Abstract

Extraordinary light rays propagating inside a hyperbolic metamaterial look similar to particle world lines in a 2 + 1 dimensional Minkowski spacetime. Magnetic nanoparticles in a ferrofluid are known to form nanocolumns aligned along the magnetic field, so that a hyperbolic metamaterial may be formed at large enough nanoparticle concentration nH. Here we investigate optical properties of such a metamaterial just below nH. While on average such a metamaterial is elliptical, thermal fluctuations of nanoparticle concentration lead to transient formation of hyperbolic regions (3D Minkowski spacetimes) inside this metamaterial. Thus, thermal fluctuations in a ferrofluid look similar to creation and disappearance of individual Minkowski spacetimes (universes) in the cosmological multiverse. This theoretical picture is supported by experimental measurements of polarization-dependent optical transmission of a cobalt based ferrofluid at 1500 nm.

© 2013 OSA

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  1. I. I. Smolyaninov and Y. J. Hung, “Modeling of time with metamaterials,” J. Opt. Soc. Am. B28(7), 1591–1595 (2011).
    [CrossRef]
  2. I. I. Smolyaninov, “Critical opalescence in hyperbolic metamaterials,” J. Opt.13(12), 125101 (2011).
    [CrossRef]
  3. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
    [CrossRef]
  4. E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett.95(4), 041106 (2009).
    [CrossRef]
  5. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
    [CrossRef] [PubMed]
  6. I. I. Smolyaninov, “Metamaterial-based model of the Alcubierre warp drive,” Phys. Rev. B84(11), 113103 (2011).
    [CrossRef]
  7. T. G. Mackay and A. Lakhtakia, “Towards a metamaterial simulation of a spinning cosmic string,” Phys. Lett. A374(23), 2305–2308 (2010).
    [CrossRef]
  8. I. I. Smolyaninov and Y. J. Hung, “Minkowski domain walls in hyperbolic metamaterials,” Phys. Lett. A377(5), 353–356 (2013).
    [CrossRef]
  9. I. I. Smolyaninov, “Metamaterial “Multiverse”,” J. Opt.13(2), 024004 (2010).
    [CrossRef]
  10. I. I. Smolyaninov and E. E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105(6), 067402 (2011).
    [CrossRef] [PubMed]
  11. I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, “Hyperbolic metamaterial interfaces: Hawking radiation from Rindler horizons and spacetime signature transitions,” Phys. Rev. B85(23), 235122 (2012).
    [CrossRef]
  12. I. I. Smolyaninov, “Vacuum in a strong magnetic field as a hyperbolic metamaterial,” Phys. Rev. Lett.107(25), 253903 (2011).
    [CrossRef] [PubMed]
  13. I. I. Smolyaninov, “Planck-scale physics of vacuum in a strong magnetic field,” Phys. Rev. D Part. Fields Gravit. Cosmol.85(11), 114013 (2012).
    [CrossRef]
  14. I. I. Smolyaninov, “Quantum electromagnetic “black holes” in a strong magnetic field,” J. Phys. G Nucl. Part. Phys.40(1), 015005 (2013).
    [CrossRef]
  15. Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett.104(3), 034501 (2010).
    [CrossRef] [PubMed]
  16. M. Tegmark, “Parallel Universes”. In “Science and Ultimate Reality: from Quantum to Cosmos,” honoring John Wheeler's 90th birthday. J. D. Barrow, P.C.W. Davies, & C.L. Harper eds. Cambridge University Press (2003).
  17. R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media,” J. Opt. Soc. Am. B23(3), 498–505 (2006).
    [CrossRef]
  18. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Course of Theoretical Physics (Reed, 1984). Vol. 5.
  19. CRC Handbook of Chemistry and Physics, D. R. Lide eds. (CRC Press, 2005).
  20. T. Tumkur, G. Zhu, P. Black, Yu. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission in a volume of functionalized hyperbolic metamaterial,” Appl. Phys. Lett.99(15), 151115 (2011).
    [CrossRef]
  21. I. I. Smolyaninov and A. V. Kildishev, “Light propagation through random hyperbolic media,” Opt. Lett.38(6), 971–973 (2013).
    [CrossRef] [PubMed]

2013 (3)

I. I. Smolyaninov and Y. J. Hung, “Minkowski domain walls in hyperbolic metamaterials,” Phys. Lett. A377(5), 353–356 (2013).
[CrossRef]

I. I. Smolyaninov, “Quantum electromagnetic “black holes” in a strong magnetic field,” J. Phys. G Nucl. Part. Phys.40(1), 015005 (2013).
[CrossRef]

I. I. Smolyaninov and A. V. Kildishev, “Light propagation through random hyperbolic media,” Opt. Lett.38(6), 971–973 (2013).
[CrossRef] [PubMed]

2012 (2)

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, “Hyperbolic metamaterial interfaces: Hawking radiation from Rindler horizons and spacetime signature transitions,” Phys. Rev. B85(23), 235122 (2012).
[CrossRef]

I. I. Smolyaninov, “Planck-scale physics of vacuum in a strong magnetic field,” Phys. Rev. D Part. Fields Gravit. Cosmol.85(11), 114013 (2012).
[CrossRef]

2011 (6)

I. I. Smolyaninov and E. E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105(6), 067402 (2011).
[CrossRef] [PubMed]

I. I. Smolyaninov, “Vacuum in a strong magnetic field as a hyperbolic metamaterial,” Phys. Rev. Lett.107(25), 253903 (2011).
[CrossRef] [PubMed]

T. Tumkur, G. Zhu, P. Black, Yu. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission in a volume of functionalized hyperbolic metamaterial,” Appl. Phys. Lett.99(15), 151115 (2011).
[CrossRef]

I. I. Smolyaninov, “Metamaterial-based model of the Alcubierre warp drive,” Phys. Rev. B84(11), 113103 (2011).
[CrossRef]

I. I. Smolyaninov, “Critical opalescence in hyperbolic metamaterials,” J. Opt.13(12), 125101 (2011).
[CrossRef]

I. I. Smolyaninov and Y. J. Hung, “Modeling of time with metamaterials,” J. Opt. Soc. Am. B28(7), 1591–1595 (2011).
[CrossRef]

2010 (3)

T. G. Mackay and A. Lakhtakia, “Towards a metamaterial simulation of a spinning cosmic string,” Phys. Lett. A374(23), 2305–2308 (2010).
[CrossRef]

I. I. Smolyaninov, “Metamaterial “Multiverse”,” J. Opt.13(2), 024004 (2010).
[CrossRef]

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett.104(3), 034501 (2010).
[CrossRef] [PubMed]

2009 (2)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett.95(4), 041106 (2009).
[CrossRef]

2007 (1)

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

2006 (1)

Barnakov, Yu. A.

T. Tumkur, G. Zhu, P. Black, Yu. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission in a volume of functionalized hyperbolic metamaterial,” Appl. Phys. Lett.99(15), 151115 (2011).
[CrossRef]

Black, P.

T. Tumkur, G. Zhu, P. Black, Yu. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission in a volume of functionalized hyperbolic metamaterial,” Appl. Phys. Lett.99(15), 151115 (2011).
[CrossRef]

Bonner, C. E.

T. Tumkur, G. Zhu, P. Black, Yu. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission in a volume of functionalized hyperbolic metamaterial,” Appl. Phys. Lett.99(15), 151115 (2011).
[CrossRef]

Elser, J.

Gao, L.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett.104(3), 034501 (2010).
[CrossRef] [PubMed]

Gao, Y.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett.104(3), 034501 (2010).
[CrossRef] [PubMed]

Genov, D. A.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
[CrossRef]

Greenleaf, A.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

Huang, J. P.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett.104(3), 034501 (2010).
[CrossRef] [PubMed]

Hung, Y. J.

I. I. Smolyaninov and Y. J. Hung, “Minkowski domain walls in hyperbolic metamaterials,” Phys. Lett. A377(5), 353–356 (2013).
[CrossRef]

I. I. Smolyaninov and Y. J. Hung, “Modeling of time with metamaterials,” J. Opt. Soc. Am. B28(7), 1591–1595 (2011).
[CrossRef]

Hwang, E.

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, “Hyperbolic metamaterial interfaces: Hawking radiation from Rindler horizons and spacetime signature transitions,” Phys. Rev. B85(23), 235122 (2012).
[CrossRef]

Kildishev, A. V.

I. I. Smolyaninov and A. V. Kildishev, “Light propagation through random hyperbolic media,” Opt. Lett.38(6), 971–973 (2013).
[CrossRef] [PubMed]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett.95(4), 041106 (2009).
[CrossRef]

Kurylev, Y.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, “Towards a metamaterial simulation of a spinning cosmic string,” Phys. Lett. A374(23), 2305–2308 (2010).
[CrossRef]

Lassas, M.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

Liu, Y. M.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett.104(3), 034501 (2010).
[CrossRef] [PubMed]

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, “Towards a metamaterial simulation of a spinning cosmic string,” Phys. Lett. A374(23), 2305–2308 (2010).
[CrossRef]

Narimanov, E. E.

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, “Hyperbolic metamaterial interfaces: Hawking radiation from Rindler horizons and spacetime signature transitions,” Phys. Rev. B85(23), 235122 (2012).
[CrossRef]

I. I. Smolyaninov and E. E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105(6), 067402 (2011).
[CrossRef] [PubMed]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett.95(4), 041106 (2009).
[CrossRef]

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media,” J. Opt. Soc. Am. B23(3), 498–505 (2006).
[CrossRef]

Noginov, M. A.

T. Tumkur, G. Zhu, P. Black, Yu. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission in a volume of functionalized hyperbolic metamaterial,” Appl. Phys. Lett.99(15), 151115 (2011).
[CrossRef]

Podolskiy, V. A.

Smolyaninov, I. I.

I. I. Smolyaninov and Y. J. Hung, “Minkowski domain walls in hyperbolic metamaterials,” Phys. Lett. A377(5), 353–356 (2013).
[CrossRef]

I. I. Smolyaninov and A. V. Kildishev, “Light propagation through random hyperbolic media,” Opt. Lett.38(6), 971–973 (2013).
[CrossRef] [PubMed]

I. I. Smolyaninov, “Quantum electromagnetic “black holes” in a strong magnetic field,” J. Phys. G Nucl. Part. Phys.40(1), 015005 (2013).
[CrossRef]

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, “Hyperbolic metamaterial interfaces: Hawking radiation from Rindler horizons and spacetime signature transitions,” Phys. Rev. B85(23), 235122 (2012).
[CrossRef]

I. I. Smolyaninov, “Planck-scale physics of vacuum in a strong magnetic field,” Phys. Rev. D Part. Fields Gravit. Cosmol.85(11), 114013 (2012).
[CrossRef]

I. I. Smolyaninov, “Vacuum in a strong magnetic field as a hyperbolic metamaterial,” Phys. Rev. Lett.107(25), 253903 (2011).
[CrossRef] [PubMed]

I. I. Smolyaninov, “Critical opalescence in hyperbolic metamaterials,” J. Opt.13(12), 125101 (2011).
[CrossRef]

I. I. Smolyaninov, “Metamaterial-based model of the Alcubierre warp drive,” Phys. Rev. B84(11), 113103 (2011).
[CrossRef]

I. I. Smolyaninov and E. E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105(6), 067402 (2011).
[CrossRef] [PubMed]

I. I. Smolyaninov and Y. J. Hung, “Modeling of time with metamaterials,” J. Opt. Soc. Am. B28(7), 1591–1595 (2011).
[CrossRef]

I. I. Smolyaninov, “Metamaterial “Multiverse”,” J. Opt.13(2), 024004 (2010).
[CrossRef]

Tumkur, T.

T. Tumkur, G. Zhu, P. Black, Yu. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission in a volume of functionalized hyperbolic metamaterial,” Appl. Phys. Lett.99(15), 151115 (2011).
[CrossRef]

Uhlmann, G.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

Wangberg, R.

Yu, K. W.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett.104(3), 034501 (2010).
[CrossRef] [PubMed]

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
[CrossRef]

Zhang, X.

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett.104(3), 034501 (2010).
[CrossRef] [PubMed]

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
[CrossRef]

Zhu, G.

T. Tumkur, G. Zhu, P. Black, Yu. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission in a volume of functionalized hyperbolic metamaterial,” Appl. Phys. Lett.99(15), 151115 (2011).
[CrossRef]

Appl. Phys. Lett. (2)

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett.95(4), 041106 (2009).
[CrossRef]

T. Tumkur, G. Zhu, P. Black, Yu. A. Barnakov, C. E. Bonner, and M. A. Noginov, “Control of spontaneous emission in a volume of functionalized hyperbolic metamaterial,” Appl. Phys. Lett.99(15), 151115 (2011).
[CrossRef]

J. Opt. (2)

I. I. Smolyaninov, “Critical opalescence in hyperbolic metamaterials,” J. Opt.13(12), 125101 (2011).
[CrossRef]

I. I. Smolyaninov, “Metamaterial “Multiverse”,” J. Opt.13(2), 024004 (2010).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. G Nucl. Part. Phys. (1)

I. I. Smolyaninov, “Quantum electromagnetic “black holes” in a strong magnetic field,” J. Phys. G Nucl. Part. Phys.40(1), 015005 (2013).
[CrossRef]

Nat. Phys. (1)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (2)

T. G. Mackay and A. Lakhtakia, “Towards a metamaterial simulation of a spinning cosmic string,” Phys. Lett. A374(23), 2305–2308 (2010).
[CrossRef]

I. I. Smolyaninov and Y. J. Hung, “Minkowski domain walls in hyperbolic metamaterials,” Phys. Lett. A377(5), 353–356 (2013).
[CrossRef]

Phys. Rev. B (2)

I. I. Smolyaninov, E. Hwang, and E. E. Narimanov, “Hyperbolic metamaterial interfaces: Hawking radiation from Rindler horizons and spacetime signature transitions,” Phys. Rev. B85(23), 235122 (2012).
[CrossRef]

I. I. Smolyaninov, “Metamaterial-based model of the Alcubierre warp drive,” Phys. Rev. B84(11), 113103 (2011).
[CrossRef]

Phys. Rev. D Part. Fields Gravit. Cosmol. (1)

I. I. Smolyaninov, “Planck-scale physics of vacuum in a strong magnetic field,” Phys. Rev. D Part. Fields Gravit. Cosmol.85(11), 114013 (2012).
[CrossRef]

Phys. Rev. Lett. (4)

I. I. Smolyaninov, “Vacuum in a strong magnetic field as a hyperbolic metamaterial,” Phys. Rev. Lett.107(25), 253903 (2011).
[CrossRef] [PubMed]

Y. Gao, J. P. Huang, Y. M. Liu, L. Gao, K. W. Yu, and X. Zhang, “Optical negative refraction in ferrofluids with magnetocontrollability,” Phys. Rev. Lett.104(3), 034501 (2010).
[CrossRef] [PubMed]

I. I. Smolyaninov and E. E. Narimanov, “Metric signature transitions in optical metamaterials,” Phys. Rev. Lett.105(6), 067402 (2011).
[CrossRef] [PubMed]

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007).
[CrossRef] [PubMed]

Other (3)

M. Tegmark, “Parallel Universes”. In “Science and Ultimate Reality: from Quantum to Cosmos,” honoring John Wheeler's 90th birthday. J. D. Barrow, P.C.W. Davies, & C.L. Harper eds. Cambridge University Press (2003).

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Course of Theoretical Physics (Reed, 1984). Vol. 5.

CRC Handbook of Chemistry and Physics, D. R. Lide eds. (CRC Press, 2005).

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Figures (6)

Fig. 1
Fig. 1

Typical geometries of hyperbolic metamaterials: (a) multilayer metal-dielectric structure (b) metal wire array structure (c) effective medium parameters of the ferrofluid metamaterial.

Fig. 2
Fig. 2

Typical instantaneous distribution of fluctuating hyperbolic regions in the cobalt-based ferrofluid sample calculated using Eq. (6). Hyperbolic regions are shown in red. These regions behave as transient 2 + 1 dimensional Minkowski spacetimes which temporarily appear and diappear inside a larger metamaterial “multiverse”.

Fig. 3
Fig. 3

(a) Schematic view of our experimental setup. (b) Photo of the ferrofluid metamaterial sample next to a permanent magnet. The inset shows excessive ferrofluid on the side of the cuvette, which forms “spikes” along the applied magnetic field.

Fig. 4
Fig. 4

Experimentally measured transmission of the cobalt based ferrofluid as a function of external magnetic field and polarization angle. Transmission signal was averaged over 2 minutes.

Fig. 5
Fig. 5

Measured temporal fluctuations of the sample transmission as a function of light polarization and applied magnetic field: (a) measurements in zero field, (b) measurements in B0 = 1400G. Angle between B0 and E is indicated for each time dependency.

Fig. 6
Fig. 6

Temporal fluctuations of normalized transmission in applied magnetic field at different concentrations of cobalt nanoparticles in the ferrofluid: (a) measured fluctuations as a function of light polarization at 1% volume concentration of cobalt nanoparticles, (b) measured fluctuations as a function of light polarization at 8.2% volume concentration of cobalt nanoparticles.

Equations (6)

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

ω 2 c 2 φ ω = 2 φ ω ε 1 z 2 1 ε 2 ( 2 φ ω x 2 + 2 φ ω y 2 )
ε 2 = ε z =n ε m +( 1n ) ε d
ε 1 = ε x,y = 2n ε m ε d +(1n) ε d ( ε d + ε m ) ( 1n )( ε d + ε m )+2n ε d
n> n H = ε d ε d ε m
( ΔN ) 2 =N
( Δn ) 2 1/2 = n 1/2 v 1/2 V 1/2

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