Abstract

We present a subwavelength unit cell constructed of nanoantennas which can independently manipulate the amplitude and phase of an incident wave. The unit cell is made of two layers of scatterers, where the first can tune the amplitude and the second the desired phase. We show that metasurfaces composed of this unit cell can be used to achieve arbitrary transmission amplitude and phase profiles. Furthermore, we show that graded metasurfaces nanoantennas along with Fourier transform blocks can be used to realize unique linear space invariant transfer functions. This approach opens opportunity for light processing on flat platforms. Novel examples are presented.

© 2013 Optical Society of America

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References

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  1. H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
    [CrossRef]
  2. F. M. Huang, N. Zheludev, Y. Chen, and F. J. G. de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett. 90, 091119 (2007).
    [CrossRef]
  3. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
    [CrossRef]
  4. A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express 18, 123–133 (2010).
    [CrossRef]
  5. L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10, 1936–1940 (2010).
    [CrossRef]
  6. D. J. Shelton, K. R. Coffey, and G. D. Boreman, “Experimental demonstration of tunable phase in a thermochromic infrared-reflectarray metamaterial,” Opt. Express 18, 1330–1335 (2010).
    [CrossRef]
  7. E. H. Khoo, E. P. Li, and K. B. Crozier, “Plasmonic wave plate based on subwavelength nanoslits,” Opt. Lett. 36, 2498–2500 (2011).
    [CrossRef]
  8. B. Memarzadeh and H. Mosallaei, “Array of planar plasmonic scatterers functioning as light concentrator,” Opt. Lett. 36, 2569–2571 (2011).
    [CrossRef]
  9. 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, 333–337 (2011).
    [CrossRef]
  10. Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
    [CrossRef]
  11. A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett. 37, 1820–1822 (2012).
    [CrossRef]
  12. E. Carrasco and J. Perruisseau-Carrier, “Reflectarray antenna at terahertz using graphene,” IEEE Antennas Wireless Propag. Lett. 12, 253–256 (2013).
    [CrossRef]
  13. M. Farmahini-Farahani and H. Mosallaei, “Birefringent reflectarray metasurface for beam engineering in infrared,” Opt. Lett. 38, 462–464 (2013).
    [CrossRef]
  14. T. Niu, W. Withayachumnankul, B. S. Y. Ung, H. Menekse, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Experimental demonstration of reflectarray antennas at terahertz frequencies,” Opt. Express 21, 2875–2889 (2013).
    [CrossRef]
  15. M. V. P. C. Gomez-Reino and C. Bao, Gradient-Index Optics (Springer, 2002).
  16. A. Vakil and N. Engheta, “Fourier optics on graphene,” Phys. Rev. B 85, 075434 (2012).
    [CrossRef]
  17. www.Lumerical.com .
  18. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  19. N. Engheta, “Functionalizing metamaterials as metasystems,” presented at 2012 MRS Fall Meeting and Exhibit, Boston, Massachusetts, November27, 2012.
  20. Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D 43, 055404 (2010).
    [CrossRef]

2013 (3)

2012 (2)

A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett. 37, 1820–1822 (2012).
[CrossRef]

A. Vakil and N. Engheta, “Fourier optics on graphene,” Phys. Rev. B 85, 075434 (2012).
[CrossRef]

2011 (4)

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, 333–337 (2011).
[CrossRef]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[CrossRef]

E. H. Khoo, E. P. Li, and K. B. Crozier, “Plasmonic wave plate based on subwavelength nanoslits,” Opt. Lett. 36, 2498–2500 (2011).
[CrossRef]

B. Memarzadeh and H. Mosallaei, “Array of planar plasmonic scatterers functioning as light concentrator,” Opt. Lett. 36, 2569–2571 (2011).
[CrossRef]

2010 (4)

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D 43, 055404 (2010).
[CrossRef]

A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express 18, 123–133 (2010).
[CrossRef]

D. J. Shelton, K. R. Coffey, and G. D. Boreman, “Experimental demonstration of tunable phase in a thermochromic infrared-reflectarray metamaterial,” Opt. Express 18, 1330–1335 (2010).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10, 1936–1940 (2010).
[CrossRef]

2009 (1)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

2007 (1)

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

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

Ahmadi, A.

Aieta, F.

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, 333–337 (2011).
[CrossRef]

Alù, A.

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[CrossRef]

Bai, J.

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D 43, 055404 (2010).
[CrossRef]

Bao, C.

M. V. P. C. Gomez-Reino and C. Bao, Gradient-Index Optics (Springer, 2002).

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

Bhaskaran, M.

Boreman, G. D.

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

Capasso, F.

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, 333–337 (2011).
[CrossRef]

Carrasco, E.

E. Carrasco and J. Perruisseau-Carrier, “Reflectarray antenna at terahertz using graphene,” IEEE Antennas Wireless Propag. Lett. 12, 253–256 (2013).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

Chen, Y.

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

Coffey, K. R.

Crozier, K. B.

Cui, T. J.

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D 43, 055404 (2010).
[CrossRef]

de Abajo, F. J. G.

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

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

Ebbesen, T.

H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

Engheta, N.

A. Vakil and N. Engheta, “Fourier optics on graphene,” Phys. Rev. B 85, 075434 (2012).
[CrossRef]

N. Engheta, “Functionalizing metamaterials as metasystems,” presented at 2012 MRS Fall Meeting and Exhibit, Boston, Massachusetts, November27, 2012.

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

Farmahini-Farahani, M.

Fumeaux, C.

Gaburro, Z.

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, 333–337 (2011).
[CrossRef]

Garcia-Vidal, F.

H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

Genevet, P.

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, 333–337 (2011).
[CrossRef]

Ghadarghadr, S.

Goh, X. M.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10, 1936–1940 (2010).
[CrossRef]

Gomez-Reino, M. V. P. C.

M. V. P. C. Gomez-Reino and C. Bao, Gradient-Index Optics (Springer, 2002).

Huang, F. M.

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

Kats, M. A.

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, 333–337 (2011).
[CrossRef]

Khoo, E. H.

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

Li, E. P.

Lin, L.

A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett. 37, 1820–1822 (2012).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10, 1936–1940 (2010).
[CrossRef]

Linke, R.

H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

Martin-Moreno, L.

H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

McGuinness, L. P.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10, 1936–1940 (2010).
[CrossRef]

Mei, Z. L.

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D 43, 055404 (2010).
[CrossRef]

Memarzadeh, B.

Menekse, H.

Mosallaei, H.

Niu, T.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Perruisseau-Carrier, J.

E. Carrasco and J. Perruisseau-Carrier, “Reflectarray antenna at terahertz using graphene,” IEEE Antennas Wireless Propag. Lett. 12, 253–256 (2013).
[CrossRef]

Roberts, A.

A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett. 37, 1820–1822 (2012).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10, 1936–1940 (2010).
[CrossRef]

Shelton, D. J.

Sriram, S.

Tetienne, J.-P.

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, 333–337 (2011).
[CrossRef]

Ung, B. S. Y.

Vakil, A.

A. Vakil and N. Engheta, “Fourier optics on graphene,” Phys. Rev. B 85, 075434 (2012).
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

Withayachumnankul, W.

Yu, N.

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, 333–337 (2011).
[CrossRef]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

Zhao, Y.

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[CrossRef]

Zheludev, N.

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

Appl. Phys. Lett. (1)

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

IEEE Antennas Wireless Propag. Lett. (1)

E. Carrasco and J. Perruisseau-Carrier, “Reflectarray antenna at terahertz using graphene,” IEEE Antennas Wireless Propag. Lett. 12, 253–256 (2013).
[CrossRef]

J. Phys. D (1)

Z. L. Mei, J. Bai, and T. J. Cui, “Gradient index metamaterials realized by drilling hole arrays,” J. Phys. D 43, 055404 (2010).
[CrossRef]

Nano Lett. (2)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009).
[CrossRef]

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10, 1936–1940 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. B (2)

A. Vakil and N. Engheta, “Fourier optics on graphene,” Phys. Rev. B 85, 075434 (2012).
[CrossRef]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[CrossRef]

Science (2)

H. J. Lezec, A. Degiron, E. Devaux, R. Linke, L. Martin-Moreno, F. Garcia-Vidal, and T. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef]

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, 333–337 (2011).
[CrossRef]

Other (4)

M. V. P. C. Gomez-Reino and C. Bao, Gradient-Index Optics (Springer, 2002).

www.Lumerical.com .

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

N. Engheta, “Functionalizing metamaterials as metasystems,” presented at 2012 MRS Fall Meeting and Exhibit, Boston, Massachusetts, November27, 2012.

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Figures (9)

Fig. 1.
Fig. 1.

Block diagram of a system with metasurface, FT and IFT blocks.

Fig. 2.
Fig. 2.

(a) L-shaped slot in a thin metal film. The total slot length is h=h1+h2. (b) Symmetric L-shaped slot (h1=h2) only transmits Ex when illuminated by Ex. (c) Asymmetric L-shaped slot (h1h2) scatters a y-directed component as well. (Superscripts in and t stand for incident and transmitted, respectively, and subscript ind stands for induced. Solid arrows and dashed arrows show electric filed and magnetic current, respectively.)

Fig. 3.
Fig. 3.

(a) Scattered Ey amplitude. The resonance of the L-shaped slot is at 60 THz. The scattered Ey amplitude changes considerably as we change Δh=|h1h2|. (b) Scattered Ey phase. Since we have fixed the total length of the L-shaped slot, h=h1+h2=1μm, the phase variation is very small at resonant frequency. [The right plot in (b) shows phase variation in detail.]

Fig. 4.
Fig. 4.

(a) Unit cell of concentric metal loops. The background refractive index is 3.15, wo=100nm and wi=50nm. (b) Transmission amplitude. (c) Phase variation versus Li and Lo at λ=5μm. The amplitude variations are very small while phase changes are considerable.

Fig. 5.
Fig. 5.

(a) Double-layered unit cell composed of the unit cells in Figs. 2(a) and 4(a). (b) and (c) Amplitude changes strongly versus |h1h2| and phase remains virtually unchanged. (d) and (e) The amplitude remains almost constant when concentric loops parameters are swept while the phase undergoes considerable variations. (Li is the sweep variable in all curves.)

Fig. 6.
Fig. 6.

(a) Metasurface of L-shaped slots designed to multiply the incident wave by Ts(y¯)y¯. (b) Uniform amplitude of the rectangular pulse is reformed into linear amplitude after passing the metasurface. (c) Phase is shifted 180° for negative values of y¯. (Solid lines are simulation results and dashed lines are ideal output profile.)

Fig. 7.
Fig. 7.

GRIN material taking FT. The GRIN material with the profile defined in Eq. (4) gives accurate FT as long as refractive index variations are small. Therefore, the beam spatial extent should be concentrated in the center of the GRIN material for the best performance. The refractive index variation is shown in the right curve.

Fig. 8.
Fig. 8.

(a) FT-metasurface-IFT blocks cascaded to perform differentiation. (b) Profile monitors at each block. A Sinc function is sourced into the spatial differentiator and its derivation is obtained on the other side.

Fig. 9.
Fig. 9.

(a) Cascaded metasurface array for controlling both amplitude and phase of the transmitted beam independent of each other. This metasurface reshapes the rectangular pulse profile of the input beam to a triangular pulse. The transmission phase is reformed to an inverse triangle shape at the same time. The top layer, L-shaped slots, control the amplitude and the bottom layer, loops, tailor the phase (b) Output amplitude and (c) phase. (The squared lines are the designed values obtained from the simulation of the separate unit cells. Data obtained from Figs. 3 and 4. The red solid line is from full wave FDTD with Lumerical solver and the thick black line is the input beam amplitude.)

Tables (1)

Tables Icon

Table 1. Dimensions of L-Shaped Slots used to Realize Spatial Derivation Functionality

Equations (4)

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

φt(x,y)=ts(x,y)*φin(x,y),
ψt(x¯,y¯)=Ts(x¯,y¯)ψin(x¯,y¯),
M⃗ind=E⃗ind×n^,
n(y)=n01(y/h0)2.

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