Abstract

The mathematical solution for Cerenkov radiation (CR) in lossless chiral media, which has the strong chiral parameters, is introduced in this paper. We reveal unique behavior for the CR in strong chiral medium under different particle-velocity regimes. Within one particle-velocity range, a radiation pattern with double cone of propagation can be expected, and the radiation is associated with forward and backward directions of emission.

© 2007 Optical Society of America

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References

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000)
    [CrossRef] [PubMed]
  4. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79(2001).
    [CrossRef] [PubMed]
  5. J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004).
    [CrossRef] [PubMed]
  6. T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E. 69,026602-026610 (2004).
    [CrossRef]
  7. T. G. Mackay, "Plane waves with negative phase velocity in isotropic chiral mediums," Microwave Opt. Technol. Lett. 45, 120-121 (2005).
    [CrossRef]
  8. Q. Cheng and T. J. Cui, "Negative refractions and backward waves in biaxially anisotropic chiral media," Opt. Express 14, 6322-6332 (2006).
    [CrossRef] [PubMed]
  9. S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-117 (2005).
    [CrossRef]
  10. Y. Jin and S. He, "Focusing by a slab of chiral medium," Opt. Express 13, 4974-4979 (2005).
    [CrossRef] [PubMed]
  11. L. D. Landau, E. M. Liftshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, New York, ed. 2, 1984).
  12. J. Lu, T. Grzegorczyk, Y. Zhang, J. PachecoJr., B. -I. Wu, J. A. Kong, and M. Chen, "Èerenkov radiation in materials with negative permittivity and permeability," Opt. Express 11, 723-734 (2003)
    [CrossRef] [PubMed]
  13. S. J. Smith, E. M. Purcell, "Visible light from Localized surface charges moving across a grating," Phys. Rev. 92, 1069-1069 (1953).
    [CrossRef]
  14. B. Lastdrager, A. Tip, and J. Verhoeven, "Theory of Èerenkov and transition radiation from layered structures," Phys. Rev. E 61, 5767-5778 (2000).
    [CrossRef]
  15. C. Y. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in Photonic Crystals," Science 299,368-371 (2003).
    [CrossRef] [PubMed]
  16. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and BiIsotropic Media (Artech House, Boston, 1994)
  17. S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility, " J. Electromagn. Waves Appl. 17, 695-706 (2003).
    [CrossRef]
  18. C. Zhang and T. J. Cui, "Spatial dispersion and energy in strong chiral medium," Opt. Express 15, 5114-5119 (2007).
    [CrossRef] [PubMed]
  19. S. Bassiri, N. Engheta, and C. H. Papas, "Dyadic Green’s function and dipole radiation in chiral media," Alta Freq. LV-2, 83-88 (1986).
  20. M. H. Saffouri, "Treatment of Cerenkov radiation from electric and magnetic charges in dispersive and dissipative media," Nuovo Cimento 3D, 589-622 (1984).
    [CrossRef]
  21. J. V. Jelly, Cerenkov radiation and Its Applications (Pergamon, London, 1958).

2007

2006

2005

Y. Jin and S. He, "Focusing by a slab of chiral medium," Opt. Express 13, 4974-4979 (2005).
[CrossRef] [PubMed]

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-117 (2005).
[CrossRef]

T. G. Mackay, "Plane waves with negative phase velocity in isotropic chiral mediums," Microwave Opt. Technol. Lett. 45, 120-121 (2005).
[CrossRef]

2004

J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004).
[CrossRef] [PubMed]

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E. 69,026602-026610 (2004).
[CrossRef]

2003

C. Y. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in Photonic Crystals," Science 299,368-371 (2003).
[CrossRef] [PubMed]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility, " J. Electromagn. Waves Appl. 17, 695-706 (2003).
[CrossRef]

J. Lu, T. Grzegorczyk, Y. Zhang, J. PachecoJr., B. -I. Wu, J. A. Kong, and M. Chen, "Èerenkov radiation in materials with negative permittivity and permeability," Opt. Express 11, 723-734 (2003)
[CrossRef] [PubMed]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79(2001).
[CrossRef] [PubMed]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000)
[CrossRef] [PubMed]

B. Lastdrager, A. Tip, and J. Verhoeven, "Theory of Èerenkov and transition radiation from layered structures," Phys. Rev. E 61, 5767-5778 (2000).
[CrossRef]

1999

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1986

S. Bassiri, N. Engheta, and C. H. Papas, "Dyadic Green’s function and dipole radiation in chiral media," Alta Freq. LV-2, 83-88 (1986).

1984

M. H. Saffouri, "Treatment of Cerenkov radiation from electric and magnetic charges in dispersive and dissipative media," Nuovo Cimento 3D, 589-622 (1984).
[CrossRef]

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1953

S. J. Smith, E. M. Purcell, "Visible light from Localized surface charges moving across a grating," Phys. Rev. 92, 1069-1069 (1953).
[CrossRef]

Bassiri, S.

S. Bassiri, N. Engheta, and C. H. Papas, "Dyadic Green’s function and dipole radiation in chiral media," Alta Freq. LV-2, 83-88 (1986).

Chen, M.

Cheng, Q.

Cui, T. J.

Engheta, N.

S. Bassiri, N. Engheta, and C. H. Papas, "Dyadic Green’s function and dipole radiation in chiral media," Alta Freq. LV-2, 83-88 (1986).

Grzegorczyk, T.

He, S.

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Ibanescu, M.

C. Y. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in Photonic Crystals," Science 299,368-371 (2003).
[CrossRef] [PubMed]

Jin, Y.

Joannopoulos, J. D.

C. Y. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in Photonic Crystals," Science 299,368-371 (2003).
[CrossRef] [PubMed]

Johnson, S. G.

C. Y. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in Photonic Crystals," Science 299,368-371 (2003).
[CrossRef] [PubMed]

Jylha, L.

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-117 (2005).
[CrossRef]

Kong, J. A.

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E. 69,026602-026610 (2004).
[CrossRef]

Lastdrager, B.

B. Lastdrager, A. Tip, and J. Verhoeven, "Theory of Èerenkov and transition radiation from layered structures," Phys. Rev. E 61, 5767-5778 (2000).
[CrossRef]

Lu, J.

Luo, C. Y.

C. Y. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in Photonic Crystals," Science 299,368-371 (2003).
[CrossRef] [PubMed]

Mackay, T. G.

T. G. Mackay, "Plane waves with negative phase velocity in isotropic chiral mediums," Microwave Opt. Technol. Lett. 45, 120-121 (2005).
[CrossRef]

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E. 69,026602-026610 (2004).
[CrossRef]

Maslovski, S.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility, " J. Electromagn. Waves Appl. 17, 695-706 (2003).
[CrossRef]

Nefedov, I.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility, " J. Electromagn. Waves Appl. 17, 695-706 (2003).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000)
[CrossRef] [PubMed]

Pacheco, J.

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000)
[CrossRef] [PubMed]

Papas, C. H.

S. Bassiri, N. Engheta, and C. H. Papas, "Dyadic Green’s function and dipole radiation in chiral media," Alta Freq. LV-2, 83-88 (1986).

Pendry, J. B.

J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Purcell, E. M.

S. J. Smith, E. M. Purcell, "Visible light from Localized surface charges moving across a grating," Phys. Rev. 92, 1069-1069 (1953).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Saffouri, M. H.

M. H. Saffouri, "Treatment of Cerenkov radiation from electric and magnetic charges in dispersive and dissipative media," Nuovo Cimento 3D, 589-622 (1984).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79(2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000)
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79(2001).
[CrossRef] [PubMed]

Sihvola, A.

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-117 (2005).
[CrossRef]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility, " J. Electromagn. Waves Appl. 17, 695-706 (2003).
[CrossRef]

Simovski, C.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility, " J. Electromagn. Waves Appl. 17, 695-706 (2003).
[CrossRef]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79(2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000)
[CrossRef] [PubMed]

Smith, S. J.

S. J. Smith, E. M. Purcell, "Visible light from Localized surface charges moving across a grating," Phys. Rev. 92, 1069-1069 (1953).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Tip, A.

B. Lastdrager, A. Tip, and J. Verhoeven, "Theory of Èerenkov and transition radiation from layered structures," Phys. Rev. E 61, 5767-5778 (2000).
[CrossRef]

Tretyakov, S.

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-117 (2005).
[CrossRef]

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility, " J. Electromagn. Waves Appl. 17, 695-706 (2003).
[CrossRef]

Verhoeven, J.

B. Lastdrager, A. Tip, and J. Verhoeven, "Theory of Èerenkov and transition radiation from layered structures," Phys. Rev. E 61, 5767-5778 (2000).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000)
[CrossRef] [PubMed]

Wu, B. -I.

Zhang, C.

Zhang, Y.

Alta Freq.

S. Bassiri, N. Engheta, and C. H. Papas, "Dyadic Green’s function and dipole radiation in chiral media," Alta Freq. LV-2, 83-88 (1986).

IEEE Trans. Microwave Theory Tech.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Electromagn. Waves Appl.

S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski, "Waves and energy in chiral nihility, " J. Electromagn. Waves Appl. 17, 695-706 (2003).
[CrossRef]

Microwave Opt. Technol. Lett.

T. G. Mackay, "Plane waves with negative phase velocity in isotropic chiral mediums," Microwave Opt. Technol. Lett. 45, 120-121 (2005).
[CrossRef]

Nuovo Cimento

M. H. Saffouri, "Treatment of Cerenkov radiation from electric and magnetic charges in dispersive and dissipative media," Nuovo Cimento 3D, 589-622 (1984).
[CrossRef]

Opt. Express

Photonics Nanostruct. Fundam. Appl.

S. Tretyakov, A. Sihvola, and L. Jylha, "Backward-wave regime and negative refraction in chiral composites," Photonics Nanostruct. Fundam. Appl. 3, 107-117 (2005).
[CrossRef]

Phys. Rev.

S. J. Smith, E. M. Purcell, "Visible light from Localized surface charges moving across a grating," Phys. Rev. 92, 1069-1069 (1953).
[CrossRef]

Phys. Rev. E

B. Lastdrager, A. Tip, and J. Verhoeven, "Theory of Èerenkov and transition radiation from layered structures," Phys. Rev. E 61, 5767-5778 (2000).
[CrossRef]

Phys. Rev. E.

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E. 69,026602-026610 (2004).
[CrossRef]

Phys. Rev. Lett.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000)
[CrossRef] [PubMed]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79(2001).
[CrossRef] [PubMed]

J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353-1355 (2004).
[CrossRef] [PubMed]

C. Y. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in Photonic Crystals," Science 299,368-371 (2003).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other

L. D. Landau, E. M. Liftshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, New York, ed. 2, 1984).

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and BiIsotropic Media (Artech House, Boston, 1994)

J. V. Jelly, Cerenkov radiation and Its Applications (Pergamon, London, 1958).

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Figures (1)

Fig. 1.
Fig. 1.

CR in strong chiral media κ > μ ε . (a): case 1(|ν±|<ν); (b): case 2(ν+<ν<ν-|).

Equations (25)

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

D = ε E + i κ H ,
B = μ H i κ E ,
v ± = ω k ± = ( μ ε + κ ) 1 ,
J ˜ ( r , ω ) = 1 2 π dt J ( t ) e i ω t = z q 4 π 2 ρ δ ( ρ ) e i ω z v ,
μ × ( 1 μ × E ˜ ) ( ε μ κ 2 ) ω 2 c 2 E ˜ ω c [ κ × E ˜ + μ × ( κ μ E ˜ ) ] = i ω μ J ˜ ,
ε × ( 1 ε × H ˜ ) ( ε μ κ 2 ) ω 2 c 2 H ˜ ω c [ κ × H ˜ + ε × ( κ ε H ˜ ) ] = i ω μ J ˜ ,
E ˜ ( r ) = i ω μ V d V J ˜ ( r ) · Γ ̂ ( r , r ) ,
E ˜ ( ρ , z ) = i ( ω μ q 2 π ) z ̂ · Γ ̂ ( ρ , z ; ρ ' , ω v ) .
Γ ̂ ( ρ , φ , z ; ρ , φ , ω v ) = χ + M + ( k + ) G ̂ + ( ρ , φ , z ; ρ , φ , ω v )
+ χ M ( k ) G ̂ ( ρ , φ , z ; ρ , φ , ω v ) ,
E ˜ = Ω e i β z [ ( β γ + k + e i π 2 ρ ̂ + γ + φ ̂ ) H 1 ( 1 ) ( τ + ) + γ + 2 k + H 0 ( 1 ) ( τ + ) z ̂
+ ( β γ k e i π 2 ρ ̂ γ φ ̂ ) H 1 ( 1 ) ( τ ) + γ 2 k H 0 ( 1 ) ( τ ) z ̂ ] ,
H ˜ = q 16 π ± e i β z + i π 2 [ ( β γ + k + e i π 2 ρ ̂ + γ + φ ̂ ) H 1 ( 1 ) ( τ + ) + γ + 2 k + H 0 ( 1 ) ( τ + ) z ̂
+ ( β γ k e i π 2 ρ ̂ + γ φ ̂ ) H 1 ( 1 ) ( τ ) γ 2 k H 0 ( 1 ) ( τ ) z ̂ ] ,
E ˜ = E ˜ + + E ˜ = η { γ + [ ( β k + ρ ̂ + γ + k + z ̂ ) i φ ̂ ] e i ( β z + τ + π 4 )
+ γ [ ( β k ρ ̂ + γ k z ̂ ) i φ ̂ ] e i ( β z + τ π 4 ) } ,
H ˜ = H ˜ + + H ˜ = η ε μ { i γ + [ ( β k + ρ ̂ + γ + k + z ̂ ) i φ ̂ ] e i ( β z + τ + π 4 )
i γ [ ( β k ρ ̂ + γ k z ̂ ) + i φ ̂ ] e i ( β z + τ π 4 ) } ,
E ˜ ± = η γ ± [ ( cos θ ± ρ ̂ + sin θ ± z ̂ ) i φ ̂ ] e i ( β z + τ ± π 4 ) ,
H ˜ ± = ( ± i ε μ ) η γ ± [ ( cos θ ± ρ ̂ + sin θ ± z ̂ ) i φ ̂ ] e i ( β z + τ ± π 4 ) ,
cos θ ± = β k ±
S ˜ = 1 2 Re ( E ˜ × H ˜ * ) = S ˜ + + S ˜
S ˜ ± = 1 2 Re ( E ˜ ± × H ˜ ± * ) = 1 2 ( q 8 π ) 2 ( γ ± π ρ ) μ ε ( γ ± k ± ρ ̂ + β k ± z ̂ ) = S ± ρ ρ ̂ + S ± z z ̂
W ˜ ± z = W ± z z ̂ = 2 0 S ˜ ± z d ω = 0 { ( q 8 π ) 2 ( β γ ± k ± π ρ ) μ ε } d ω
W ˜ ± ρ = W ± ρ ρ ̂ = 2 0 S ˜ ± ρ d ω = 0 { ( q 8 π ) 2 ( γ ± 2 k ± π ρ ) μ ε } d ω

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