. Paul, R. Beigang, and M. Rahm, Opt. Lett. 35, 1320 (2010).
[CrossRef]

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
[CrossRef]

O. Paul, C. Imhof, B. Reinhard, R. Zengerle, and R. Beigang, Opt. Express 16, 6736 (2008).
[CrossRef]

C. Rau, G. Torosyan, R. Beigang, and K. Nerkararyan, Appl. Phys. Lett. 86, 211119 (2005).
[CrossRef]

Beruete, M.

Brener, I.

Cho, S. Y.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

Dereux, A.

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

Driscoll, T.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

Ebbesen, T. W.

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

Ekmekci, E.

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Falcone, F.

Fan, K.

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Grischkowsky, D.

M. Theuer, R. Beigang, and D. Grischkowsky, Appl. Phys. Lett. 97, 071106 (2010).
[CrossRef]

Han, J.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

Hendry, E.

T. H. Isaac, W. L. Barnes, and E. Hendry, Appl. Phys. Lett. 93, 241115 (2008).
[CrossRef]

Imhof, C.

Isaac, T. H.

T. H. Isaac, W. L. Barnes, and E. Hendry, Appl. Phys. Lett. 93, 241115 (2008).
[CrossRef]

Jokerst, N. M.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

Kaplan, D. L.

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Krolla, B.

Liu, M.

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Maier, S. A.

Minowa, Y.

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

Mondia, J. P.

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Nagai, M.

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

Navarro-Cía, M.

Nerkararyan, K.

C. Rau, G. Torosyan, R. Beigang, and K. Nerkararyan, Appl. Phys. Lett. 86, 211119 (2005).
[CrossRef]

Neu, J.

B. Reinhard, K. M. Schmitt, V. Wollrab, J. Neu, R. Beigang, and M. Rahm, Appl. Phys. Lett. 100, 221101 (2012).
[CrossRef]

J. Neu, B. Krolla, O. Paul, B. Reinhard, R. Beigang, and M. Rahm, Opt. Express 18, 27748 (2010).
[CrossRef]

O’Hara, J. F.

Omenetto, F. G.

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Padilla, W. J.

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Palit, S.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

Paul, O.

Planken, P. C. M.

N. C. J. van der Valk and P. C. M. Planken, Appl. Phys. Lett. 81, 1558 (2002).
[CrossRef]

Rahm, M.

Rau, C.

C. Rau, G. Torosyan, R. Beigang, and K. Nerkararyan, Appl. Phys. Lett. 86, 211119 (2005).
[CrossRef]

Reinhard, B.

Schmitt, K. M.

B. Reinhard, K. M. Schmitt, V. Wollrab, J. Neu, R. Beigang, and M. Rahm, Appl. Phys. Lett. 100, 221101 (2012).
[CrossRef]

Singh, R.

Smirnova, E.

Smith, D. R.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

Sorolla, M.

Strikwerda, A.

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

Strikwerda, A. C.

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Tanaka, K.

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

Tao, H.

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Taylor, A. J.

Theuer, M.

M. Theuer, R. Beigang, and D. Grischkowsky, Appl. Phys. Lett. 97, 071106 (2010).
[CrossRef]

Torosyan, G.

C. Rau, G. Torosyan, R. Beigang, and K. Nerkararyan, Appl. Phys. Lett. 86, 211119 (2005).
[CrossRef]

van der Valk, N. C. J.

N. C. J. van der Valk and P. C. M. Planken, Appl. Phys. Lett. 81, 1558 (2002).
[CrossRef]

Wollrab, V.

B. Reinhard, K. M. Schmitt, V. Wollrab, J. Neu, R. Beigang, and M. Rahm, Appl. Phys. Lett. 100, 221101 (2012).
[CrossRef]

Zengerle, R.

Zhang, W.

Zhang, X.

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

Appl. Phys. Lett. (7)

H. Tao, A. C. Strikwerda, M. Liu, J. P. Mondia, E. Ekmekci, K. Fan, D. L. Kaplan, W. J. Padilla, X. Zhang, R. D. Averitt, and F. G. Omenetto, Appl. Phys. Lett. 97, 261909 (2010).
[CrossRef]

B. Reinhard, K. M. Schmitt, V. Wollrab, J. Neu, R. Beigang, and M. Rahm, Appl. Phys. Lett. 100, 221101 (2012).
[CrossRef]

C. Rau, G. Torosyan, R. Beigang, and K. Nerkararyan, Appl. Phys. Lett. 86, 211119 (2005).
[CrossRef]

T. H. Isaac, W. L. Barnes, and E. Hendry, Appl. Phys. Lett. 93, 241115 (2008).
[CrossRef]

M. Theuer, R. Beigang, and D. Grischkowsky, Appl. Phys. Lett. 97, 071106 (2010).
[CrossRef]

N. C. J. van der Valk and P. C. M. Planken, Appl. Phys. Lett. 81, 1558 (2002).
[CrossRef]

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

IEEE Trans. Terahertz Sci. Technol. (1)

Y. Minowa, M. Nagai, H. Tao, K. Fan, A. Strikwerda, X. Zhang, R. Averitt, and K. Tanaka, IEEE Trans. Terahertz Sci. Technol. 1, 441 (2011).
[CrossRef]

Nature (1)

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

Opt. Express (4)

Opt. Lett. (1)

Other (1)

E. Hecht, Optics, 4th ed. (Addison Wesley, 2002).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Unit cell of the metamaterial: d=52μm, r=23.5μm, and α1=53.7°. The width of the metal strips and the gap between the inner and outer ring are equal to 5 μm. The opening angle α2 is varied to change the refractive index. Vectors E, H, and β indicate the directions of the electric field, magnetic field, and wave vector of the localized waves, respectively. (b) Dispersion relation of the surface waves for different values of the opening angle α2 (16° to 226° in steps of 30°). (c) Dependence of the refractive index of the metamaterial structure on the opening angle α2 at a frequency of 0.5 THz. The data in (b) and (c) are taken from numerical calculations performed with CST Microwave Studio simulation software.

Fig. 2.
Fig. 2.

Layout of the GRIN metasurface with an artificial grating in the excitation region and a parabolic refractive index profile in the GRIN region where the confined surface waves propagate and are focused. The refractive index n varies between 1.5 (center line) and 1.1 (edge lines). The focal length is f=2.15mm. The dashed white line denotes the region that we mapped in the near-field measurement.

Fig. 3.
Fig. 3.

Schematic of the near-field spectroscope. The GaP detector crystal is brought in direct contact with the metamaterial. The detector unit can be moved in two dimensions relative to the sample, while the position of the THz beam is fixed.

Fig. 4.
Fig. 4.

Measured electric near field of the GRIN metasurface. The real part of the y component of the complex electric field amplitude at 0.45 THz is shown.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

n(y)=ncΔn4y2w2,
f=π4wnc2Δn.

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