Abstract

Point group theoretical methods are used to determine the electromagnetic properties of metamaterials, based solely upon the symmetries of the underlying constituent particles. From the transformation properties of an electromagnetic (EM) basis under symmetries of the particles, it is possible to determine, (i) the EM modes of the particles, (ii) the form of constitutive relations (iii) magneto-optical response of a metamaterial or lack thereof. Based upon these methods, we predict an ideal planar artificial magnetic metamaterial, and determine the subset of point groups of which particles must belong to in order to yield an isotropic 3D magnetic response, and we show an example.

© 2007 Optical Society of America

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  1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef]
  2. V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,"Soviet Physics USPEKI 10, 509-514 (1968).
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  6. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Steward, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
  7. J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef]
  8. R. A. Shelby, D. R. Smith, S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
    [CrossRef]
  9. D. Schurig and D. R. Smith, "Negative Index Lens Aberrations," Phys. Rev. E 70, 065601(R) (2004).
  10. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).
  11. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314977-980 (2006).
    [CrossRef]
  12. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
    [CrossRef]
  13. M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
    [CrossRef]
  14. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
    [CrossRef]
  15. W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
    [CrossRef]
  16. W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
    [CrossRef]
  17. Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
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  19. Here we only consider point groups and do not consider other symmetries, i.e. translations (lattice groups), screw axis and glide planes (space groups).
  20. For a review of the conditions of effective media applicable to metamaterials see ref. [17] and the references therein.
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  27. Enantiomer in this sense is defined as "the exact opposite" meaning that the polarization mixing which results from one orientation of the split gap can be corrected by another SRR with the split gap oriented oppositely.
  28. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split Ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
    [CrossRef]

2006 (5)

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314977-980 (2006).
[CrossRef]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef]

W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
[CrossRef]

W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
[CrossRef]

2005 (1)

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

2004 (3)

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split Ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

D. Schurig and D. R. Smith, "Negative Index Lens Aberrations," Phys. Rev. E 70, 065601(R) (2004).

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef]

2002 (1)

R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

2001 (2)

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef]

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef]

2000 (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Steward, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).

1968 (1)

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,"Soviet Physics USPEKI 10, 509-514 (1968).

1962 (1)

W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propag. AP10, 82-95 (1962).

1948 (1)

W. E. Kock, Metallic delay lenses, Bell System Technical J. 27, 58 (1948).

Averitt, R. D.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef]

Basov, D. N.

W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef]

Chen, H.-T.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314977-980 (2006).
[CrossRef]

Economou, E. N.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split Ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef]

Gilderdale, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef]

Gossard, A. C.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef]

Hajnal, J. V.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef]

Highstrete, C.

W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Steward, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314977-980 (2006).
[CrossRef]

Kafesaki, M.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split Ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Katsarakis, N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split Ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Kock, W. E.

W. E. Kock, Metallic delay lenses, Bell System Technical J. 27, 58 (1948).

Koschny, T.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split Ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Koschny, Th.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Larkman, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef]

Markos, P.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Marqués, R.

R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Medina, F.

R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314977-980 (2006).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

Padilla, W. J.

W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
[CrossRef]

W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
[CrossRef]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314977-980 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef]

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef]

J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Steward, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).

Rafii-El-Idrissi, R.

R. Marqués, F. Medina, R. Rafii-El-Idrissi, "Role of Bianisotropy in Negative Permeability and Left-Handed Metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Steward, "Magnetism from Conductors and Enhanced Nonlinear Phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).

Rotman, W.

W. Rotman, "Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media," IRE Trans. Antennas Propag. AP10, 82-95 (1962).

Schultz, S.

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314977-980 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).

D. Schurig and D. R. Smith, "Negative Index Lens Aberrations," Phys. Rev. E 70, 065601(R) (2004).

Shelby, R. A.

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 17801782 (2006).

W. J. Padilla, D. R. Smith, and D. N. Basov, "Spectroscopy of Metamaterials from Infrared to Optical Frequencies," J. Opt. Soc. Am. B 23404-414 (2006)
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314977-980 (2006).
[CrossRef]

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef]

D. Schurig and D. R. Smith, "Negative Index Lens Aberrations," Phys. Rev. E 70, 065601(R) (2004).

R. A. Shelby, D. R. Smith, S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2001).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

Soukoulis, C. M.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric Coupling to the Magnetic Resonance of Split Ring Resonators," Appl. Phys. Lett. 84, 2943-2945 (2004).
[CrossRef]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314977-980 (2006).
[CrossRef]

Taylor, A. J.

W. J. Padilla, A. J. Taylor, C. Highstrete, Mark Lee, and R. D. Averitt, "Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies," Phys. Rev. Lett. 96107401 (2006).
[CrossRef]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor and R. D. Averitt, "Active Terahertz Metamaterial Devices," Nature 444597-600 (2006).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,"Soviet Physics USPEKI 10, 509-514 (1968).

Vier, D. C.

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of Inherent Periodic Structure on Effective Medium Description of Left-Handed and Related Metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang "Terahertz Magnetic Response from Artificial Materials," Science 303, 1494-1496 (2004).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef]

Wiltshire, M. C. K.

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Here we only consider point groups and do not consider other symmetries, i.e. translations (lattice groups), screw axis and glide planes (space groups).

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Enantiomer in this sense is defined as "the exact opposite" meaning that the polarization mixing which results from one orientation of the split gap can be corrected by another SRR with the split gap oriented oppositely.

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