Abstract

We propose a novel scheme in realizing tunable slow-light performance by manipulating dark photonic angular momentum states (PAMSs) in metamaterials via the magneto-optical effect. We show that by applying a static magnetic field B, some pairs of sharp transmission dips can be observed in the background transparency window of a complex metamaterial design. Each pair of transmission dips are related to the excitation of dark PAMSs with opposite topological charges −m and +m, with a lifted degeneracy due to the classic analogue of Zeeman effect. Nonreciprocal characteristics can be observed in the distributions of field amplitude and transverse energy flux. The performance of slow light, including the group index ng, its abnormal feature, the associated strong absorption and the dependence with B are also discussed.

© 2013 OSA

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  1. M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett.97, 263902 (2006).
    [CrossRef]
  2. L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98, 157403 (2007).
    [CrossRef] [PubMed]
  3. L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mat.8, 643–647 (2009).
    [CrossRef]
  4. Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett.105, 013901 (2010).
    [CrossRef] [PubMed]
  5. J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
    [CrossRef] [PubMed]
  6. J. Du, Z. Lin, S. T. Chui, G. Dong, and W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett.110, 163902 (2013).
    [CrossRef] [PubMed]
  7. F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun.209, 17–22 (2002).
    [CrossRef]
  8. F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B79, 1–8 (2004).
    [CrossRef]
  9. M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett.94,193902 (2005).
    [CrossRef] [PubMed]
  10. P. Banzer, J. Kindler, S. Quabis, U. Peschel, and G. Leuchs, “Extraordinary transmission through a single coaxial aperture in a thin metal film,” Opt. Express18, 10896–10904 (2010).
    [CrossRef] [PubMed]
  11. S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mat.9, 407–412 (2010).
    [CrossRef]
  12. Q. H. Guo, M. Kang, T. F. Li, H. X. Cui, and J. Chen, “Slow light from sharp dispersion by exciting dark photonic angular momentum states,” Opt. Lett.38, 250–252 (2013).
    [CrossRef] [PubMed]
  13. Q. H. Guo, M. Yang, T. F. Li, T. J. Guo, H. X. Cui, M. Kang, and J. Chen, “Circular polarizer via selective excitation of photonic angular momentum states in metamaterials,” Appl. Phys. Lett.102, 211906 (2013).
    [CrossRef]
  14. J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B84, 235122 (2011).
    [CrossRef]
  15. T. F. Li, T. J. Guo, H. X. Cui, M. Yang, M. Kang, Q. H. Guo, and J. Chen, “Guided modes in magneto-optical waveguides and the role in resonant transmission,” Opt. Express21, 9563–9572 (2013).
    [CrossRef] [PubMed]
  16. J. B. Khurgin, “Optical isolating action in surface plasmon polaritons,” Appl. Phys. Lett.89, 251115 (2006).
    [CrossRef]
  17. Y. M. Bahk, J. W. Choi, J. Kyoung, H. R. Park, K. J. Ahn, and D. S. Kim, “Selective enhanced resonances of two asymmetric terahertz nano resonators,” Opt. Express20, 25644–25653 (2012).
    [CrossRef] [PubMed]
  18. Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
    [CrossRef] [PubMed]
  19. H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
    [CrossRef] [PubMed]
  20. H. R. Park, Y. M. Bahk, J. H. Choe, S. Han, S. S. Choi, K. J. Ahn, N. Park, Q. H. Park, and D. S. Kim, “Terahertz pinch harmonics enabled by single nano rods,” Opt. Express19, 24775–24781 (2011).
    [CrossRef] [PubMed]
  21. K. Kozuki, T. Nagashima, and M. Hangyo, “Measurement of electron paramagnetic resonance using terahertz time-domain spectroscopy,” Opt. Express19, 24950–24956 (2011).
    [CrossRef]
  22. J. Nishitani, T. Nagashima, and M. Hangyo, “Terahertz radiation from antiferromagnetic MnO excited by optical laser pulses,” Appl. Phys. Lett.103, 081907 (2013).
    [CrossRef]
  23. Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100, 023902 (2008).
    [CrossRef] [PubMed]
  24. H. Yin and P. M. Hui, “Controlling enhanced transmission through semiconductor gratings with subwavelength slits by a magnetic field: Numerical and analytical results,” Appl. Phys. Lett.95, 011115 (2009).
    [CrossRef]
  25. A. K. Geim, “Graphene: status and prospects,” Science324, 1530–1534 (2009).
    [CrossRef] [PubMed]
  26. A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phy.3, 36–40 (2007).
    [CrossRef]
  27. P. B. Catryssea and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett.94, 231111 (2009).
    [CrossRef]
  28. J. B. Khurgin, “Slow light in various media: a tutorial,” Adv. Opt. Photon.2, 287–318 (2010).
    [CrossRef]

2013

J. Du, Z. Lin, S. T. Chui, G. Dong, and W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett.110, 163902 (2013).
[CrossRef] [PubMed]

Q. H. Guo, M. Yang, T. F. Li, T. J. Guo, H. X. Cui, M. Kang, and J. Chen, “Circular polarizer via selective excitation of photonic angular momentum states in metamaterials,” Appl. Phys. Lett.102, 211906 (2013).
[CrossRef]

J. Nishitani, T. Nagashima, and M. Hangyo, “Terahertz radiation from antiferromagnetic MnO excited by optical laser pulses,” Appl. Phys. Lett.103, 081907 (2013).
[CrossRef]

Q. H. Guo, M. Kang, T. F. Li, H. X. Cui, and J. Chen, “Slow light from sharp dispersion by exciting dark photonic angular momentum states,” Opt. Lett.38, 250–252 (2013).
[CrossRef] [PubMed]

T. F. Li, T. J. Guo, H. X. Cui, M. Yang, M. Kang, Q. H. Guo, and J. Chen, “Guided modes in magneto-optical waveguides and the role in resonant transmission,” Opt. Express21, 9563–9572 (2013).
[CrossRef] [PubMed]

2012

2011

H. R. Park, Y. M. Bahk, J. H. Choe, S. Han, S. S. Choi, K. J. Ahn, N. Park, Q. H. Park, and D. S. Kim, “Terahertz pinch harmonics enabled by single nano rods,” Opt. Express19, 24775–24781 (2011).
[CrossRef] [PubMed]

K. Kozuki, T. Nagashima, and M. Hangyo, “Measurement of electron paramagnetic resonance using terahertz time-domain spectroscopy,” Opt. Express19, 24950–24956 (2011).
[CrossRef]

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B84, 235122 (2011).
[CrossRef]

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

2010

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett.105, 013901 (2010).
[CrossRef] [PubMed]

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mat.9, 407–412 (2010).
[CrossRef]

J. B. Khurgin, “Slow light in various media: a tutorial,” Adv. Opt. Photon.2, 287–318 (2010).
[CrossRef]

P. Banzer, J. Kindler, S. Quabis, U. Peschel, and G. Leuchs, “Extraordinary transmission through a single coaxial aperture in a thin metal film,” Opt. Express18, 10896–10904 (2010).
[CrossRef] [PubMed]

2009

H. Yin and P. M. Hui, “Controlling enhanced transmission through semiconductor gratings with subwavelength slits by a magnetic field: Numerical and analytical results,” Appl. Phys. Lett.95, 011115 (2009).
[CrossRef]

A. K. Geim, “Graphene: status and prospects,” Science324, 1530–1534 (2009).
[CrossRef] [PubMed]

P. B. Catryssea and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett.94, 231111 (2009).
[CrossRef]

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mat.8, 643–647 (2009).
[CrossRef]

2008

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100, 023902 (2008).
[CrossRef] [PubMed]

2007

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98, 157403 (2007).
[CrossRef] [PubMed]

A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phy.3, 36–40 (2007).
[CrossRef]

2006

J. B. Khurgin, “Optical isolating action in surface plasmon polaritons,” Appl. Phys. Lett.89, 251115 (2006).
[CrossRef]

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett.97, 263902 (2006).
[CrossRef]

2005

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett.94,193902 (2005).
[CrossRef] [PubMed]

2004

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B79, 1–8 (2004).
[CrossRef]

2002

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun.209, 17–22 (2002).
[CrossRef]

Ahn, K. J.

Y. M. Bahk, J. W. Choi, J. Kyoung, H. R. Park, K. J. Ahn, and D. S. Kim, “Selective enhanced resonances of two asymmetric terahertz nano resonators,” Opt. Express20, 25644–25653 (2012).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, J. H. Choe, S. Han, S. S. Choi, K. J. Ahn, N. Park, Q. H. Park, and D. S. Kim, “Terahertz pinch harmonics enabled by single nano rods,” Opt. Express19, 24775–24781 (2011).
[CrossRef] [PubMed]

Ahn, Y. H.

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

Atwater, H. A.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mat.9, 407–412 (2010).
[CrossRef]

Bahk, Y. M.

Y. M. Bahk, J. W. Choi, J. Kyoung, H. R. Park, K. J. Ahn, and D. S. Kim, “Selective enhanced resonances of two asymmetric terahertz nano resonators,” Opt. Express20, 25644–25653 (2012).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, J. H. Choe, S. Han, S. S. Choi, K. J. Ahn, N. Park, Q. H. Park, and D. S. Kim, “Terahertz pinch harmonics enabled by single nano rods,” Opt. Express19, 24775–24781 (2011).
[CrossRef] [PubMed]

Baida, F. I.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B79, 1–8 (2004).
[CrossRef]

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun.209, 17–22 (2002).
[CrossRef]

Banzer, P.

Belkhir, A.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B79, 1–8 (2004).
[CrossRef]

Bostwick, A.

A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phy.3, 36–40 (2007).
[CrossRef]

Bravo-Abad, J.

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

Brongersma, M. L.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mat.8, 643–647 (2009).
[CrossRef]

Burgos, S. P.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mat.9, 407–412 (2010).
[CrossRef]

Cao, L.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mat.8, 643–647 (2009).
[CrossRef]

Catryssea, P. B.

P. B. Catryssea and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett.94, 231111 (2009).
[CrossRef]

Chen, H.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98, 157403 (2007).
[CrossRef] [PubMed]

Chen, J.

Choe, J. H.

Choi, J. W.

Choi, S. S.

Chui, S. T.

J. Du, Z. Lin, S. T. Chui, G. Dong, and W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett.110, 163902 (2013).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Clemens, B. M.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mat.8, 643–647 (2009).
[CrossRef]

Cui, H. X.

de Waele, R.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mat.9, 407–412 (2010).
[CrossRef]

Dong, G.

J. Du, Z. Lin, S. T. Chui, G. Dong, and W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett.110, 163902 (2013).
[CrossRef] [PubMed]

Dong, H. Y.

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B84, 235122 (2011).
[CrossRef]

Du, J.

J. Du, Z. Lin, S. T. Chui, G. Dong, and W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett.110, 163902 (2013).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Fan, S.

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett.105, 013901 (2010).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100, 023902 (2008).
[CrossRef] [PubMed]

Fan, S. H.

P. B. Catryssea and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett.94, 231111 (2009).
[CrossRef]

Fang, N. X.

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B84, 235122 (2011).
[CrossRef]

Fung, K. H.

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B84, 235122 (2011).
[CrossRef]

Gan, F.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

Geim, A. K.

A. K. Geim, “Graphene: status and prospects,” Science324, 1530–1534 (2009).
[CrossRef] [PubMed]

Granet, G.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B79, 1–8 (2004).
[CrossRef]

Grzegorczyk, T. M.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98, 157403 (2007).
[CrossRef] [PubMed]

Guo, Q. H.

Guo, T. J.

Q. H. Guo, M. Yang, T. F. Li, T. J. Guo, H. X. Cui, M. Kang, and J. Chen, “Circular polarizer via selective excitation of photonic angular momentum states in metamaterials,” Appl. Phys. Lett.102, 211906 (2013).
[CrossRef]

T. F. Li, T. J. Guo, H. X. Cui, M. Yang, M. Kang, Q. H. Guo, and J. Chen, “Guided modes in magneto-optical waveguides and the role in resonant transmission,” Opt. Express21, 9563–9572 (2013).
[CrossRef] [PubMed]

Han, S.

Hangyo, M.

J. Nishitani, T. Nagashima, and M. Hangyo, “Terahertz radiation from antiferromagnetic MnO excited by optical laser pulses,” Appl. Phys. Lett.103, 081907 (2013).
[CrossRef]

K. Kozuki, T. Nagashima, and M. Hangyo, “Measurement of electron paramagnetic resonance using terahertz time-domain spectroscopy,” Opt. Express19, 24950–24956 (2011).
[CrossRef]

Hibbins, A. P.

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett.94,193902 (2005).
[CrossRef] [PubMed]

Horn, K.

A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phy.3, 36–40 (2007).
[CrossRef]

Hui, P. M.

H. Yin and P. M. Hui, “Controlling enhanced transmission through semiconductor gratings with subwavelength slits by a magnetic field: Numerical and analytical results,” Appl. Phys. Lett.95, 011115 (2009).
[CrossRef]

Kang, M.

Khurgin, J. B.

J. B. Khurgin, “Slow light in various media: a tutorial,” Adv. Opt. Photon.2, 287–318 (2010).
[CrossRef]

J. B. Khurgin, “Optical isolating action in surface plasmon polaritons,” Appl. Phys. Lett.89, 251115 (2006).
[CrossRef]

Kim, D. S.

Y. M. Bahk, J. W. Choi, J. Kyoung, H. R. Park, K. J. Ahn, and D. S. Kim, “Selective enhanced resonances of two asymmetric terahertz nano resonators,” Opt. Express20, 25644–25653 (2012).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, J. H. Choe, S. Han, S. S. Choi, K. J. Ahn, N. Park, Q. H. Park, and D. S. Kim, “Terahertz pinch harmonics enabled by single nano rods,” Opt. Express19, 24775–24781 (2011).
[CrossRef] [PubMed]

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

Kim, H. S.

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

Kindler, J.

Kong, J. A.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98, 157403 (2007).
[CrossRef] [PubMed]

Kozuki, K.

Kyoung, J.

Lawrence, C. R.

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett.94,193902 (2005).
[CrossRef] [PubMed]

Leuchs, G.

Li, H.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Li, T. F.

Lin, Z.

J. Du, Z. Lin, S. T. Chui, G. Dong, and W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett.110, 163902 (2013).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Lockyear, M. J.

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett.94,193902 (2005).
[CrossRef] [PubMed]

Lu, W.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Luk’yanchuk, B. S.

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett.97, 263902 (2006).
[CrossRef]

Martin-Moreno, L.

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

Moreau, A.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B79, 1–8 (2004).
[CrossRef]

Nagashima, T.

J. Nishitani, T. Nagashima, and M. Hangyo, “Terahertz radiation from antiferromagnetic MnO excited by optical laser pulses,” Appl. Phys. Lett.103, 081907 (2013).
[CrossRef]

K. Kozuki, T. Nagashima, and M. Hangyo, “Measurement of electron paramagnetic resonance using terahertz time-domain spectroscopy,” Opt. Express19, 24950–24956 (2011).
[CrossRef]

Nishitani, J.

J. Nishitani, T. Nagashima, and M. Hangyo, “Terahertz radiation from antiferromagnetic MnO excited by optical laser pulses,” Appl. Phys. Lett.103, 081907 (2013).
[CrossRef]

Ohta, T.

A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phy.3, 36–40 (2007).
[CrossRef]

Park, H. R.

Y. M. Bahk, J. W. Choi, J. Kyoung, H. R. Park, K. J. Ahn, and D. S. Kim, “Selective enhanced resonances of two asymmetric terahertz nano resonators,” Opt. Express20, 25644–25653 (2012).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, J. H. Choe, S. Han, S. S. Choi, K. J. Ahn, N. Park, Q. H. Park, and D. S. Kim, “Terahertz pinch harmonics enabled by single nano rods,” Opt. Express19, 24775–24781 (2011).
[CrossRef] [PubMed]

Park, J. S.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mat.8, 643–647 (2009).
[CrossRef]

Park, N.

Park, Q. H.

H. R. Park, Y. M. Bahk, J. H. Choe, S. Han, S. S. Choi, K. J. Ahn, N. Park, Q. H. Park, and D. S. Kim, “Terahertz pinch harmonics enabled by single nano rods,” Opt. Express19, 24775–24781 (2011).
[CrossRef] [PubMed]

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

Peng, L.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98, 157403 (2007).
[CrossRef] [PubMed]

Peschel, U.

Polman, A.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mat.9, 407–412 (2010).
[CrossRef]

Quabis, S.

Ran, L.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98, 157403 (2007).
[CrossRef] [PubMed]

Rotenberg, E.

A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phy.3, 36–40 (2007).
[CrossRef]

Ruan, Z.

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett.105, 013901 (2010).
[CrossRef] [PubMed]

Sambles, J. R.

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett.94,193902 (2005).
[CrossRef] [PubMed]

Schuller, J. A.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mat.8, 643–647 (2009).
[CrossRef]

Seyller, T.

A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phy.3, 36–40 (2007).
[CrossRef]

Sheng, Z.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Tribelsky, M. I.

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett.97, 263902 (2006).
[CrossRef]

Van Labeke, D.

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B79, 1–8 (2004).
[CrossRef]

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun.209, 17–22 (2002).
[CrossRef]

Veronis, G.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100, 023902 (2008).
[CrossRef] [PubMed]

Wang, J.

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B84, 235122 (2011).
[CrossRef]

Wang, X.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Wang, Z.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100, 023902 (2008).
[CrossRef] [PubMed]

White, J. S.

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mat.8, 643–647 (2009).
[CrossRef]

Wu, A.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Yang, M.

T. F. Li, T. J. Guo, H. X. Cui, M. Yang, M. Kang, Q. H. Guo, and J. Chen, “Guided modes in magneto-optical waveguides and the role in resonant transmission,” Opt. Express21, 9563–9572 (2013).
[CrossRef] [PubMed]

Q. H. Guo, M. Yang, T. F. Li, T. J. Guo, H. X. Cui, M. Kang, and J. Chen, “Circular polarizer via selective excitation of photonic angular momentum states in metamaterials,” Appl. Phys. Lett.102, 211906 (2013).
[CrossRef]

Yin, H.

H. Yin and P. M. Hui, “Controlling enhanced transmission through semiconductor gratings with subwavelength slits by a magnetic field: Numerical and analytical results,” Appl. Phys. Lett.95, 011115 (2009).
[CrossRef]

Yu, Z.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100, 023902 (2008).
[CrossRef] [PubMed]

Zhang, H.

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98, 157403 (2007).
[CrossRef] [PubMed]

Zhang, W.

J. Du, Z. Lin, S. T. Chui, G. Dong, and W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett.110, 163902 (2013).
[CrossRef] [PubMed]

Zi, J.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

Zou, S.

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

ACS Nano

H. R. Park, Y. M. Bahk, K. J. Ahn, Q. H. Park, D. S. Kim, L. Martin-Moreno, F. J. Garcia-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5, 8340–8345 (2011).
[CrossRef] [PubMed]

Adv. Opt. Photon.

Appl. Phys. B

F. I. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B79, 1–8 (2004).
[CrossRef]

Appl. Phys. Lett.

J. Nishitani, T. Nagashima, and M. Hangyo, “Terahertz radiation from antiferromagnetic MnO excited by optical laser pulses,” Appl. Phys. Lett.103, 081907 (2013).
[CrossRef]

H. Yin and P. M. Hui, “Controlling enhanced transmission through semiconductor gratings with subwavelength slits by a magnetic field: Numerical and analytical results,” Appl. Phys. Lett.95, 011115 (2009).
[CrossRef]

Q. H. Guo, M. Yang, T. F. Li, T. J. Guo, H. X. Cui, M. Kang, and J. Chen, “Circular polarizer via selective excitation of photonic angular momentum states in metamaterials,” Appl. Phys. Lett.102, 211906 (2013).
[CrossRef]

P. B. Catryssea and S. H. Fan, “Understanding the dispersion of coaxial plasmonic structures through a connection with the planar metal-insulator-metal geometry,” Appl. Phys. Lett.94, 231111 (2009).
[CrossRef]

J. B. Khurgin, “Optical isolating action in surface plasmon polaritons,” Appl. Phys. Lett.89, 251115 (2006).
[CrossRef]

Nat. Mat.

S. P. Burgos, R. de Waele, A. Polman, and H. A. Atwater, “A single-layer wide-angle negative-index metamaterial at visible frequencies,” Nat. Mat.9, 407–412 (2010).
[CrossRef]

L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mat.8, 643–647 (2009).
[CrossRef]

Nat. Phy.

A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, “Quasiparticle dynamics in graphene,” Nat. Phy.3, 36–40 (2007).
[CrossRef]

Opt. Commun.

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun.209, 17–22 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B84, 235122 (2011).
[CrossRef]

Phys. Rev. Lett.

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D. S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106, 013902 (2011).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-way electromagnetic waveguide formed at the interface between a plasmonic metal under a static magnetic field and a photonic crystal,” Phys. Rev. Lett.100, 023902 (2008).
[CrossRef] [PubMed]

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett.105, 013901 (2010).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, W. Lu, H. Li, A. Wu, Z. Sheng, J. Zi, X. Wang, S. Zou, and F. Gan, “Optical beam steering based on the symmetry of resonant modes of nanoparticles,” Phys. Rev. Lett.106, 203903 (2011).
[CrossRef] [PubMed]

J. Du, Z. Lin, S. T. Chui, G. Dong, and W. Zhang, “Nearly total omnidirectional reflection by a single layer of nanorods,” Phys. Rev. Lett.110, 163902 (2013).
[CrossRef] [PubMed]

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett.94,193902 (2005).
[CrossRef] [PubMed]

M. I. Tribelsky and B. S. Luk’yanchuk, “Anomalous light scattering by small particles,” Phys. Rev. Lett.97, 263902 (2006).
[CrossRef]

L. Peng, L. Ran, H. Chen, H. Zhang, J. A. Kong, and T. M. Grzegorczyk, “Experimental observation of left-handed behavior in an array of standard dielectric resonators,” Phys. Rev. Lett.98, 157403 (2007).
[CrossRef] [PubMed]

Science

A. K. Geim, “Graphene: status and prospects,” Science324, 1530–1534 (2009).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Transmission (T) and absorption (A) spectra of the metamaterial when ωB = 0 (black curve), 0.19ωp (blue curve) and 0.20ωp (red curve), respectively. Inset shows a schematic view of the metamaterial design.

Fig. 2
Fig. 2

Distributions of field amplitude |E| and transverse energy flux S (by arrows) in a quarter of the coaxial element, at the transmission dips of (a) 152.618 GHz and (b) 152.945 GHz, respectively, when ωB = 0.20ωp. Insets show the distribution of field amplitude |E| in the whole unit cell.

Fig. 3
Fig. 3

Distributions of field amplitude |E| when ωB = 0.20ωp at the transmission peaks of (a) 152.475 GHz, (b) 152.89 GHz, and (c) 153.49 GHz, respectively. Plots (d) to (f) are the corresponding distribution of transverse energy flux S.

Fig. 4
Fig. 4

(a) Phase delay δ, (b) group index ng and (c) absorption coefficient A versus frequency when ωB = 0.19ωp (red lines) and 0.20ωp (blue lines), respectively.

Equations (4)

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

ε ¯ ¯ = ( ε j γ 0 j γ ε 0 0 0 ε | | ) ,
ε = ε ω p 2 ω 2 ω B 2 + j ω 2 Γ ,
γ = ω B ω p 2 ω ( ω 2 ω B 2 + j ω 2 Γ ) ,
ε | | = ε ω p 2 ω 2 + j ω 2 Γ .

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