Abstract

Excellent light-directing abilities are demonstrated by well-designed three-dimensional micrometer-sized parabolic mirrors that are fabricated by direct laser writing and subsequent surface coating of titanium and silver. The full-width at half-maximum of the measured light divergence for the mirrors with different geometries is much less than 20 μm, even when the height is up to 130 μm. These results are beneficial for developing highly collimating light-emitting diodes. The simulation for the mirrors reveals that the electric field intensity distribution is highly confined toward the central axis of the mirrors, which is consistent with the experimental results.

© 2013 Optical Society of America

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References

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  1. H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
    [CrossRef]
  8. M. Straub and M. Gu, Opt. Lett. 27, 1824 (2002).
    [CrossRef]
  9. Z. Gan, Y. Cao, R. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  14. www.lumerical.com .
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  16. B. H. Jia, X. S. Gan, and M. Gu, Appl. Phys. Lett. 86, 131110 (2005).
    [CrossRef]
  17. M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

2013 (3)

E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman, and H. A. Atwater, Light 2, e45 (2013).
[CrossRef]

Z. Gan, Y. Cao, R. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).

W. S. Yan, N. Stokes, B. H. Jia, and M. Gu, Opt. Lett. 38, 395 (2013).
[CrossRef]

2012 (1)

M. A. Green and S. Pillai, Nat. Photonics 6, 130 (2012).
[CrossRef]

2011 (2)

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

H. Lin, B. H. Jia, and M. Gu, Opt. Lett. 36, 406 (2011).
[CrossRef]

2010 (1)

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

2008 (1)

S. Tanriseven, P. Maaskant, and B. Corbett, Appl. Phys. Lett. 92, 123501 (2008).
[CrossRef]

2005 (1)

B. H. Jia, X. S. Gan, and M. Gu, Appl. Phys. Lett. 86, 131110 (2005).
[CrossRef]

2002 (1)

2001 (1)

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
[CrossRef]

Atwater, H. A.

E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman, and H. A. Atwater, Light 2, e45 (2013).
[CrossRef]

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

Atwater, J. H.

E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman, and H. A. Atwater, Light 2, e45 (2013).
[CrossRef]

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

Cao, Y.

Z. Gan, Y. Cao, R. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).

Chen, X.

X. Chen, B. H. Jia, Y. N. Zhang, and M. Gu, Light: Sci. Appl.2, e92 (2013).
[CrossRef]

Corbett, B.

S. Tanriseven, P. Maaskant, and B. Corbett, Appl. Phys. Lett. 92, 123501 (2008).
[CrossRef]

Evans, R.

Z. Gan, Y. Cao, R. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).

Gan, X. S.

B. H. Jia, X. S. Gan, and M. Gu, Appl. Phys. Lett. 86, 131110 (2005).
[CrossRef]

Gan, Z.

Z. Gan, Y. Cao, R. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).

Garcia de Abajo, J.

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

Green, M. A.

M. A. Green and S. Pillai, Nat. Photonics 6, 130 (2012).
[CrossRef]

Gu, M.

W. S. Yan, N. Stokes, B. H. Jia, and M. Gu, Opt. Lett. 38, 395 (2013).
[CrossRef]

Z. Gan, Y. Cao, R. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).

H. Lin, B. H. Jia, and M. Gu, Opt. Lett. 36, 406 (2011).
[CrossRef]

B. H. Jia, X. S. Gan, and M. Gu, Appl. Phys. Lett. 86, 131110 (2005).
[CrossRef]

M. Straub and M. Gu, Opt. Lett. 27, 1824 (2002).
[CrossRef]

X. Chen, B. H. Jia, Y. N. Zhang, and M. Gu, Light: Sci. Appl.2, e92 (2013).
[CrossRef]

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

Jia, B. H.

W. S. Yan, N. Stokes, B. H. Jia, and M. Gu, Opt. Lett. 38, 395 (2013).
[CrossRef]

H. Lin, B. H. Jia, and M. Gu, Opt. Lett. 36, 406 (2011).
[CrossRef]

B. H. Jia, X. S. Gan, and M. Gu, Appl. Phys. Lett. 86, 131110 (2005).
[CrossRef]

X. Chen, B. H. Jia, Y. N. Zhang, and M. Gu, Light: Sci. Appl.2, e92 (2013).
[CrossRef]

Kawata, S.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
[CrossRef]

Kosten, E.

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

Kosten, E. D.

E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman, and H. A. Atwater, Light 2, e45 (2013).
[CrossRef]

Lin, H.

Maaskant, P.

S. Tanriseven, P. Maaskant, and B. Corbett, Appl. Phys. Lett. 92, 123501 (2008).
[CrossRef]

Palik, E. D.

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

Parsons, J.

E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman, and H. A. Atwater, Light 2, e45 (2013).
[CrossRef]

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

Pillai, S.

M. A. Green and S. Pillai, Nat. Photonics 6, 130 (2012).
[CrossRef]

Polman, A.

E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman, and H. A. Atwater, Light 2, e45 (2013).
[CrossRef]

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

Spinelli, P.

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

Stokes, N.

Straub, M.

Sun, H. B.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
[CrossRef]

Takada, K.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
[CrossRef]

Tanaka, T.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
[CrossRef]

Tanriseven, S.

S. Tanriseven, P. Maaskant, and B. Corbett, Appl. Phys. Lett. 92, 123501 (2008).
[CrossRef]

van de Groep, J.

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

Van Lare, C.

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

Welford, W. T.

W. T. Welford and R. Winston, The Optics of Nonimaging Concentrators (Academic, 1978).

Winston, R.

W. T. Welford and R. Winston, The Optics of Nonimaging Concentrators (Academic, 1978).

Yan, W. S.

Zhang, Y. N.

X. Chen, B. H. Jia, Y. N. Zhang, and M. Gu, Light: Sci. Appl.2, e92 (2013).
[CrossRef]

Appl. Phys. Lett. (3)

J. H. Atwater, P. Spinelli, E. Kosten, J. Parsons, C. Van Lare, J. van de Groep, J. Garcia de Abajo, A. Polman, and H. A. Atwater, Appl. Phys. Lett. 99, 151113 (2011).
[CrossRef]

S. Tanriseven, P. Maaskant, and B. Corbett, Appl. Phys. Lett. 92, 123501 (2008).
[CrossRef]

B. H. Jia, X. S. Gan, and M. Gu, Appl. Phys. Lett. 86, 131110 (2005).
[CrossRef]

Light (1)

E. D. Kosten, J. H. Atwater, J. Parsons, A. Polman, and H. A. Atwater, Light 2, e45 (2013).
[CrossRef]

Nat. Commun. (1)

Z. Gan, Y. Cao, R. Evans, and M. Gu, Nat. Commun. 4, 2061 (2013).

Nat. Mater. (1)

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

Nat. Photonics (1)

M. A. Green and S. Pillai, Nat. Photonics 6, 130 (2012).
[CrossRef]

Nature (1)

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, Nature 412, 697 (2001).
[CrossRef]

Opt. Lett. (3)

Other (6)

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

X. Chen, B. H. Jia, Y. N. Zhang, and M. Gu, Light: Sci. Appl.2, e92 (2013).
[CrossRef]

W. T. Welford and R. Winston, The Optics of Nonimaging Concentrators (Academic, 1978).

www.lumerical.com .

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

http://www.infiniled.com/ .

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Figures (4)

Fig. 1.
Fig. 1.

SEM images of the fabricated single mirrors and mirror arrays with metal coating. (a) Three single mirrors with the bottom diameters of 1.0, 1.2, and 1.5 μm, respectively (from left to right). (b) Separate 4-by-5 mirrors in a square array. (c) Compact hexagonal 10-by-10 mirror array. (d) Cross-section image of FIB cut of mirrors.

Fig. 2.
Fig. 2.

Light-directing abilities measured for the mirrors and holes as a function of height. The three mirrors named mirrors Nos. 1, 2, and 3 have diameters of the drilled holes of 1.0, 1.2, and 1.5 μm, respectively. The three reference holes named bare No. 1, 2, and 3 have diameters of 1.0, 1.2, and 1.5 μm, respectively.

Fig. 3.
Fig. 3.

Cross-sectional electric field intensity distribution (|E(x,z)|2) for mirror No. 2, where the height (H) of the mirror is indicated.

Fig. 4.
Fig. 4.

Electric field intensity (|E(x,y)|2) distributions in the x–y planes at different heights. The images (a)–(c) are from the simulation, and the images (d)–(f) are from the measurement at the heights of 50, 90, and 130 μm. (g) Comparison of the FWHM between the simulation and experiment at the five heights of 50, 70, 90, 110, and 130 μm, where the measurement error bars are given.

Equations (3)

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

rtop=rbott/sinθ,
H=(rtop+rbott)/tanθ,
(rcosθ+zsinθ)2+rbott(1+sinθ)2r,2rbottcosθ(2+sinθ)zrbott2(1+sinθ)(3+sinθ)=0,

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