Abstract

Bi-anisotropic optical metamaterials are playing an increasingly important role in current wave-functional metamaterials and topological photonics due to their extra degree of freedom in addition to the permittivity and permeability. In this work, we derived the closed-form expressions for effective constitutive parameters of 2-dimensional (2D) bi-anisotropic metamaterials whose chirality tensors can possess both diagonal and off-diagonal components in the long-wavelength limit based on the Mie theory. Our formulas can be regarded as an extension of the Maxwell-Garnet formula to 2D bi-anisotriopic metamaterials and are verified through full wave numerical simulations. These closed-form formulas will benefit the design and analysis of the optical properties of 2D bi-anisotriopic metamaterials.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Hyperbolic metamaterials: beyond the effective medium theory

Tengfei Li and Jacob B. Khurgin
Optica 3(12) 1388-1396 (2016)

Material parameter retrieval procedure for general bi-isotropic metamaterials and its application to optical chiral negative-index metamaterial design

Do-Hoon Kwon, Douglas H. Werner, Alexander V. Kildishev, and Vladimir M. Shalaev
Opt. Express 16(16) 11822-11829 (2008)

Power analysis of multilayer structures composed of conventional materials and bi-anisotropic metamaterial slabs

Ugur Cem Hasar, Musa Bute, Joaquim J. Barroso, Cumali Sabah, Yunus Kaya, and Mehmet Ertugrul
J. Opt. Soc. Am. B 31(5) 939-947 (2014)

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004).
    [Crossref] [PubMed]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [Crossref] [PubMed]
  3. S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
    [Crossref] [PubMed]
  4. C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
    [Crossref]
  5. E. Plum, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90(22), 223113 (2007).
    [Crossref]
  6. H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
    [Crossref]
  7. T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
    [Crossref]
  8. S. L. Prosvirnin and N. I. Zheludev, “Polarization effects in the diffraction of light by a planar chiral structure,” Phys. Rev. E 71(3), 037603 (2005).
    [Crossref]
  9. V. A. Fedotov, P. L. Mladyonov, S. L. prosvirnin, A. V. Rogacheva, Y. Chan, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
    [Crossref] [PubMed]
  10. E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. O. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
    [Crossref] [PubMed]
  11. A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shevets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
    [Crossref]
  12. W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
    [Crossref] [PubMed]
  13. W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
    [Crossref] [PubMed]
  14. B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
    [Crossref] [PubMed]
  15. T. C. Choy, Effective Medium Theory: Principles and Applications (Oxford University, 1999).
  16. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
    [Crossref]
  17. Y. Wu, J. Li, Z.-Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit,” Phys. Rev. B 74(8), 085111 (2006).
    [Crossref]
  18. B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
    [Crossref]
  19. J. M. MacLaren, S. Crampin, D. D. Vvedensky, and J. B. Pendry, “Layer Korringa-Kohn-Rostoker technique for surface and interface electronic properties,” Phys. Rev. B 40(18), 12164–12175 (1989).
    [Crossref]
  20. A. Modinos, N. Stefanou, and V. Yannopapas, “Applications of the layer-KKR method to photonic crystals,” Opt. Express 8(3), 197–202 (2001).
    [Crossref] [PubMed]
  21. J. M. MacLaren, X.-G. Zhang, W. H. Butler, and X. Wang, “Layer KKR approach to Bloch-wave transmission and reflection: Application to spin-dependent tunneling,” Phys. Rev. B 59(8), 5470–5478 (1999).
    [Crossref]
  22. G.W. Milton, The Theory of Composites (Cambridge University, 2002).
    [Crossref]
  23. A. Priou, A. Sihvola, and S. Tretyakow, Advances in Complex Electromagnetic Materials (Springer Science & Business Media, 2012).
  24. J. C. M. Garnet, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London A 203, 385–420 (1904).
    [Crossref]
  25. A. H. Sihvola and I. V. Lindell, “Chiral Maxwell-Garnett mixing formula,” Electron. Lett. 26(2), 118–119 (1990).
    [Crossref]
  26. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “On the Maxwell-Garnett model of chiral composites,” J. Mater. Res. 8(4), 917–922 (1993).
    [Crossref]
  27. C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for quasiplanar chiral metamaterials,” Appl. Phys. Lett. 93(23), 233106 (2008).
    [Crossref]
  28. B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11(11), 114003 (2009).
    [Crossref]
  29. R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express 18(14), 14553–14567 (2010).
    [Crossref] [PubMed]
  30. X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71(4), 046610 (2005).
    [Crossref]
  31. Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79(2), 026610 (2009).
    [Crossref]
  32. X. Jing, R. Xia, W. Wang, Y. Tian, and Z. Hong, “Determination of the effective constitutive parameters of bianisotropic planar metamaterials in the terahertz region,” J. Opt. Soc. Am. A 33(5), 954–961 (2016).
    [Crossref]
  33. J. Zhao, X. Jing, W. Wang, Y. Tian, D. Zhu, and G. Shi, “Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz,” Opt. Laser Technol. 95, 56–62 (2017).
    [Crossref]
  34. J.A. Kong, Electromagnetic Wave Theory (Cambridge University, 2008).
  35. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley and Sons, 1983).
  36. N. Wang, J. Chen, S. Liu, and Zhifang Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87(6), 063812 (2013).
    [Crossref]
  37. A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-Anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).
  38. M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or ω medium,” Microw. Opt. Technol. Lett. 5(4), 184–188 (1992).
    [Crossref]
  39. S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75(15), 153104 (2007).
    [Crossref]
  40. N. Wang, S. Wang, Z.-Q. Zhang, and C. T. Chan, “Closed-form expressions for effective constitutive parameters: Electrostrictive and magnetostrictive tensors for bianisotropic metamaterials and their use in optical force density calculations,” Phys. Rev. B 98(4), 045426 (2018).
    [Crossref]
  41. W. Sun, S. B. Wang, Jack Ng, Lei Zhou, and C. T. Chan, “Analytic derivation of electrostrictive tensors and their application to optical force density calculations,” Phys. Rev. B 91(23), 235439 (2015).
    [Crossref]
  42. N. Wang, S. Wang, and J. Ng, “Electromagnetic stress tensor for an amorphous metamaterial medium,” Phys. Rev. A 97(3), 033839 (2018).
    [Crossref]
  43. M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
    [Crossref]
  44. www.comsol.com .

2018 (3)

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

N. Wang, S. Wang, Z.-Q. Zhang, and C. T. Chan, “Closed-form expressions for effective constitutive parameters: Electrostrictive and magnetostrictive tensors for bianisotropic metamaterials and their use in optical force density calculations,” Phys. Rev. B 98(4), 045426 (2018).
[Crossref]

N. Wang, S. Wang, and J. Ng, “Electromagnetic stress tensor for an amorphous metamaterial medium,” Phys. Rev. A 97(3), 033839 (2018).
[Crossref]

2017 (1)

J. Zhao, X. Jing, W. Wang, Y. Tian, D. Zhu, and G. Shi, “Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz,” Opt. Laser Technol. 95, 56–62 (2017).
[Crossref]

2016 (1)

2015 (2)

W. Sun, S. B. Wang, Jack Ng, Lei Zhou, and C. T. Chan, “Analytic derivation of electrostrictive tensors and their application to optical force density calculations,” Phys. Rev. B 91(23), 235439 (2015).
[Crossref]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

2014 (2)

W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

2013 (2)

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shevets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

N. Wang, J. Chen, S. Liu, and Zhifang Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87(6), 063812 (2013).
[Crossref]

2010 (2)

R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express 18(14), 14553–14567 (2010).
[Crossref] [PubMed]

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref]

2009 (4)

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. O. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[Crossref] [PubMed]

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11(11), 114003 (2009).
[Crossref]

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79(2), 026610 (2009).
[Crossref]

2008 (2)

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for quasiplanar chiral metamaterials,” Appl. Phys. Lett. 93(23), 233106 (2008).
[Crossref]

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

2007 (4)

E. Plum, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90(22), 223113 (2007).
[Crossref]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75(15), 153104 (2007).
[Crossref]

M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
[Crossref]

2006 (2)

Y. Wu, J. Li, Z.-Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit,” Phys. Rev. B 74(8), 085111 (2006).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. prosvirnin, A. V. Rogacheva, Y. Chan, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

2005 (3)

S. L. Prosvirnin and N. I. Zheludev, “Polarization effects in the diffraction of light by a planar chiral structure,” Phys. Rev. E 71(3), 037603 (2005).
[Crossref]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
[Crossref]

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71(4), 046610 (2005).
[Crossref]

2004 (1)

J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004).
[Crossref] [PubMed]

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

A. Modinos, N. Stefanou, and V. Yannopapas, “Applications of the layer-KKR method to photonic crystals,” Opt. Express 8(3), 197–202 (2001).
[Crossref] [PubMed]

1999 (1)

J. M. MacLaren, X.-G. Zhang, W. H. Butler, and X. Wang, “Layer KKR approach to Bloch-wave transmission and reflection: Application to spin-dependent tunneling,” Phys. Rev. B 59(8), 5470–5478 (1999).
[Crossref]

1993 (1)

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “On the Maxwell-Garnett model of chiral composites,” J. Mater. Res. 8(4), 917–922 (1993).
[Crossref]

1992 (1)

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or ω medium,” Microw. Opt. Technol. Lett. 5(4), 184–188 (1992).
[Crossref]

1990 (1)

A. H. Sihvola and I. V. Lindell, “Chiral Maxwell-Garnett mixing formula,” Electron. Lett. 26(2), 118–119 (1990).
[Crossref]

1989 (1)

J. M. MacLaren, S. Crampin, D. D. Vvedensky, and J. B. Pendry, “Layer Korringa-Kohn-Rostoker technique for surface and interface electronic properties,” Phys. Rev. B 40(18), 12164–12175 (1989).
[Crossref]

1904 (1)

J. C. M. Garnet, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London A 203, 385–420 (1904).
[Crossref]

Aydin, K.

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79(2), 026610 (2009).
[Crossref]

Barr, L. E.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

Beri, B.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley and Sons, 1983).

Butler, W. H.

J. M. MacLaren, X.-G. Zhang, W. H. Butler, and X. Wang, “Layer KKR approach to Bloch-wave transmission and reflection: Application to spin-dependent tunneling,” Phys. Rev. B 59(8), 5470–5478 (1999).
[Crossref]

Chan, C. T.

N. Wang, S. Wang, Z.-Q. Zhang, and C. T. Chan, “Closed-form expressions for effective constitutive parameters: Electrostrictive and magnetostrictive tensors for bianisotropic metamaterials and their use in optical force density calculations,” Phys. Rev. B 98(4), 045426 (2018).
[Crossref]

W. Sun, S. B. Wang, Jack Ng, Lei Zhou, and C. T. Chan, “Analytic derivation of electrostrictive tensors and their application to optical force density calculations,” Phys. Rev. B 91(23), 235439 (2015).
[Crossref]

W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref]

Y. Wu, J. Li, Z.-Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit,” Phys. Rev. B 74(8), 085111 (2006).
[Crossref]

Chan, Y.

V. A. Fedotov, P. L. Mladyonov, S. L. prosvirnin, A. V. Rogacheva, Y. Chan, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Chen, J.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

N. Wang, J. Chen, S. Liu, and Zhifang Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87(6), 063812 (2013).
[Crossref]

Chen, P.

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

Chen, W.-J.

W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Chen, X.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71(4), 046610 (2005).
[Crossref]

Chen, X.-D

W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Chen, Y.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. O. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[Crossref] [PubMed]

Choy, T. C.

T. C. Choy, Effective Medium Theory: Principles and Applications (Oxford University, 1999).

Crampin, S.

J. M. MacLaren, S. Crampin, D. D. Vvedensky, and J. B. Pendry, “Layer Korringa-Kohn-Rostoker technique for surface and interface electronic properties,” Phys. Rev. B 40(18), 12164–12175 (1989).
[Crossref]

Dong, J.-W.

W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Engheta, N.

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or ω medium,” Microw. Opt. Technol. Lett. 5(4), 184–188 (1992).
[Crossref]

Fang, C.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

Fang, F.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Fedotov, V. A.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. O. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[Crossref] [PubMed]

E. Plum, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90(22), 223113 (2007).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. prosvirnin, A. V. Rogacheva, Y. Chan, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Gao, W.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Garnet, J. C. M.

J. C. M. Garnet, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London A 203, 385–420 (1904).
[Crossref]

Genov, D. A.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

Grzegorczyk, T. M.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71(4), 046610 (2005).
[Crossref]

Guo, Q.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

Hibbins, A.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

Hong, Z.

Hudlicka, M.

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75(15), 153104 (2007).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley and Sons, 1983).

Jiang, S.-J.

W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Jing, X.

J. Zhao, X. Jing, W. Wang, Y. Tian, D. Zhu, and G. Shi, “Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz,” Opt. Laser Technol. 95, 56–62 (2017).
[Crossref]

X. Jing, R. Xia, W. Wang, Y. Tian, and Z. Hong, “Determination of the effective constitutive parameters of bianisotropic planar metamaterials in the terahertz region,” J. Opt. Soc. Am. A 33(5), 954–961 (2016).
[Crossref]

Kafesaki, M.

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11(11), 114003 (2009).
[Crossref]

Kargarian, M.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shevets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shevets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Kong, J. A.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71(4), 046610 (2005).
[Crossref]

Kong, J.A.

J.A. Kong, Electromagnetic Wave Theory (Cambridge University, 2008).

Koschny, T.

R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express 18(14), 14553–14567 (2010).
[Crossref] [PubMed]

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11(11), 114003 (2009).
[Crossref]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
[Crossref]

Krishnamurthy, S.

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

Lakhtakia, A.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “On the Maxwell-Garnett model of chiral composites,” J. Mater. Res. 8(4), 917–922 (1993).
[Crossref]

Lawrence, M.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Lederer, F.

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for quasiplanar chiral metamaterials,” Appl. Phys. Lett. 93(23), 233106 (2008).
[Crossref]

Li, H.

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref]

Li, J.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

Y. Wu, J. Li, Z.-Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit,” Phys. Rev. B 74(8), 085111 (2006).
[Crossref]

Li, T.

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

Li, T. Q.

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

Li, Z.

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79(2), 026610 (2009).
[Crossref]

Lin, Zhifang

N. Wang, J. Chen, S. Liu, and Zhifang Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87(6), 063812 (2013).
[Crossref]

Lindell, I. V.

A. H. Sihvola and I. V. Lindell, “Chiral Maxwell-Garnett mixing formula,” Electron. Lett. 26(2), 118–119 (1990).
[Crossref]

Liu, F.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Liu, H.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

Liu, R.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

Liu, S.

N. Wang, J. Chen, S. Liu, and Zhifang Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87(6), 063812 (2013).
[Crossref]

Liu, X. X.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. O. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[Crossref] [PubMed]

Liu, Y. M.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

Liu, Z. W.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

Lu, L.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

Lu, X.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

MacDonald, A. H.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shevets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

MacLaren, J. M.

J. M. MacLaren, X.-G. Zhang, W. H. Butler, and X. Wang, “Layer KKR approach to Bloch-wave transmission and reflection: Application to spin-dependent tunneling,” Phys. Rev. B 59(8), 5470–5478 (1999).
[Crossref]

J. M. MacLaren, S. Crampin, D. D. Vvedensky, and J. B. Pendry, “Layer Korringa-Kohn-Rostoker technique for surface and interface electronic properties,” Phys. Rev. B 40(18), 12164–12175 (1989).
[Crossref]

Menzel, C.

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for quasiplanar chiral metamaterials,” Appl. Phys. Lett. 93(23), 233106 (2008).
[Crossref]

Milton, G.W.

G.W. Milton, The Theory of Composites (Cambridge University, 2002).
[Crossref]

Mladyonov, P. L.

V. A. Fedotov, P. L. Mladyonov, S. L. prosvirnin, A. V. Rogacheva, Y. Chan, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Modinos, A.

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shevets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Ng, J.

N. Wang, S. Wang, and J. Ng, “Electromagnetic stress tensor for an amorphous metamaterial medium,” Phys. Rev. A 97(3), 033839 (2018).
[Crossref]

Ng, Jack

W. Sun, S. B. Wang, Jack Ng, Lei Zhou, and C. T. Chan, “Analytic derivation of electrostrictive tensors and their application to optical force density calculations,” Phys. Rev. B 91(23), 235439 (2015).
[Crossref]

Ozbay, E.

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79(2), 026610 (2009).
[Crossref]

Park, Y. S.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

Paul, T.

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for quasiplanar chiral metamaterials,” Appl. Phys. Lett. 93(23), 233106 (2008).
[Crossref]

Pendry, J. B.

J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004).
[Crossref] [PubMed]

J. M. MacLaren, S. Crampin, D. D. Vvedensky, and J. B. Pendry, “Layer Korringa-Kohn-Rostoker technique for surface and interface electronic properties,” Phys. Rev. B 40(18), 12164–12175 (1989).
[Crossref]

Plum, E.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. O. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[Crossref] [PubMed]

E. Plum, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90(22), 223113 (2007).
[Crossref]

Priou, A.

A. Priou, A. Sihvola, and S. Tretyakow, Advances in Complex Electromagnetic Materials (Springer Science & Business Media, 2012).

prosvirnin, S. L.

V. A. Fedotov, P. L. Mladyonov, S. L. prosvirnin, A. V. Rogacheva, Y. Chan, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

S. L. Prosvirnin and N. I. Zheludev, “Polarization effects in the diffraction of light by a planar chiral structure,” Phys. Rev. E 71(3), 037603 (2005).
[Crossref]

Rockstuhl, C.

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for quasiplanar chiral metamaterials,” Appl. Phys. Lett. 93(23), 233106 (2008).
[Crossref]

Rogacheva, A. V.

V. A. Fedotov, P. L. Mladyonov, S. L. prosvirnin, A. V. Rogacheva, Y. Chan, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

Saadoun, M. M. I.

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or ω medium,” Microw. Opt. Technol. Lett. 5(4), 184–188 (1992).
[Crossref]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Schwanecke, A. S.

E. Plum, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90(22), 223113 (2007).
[Crossref]

Semchenko, I. V.

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-Anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

Serdyukov, A. N.

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-Anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Shevets, G.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shevets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Shi, G.

J. Zhao, X. Jing, W. Wang, Y. Tian, D. Zhu, and G. Shi, “Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz,” Opt. Laser Technol. 95, 56–62 (2017).
[Crossref]

Sihvola, A.

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-Anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

A. Priou, A. Sihvola, and S. Tretyakow, Advances in Complex Electromagnetic Materials (Springer Science & Business Media, 2012).

Sihvola, A. H.

A. H. Sihvola and I. V. Lindell, “Chiral Maxwell-Garnett mixing formula,” Electron. Lett. 26(2), 118–119 (1990).
[Crossref]

Silveirinha, M. G.

M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
[Crossref]

Simovski, C. R.

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75(15), 153104 (2007).
[Crossref]

Slovick, B. A.

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

Smith, D. R.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
[Crossref]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Soukoulis, C. M.

R. Zhao, T. Koschny, and C. M. Soukoulis, “Chiral metamaterials: retrieval of the effective parameters with and without substrate,” Opt. Express 18(14), 14553–14567 (2010).
[Crossref] [PubMed]

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11(11), 114003 (2009).
[Crossref]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
[Crossref]

Stefanou, N.

Sun, C.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

Sun, W.

W. Sun, S. B. Wang, Jack Ng, Lei Zhou, and C. T. Chan, “Analytic derivation of electrostrictive tensors and their application to optical force density calculations,” Phys. Rev. B 91(23), 235439 (2015).
[Crossref]

Tian, Y.

J. Zhao, X. Jing, W. Wang, Y. Tian, D. Zhu, and G. Shi, “Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz,” Opt. Laser Technol. 95, 56–62 (2017).
[Crossref]

X. Jing, R. Xia, W. Wang, Y. Tian, and Z. Hong, “Determination of the effective constitutive parameters of bianisotropic planar metamaterials in the terahertz region,” J. Opt. Soc. Am. A 33(5), 954–961 (2016).
[Crossref]

Tremain, B.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

Tretyakov, S. A.

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75(15), 153104 (2007).
[Crossref]

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-Anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

Tretyakow, S.

A. Priou, A. Sihvola, and S. Tretyakow, Advances in Complex Electromagnetic Materials (Springer Science & Business Media, 2012).

Tsai, D. O.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. O. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[Crossref] [PubMed]

Tse, W.-K.

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shevets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Varadan, V. K.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “On the Maxwell-Garnett model of chiral composites,” J. Mater. Res. 8(4), 917–922 (1993).
[Crossref]

Varadan, V. V.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “On the Maxwell-Garnett model of chiral composites,” J. Mater. Res. 8(4), 917–922 (1993).
[Crossref]

Vier, D. C.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
[Crossref]

Vvedensky, D. D.

J. M. MacLaren, S. Crampin, D. D. Vvedensky, and J. B. Pendry, “Layer Korringa-Kohn-Rostoker technique for surface and interface electronic properties,” Phys. Rev. B 40(18), 12164–12175 (1989).
[Crossref]

Wang, B.

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11(11), 114003 (2009).
[Crossref]

Wang, F. M.

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

Wang, N.

N. Wang, S. Wang, Z.-Q. Zhang, and C. T. Chan, “Closed-form expressions for effective constitutive parameters: Electrostrictive and magnetostrictive tensors for bianisotropic metamaterials and their use in optical force density calculations,” Phys. Rev. B 98(4), 045426 (2018).
[Crossref]

N. Wang, S. Wang, and J. Ng, “Electromagnetic stress tensor for an amorphous metamaterial medium,” Phys. Rev. A 97(3), 033839 (2018).
[Crossref]

N. Wang, J. Chen, S. Liu, and Zhifang Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87(6), 063812 (2013).
[Crossref]

Wang, S.

N. Wang, S. Wang, and J. Ng, “Electromagnetic stress tensor for an amorphous metamaterial medium,” Phys. Rev. A 97(3), 033839 (2018).
[Crossref]

N. Wang, S. Wang, Z.-Q. Zhang, and C. T. Chan, “Closed-form expressions for effective constitutive parameters: Electrostrictive and magnetostrictive tensors for bianisotropic metamaterials and their use in optical force density calculations,” Phys. Rev. B 98(4), 045426 (2018).
[Crossref]

Wang, S. B.

W. Sun, S. B. Wang, Jack Ng, Lei Zhou, and C. T. Chan, “Analytic derivation of electrostrictive tensors and their application to optical force density calculations,” Phys. Rev. B 91(23), 235439 (2015).
[Crossref]

Wang, S. M.

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

Wang, W.

J. Zhao, X. Jing, W. Wang, Y. Tian, D. Zhu, and G. Shi, “Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz,” Opt. Laser Technol. 95, 56–62 (2017).
[Crossref]

X. Jing, R. Xia, W. Wang, Y. Tian, and Z. Hong, “Determination of the effective constitutive parameters of bianisotropic planar metamaterials in the terahertz region,” J. Opt. Soc. Am. A 33(5), 954–961 (2016).
[Crossref]

Wang, X.

J. M. MacLaren, X.-G. Zhang, W. H. Butler, and X. Wang, “Layer KKR approach to Bloch-wave transmission and reflection: Application to spin-dependent tunneling,” Phys. Rev. B 59(8), 5470–5478 (1999).
[Crossref]

Wei, Z.

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref]

Wu, B.-I.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71(4), 046610 (2005).
[Crossref]

Wu, C.

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref]

Wu, D. M.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

Wu, R. X.

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

Wu, Y.

Y. Wu, J. Li, Z.-Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit,” Phys. Rev. B 74(8), 085111 (2006).
[Crossref]

Xia, R.

Xiang, Y.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

Yan, Q.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

Yang, B.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Yannopapas, V.

Yu, X.

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref]

Yu, Z. G.

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

Zhang, S.

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

Zhang, W.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

Zhang, X.

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

Zhang, X.-G.

J. M. MacLaren, X.-G. Zhang, W. H. Butler, and X. Wang, “Layer KKR approach to Bloch-wave transmission and reflection: Application to spin-dependent tunneling,” Phys. Rev. B 59(8), 5470–5478 (1999).
[Crossref]

Zhang, Z.-Q.

N. Wang, S. Wang, Z.-Q. Zhang, and C. T. Chan, “Closed-form expressions for effective constitutive parameters: Electrostrictive and magnetostrictive tensors for bianisotropic metamaterials and their use in optical force density calculations,” Phys. Rev. B 98(4), 045426 (2018).
[Crossref]

Y. Wu, J. Li, Z.-Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit,” Phys. Rev. B 74(8), 085111 (2006).
[Crossref]

Zhao, J.

J. Zhao, X. Jing, W. Wang, Y. Tian, D. Zhu, and G. Shi, “Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz,” Opt. Laser Technol. 95, 56–62 (2017).
[Crossref]

Zhao, R.

Zheludev, N. I.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. O. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[Crossref] [PubMed]

E. Plum, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90(22), 223113 (2007).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. prosvirnin, A. V. Rogacheva, Y. Chan, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

S. L. Prosvirnin and N. I. Zheludev, “Polarization effects in the diffraction of light by a planar chiral structure,” Phys. Rev. E 71(3), 037603 (2005).
[Crossref]

Zhou, J.

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11(11), 114003 (2009).
[Crossref]

Zhou, L.

W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Zhou, Lei

W. Sun, S. B. Wang, Jack Ng, Lei Zhou, and C. T. Chan, “Analytic derivation of electrostrictive tensors and their application to optical force density calculations,” Phys. Rev. B 91(23), 235439 (2015).
[Crossref]

Zhu, B.

W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Zhu, D.

J. Zhao, X. Jing, W. Wang, Y. Tian, D. Zhu, and G. Shi, “Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz,” Opt. Laser Technol. 95, 56–62 (2017).
[Crossref]

Zhu, S. N.

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

Appl. Phys. Lett. (3)

T. Q. Li, H. Liu, T. Li, S. M. Wang, F. M. Wang, R. X. Wu, P. Chen, S. N. Zhu, and X. Zhang, “Magnetic resonance hybridization and optical activity of microwaves in a chiral metamaterial,” Appl. Phys. Lett. 92(13), 131111(2008).
[Crossref]

E. Plum, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. 90(22), 223113 (2007).
[Crossref]

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for quasiplanar chiral metamaterials,” Appl. Phys. Lett. 93(23), 233106 (2008).
[Crossref]

Electron. Lett. (1)

A. H. Sihvola and I. V. Lindell, “Chiral Maxwell-Garnett mixing formula,” Electron. Lett. 26(2), 118–119 (1990).
[Crossref]

J. Mater. Res. (1)

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, “On the Maxwell-Garnett model of chiral composites,” J. Mater. Res. 8(4), 917–922 (1993).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

B. Wang, J. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Chiral metamaterials: simulations and experiments,” J. Opt. A: Pure Appl. Opt. 11(11), 114003 (2009).
[Crossref]

J. Opt. Soc. Am. A (1)

Microw. Opt. Technol. Lett. (1)

M. M. I. Saadoun and N. Engheta, “A reciprocal phase shifter using novel pseudochiral or ω medium,” Microw. Opt. Technol. Lett. 5(4), 184–188 (1992).
[Crossref]

Nat. Commun. (1)

W.-J. Chen, S.-J. Jiang, X.-D Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shevets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (1)

J. Zhao, X. Jing, W. Wang, Y. Tian, D. Zhu, and G. Shi, “Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz,” Opt. Laser Technol. 95, 56–62 (2017).
[Crossref]

Philos. Trans. R. Soc. London A (1)

J. C. M. Garnet, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London A 203, 385–420 (1904).
[Crossref]

Phys. Rev. A (2)

N. Wang, J. Chen, S. Liu, and Zhifang Lin, “Dynamical and phase-diagram study on stable optical pulling force in Bessel beams,” Phys. Rev. A 87(6), 063812 (2013).
[Crossref]

N. Wang, S. Wang, and J. Ng, “Electromagnetic stress tensor for an amorphous metamaterial medium,” Phys. Rev. A 97(3), 033839 (2018).
[Crossref]

Phys. Rev. B (9)

M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
[Crossref]

S. A. Tretyakov, C. R. Simovski, and M. Hudlicka, “Bianisotropic route to the realization and matching of backward-wave metamaterial slabs,” Phys. Rev. B 75(15), 153104 (2007).
[Crossref]

N. Wang, S. Wang, Z.-Q. Zhang, and C. T. Chan, “Closed-form expressions for effective constitutive parameters: Electrostrictive and magnetostrictive tensors for bianisotropic metamaterials and their use in optical force density calculations,” Phys. Rev. B 98(4), 045426 (2018).
[Crossref]

W. Sun, S. B. Wang, Jack Ng, Lei Zhou, and C. T. Chan, “Analytic derivation of electrostrictive tensors and their application to optical force density calculations,” Phys. Rev. B 91(23), 235439 (2015).
[Crossref]

J. M. MacLaren, X.-G. Zhang, W. H. Butler, and X. Wang, “Layer KKR approach to Bloch-wave transmission and reflection: Application to spin-dependent tunneling,” Phys. Rev. B 59(8), 5470–5478 (1999).
[Crossref]

Y. Wu, J. Li, Z.-Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit,” Phys. Rev. B 74(8), 085111 (2006).
[Crossref]

B. A. Slovick, Z. G. Yu, and S. Krishnamurthy, “Generalized effective-medium theory for metamaterials,” Phys. Rev. B 89(15), 155118 (2014).
[Crossref]

J. M. MacLaren, S. Crampin, D. D. Vvedensky, and J. B. Pendry, “Layer Korringa-Kohn-Rostoker technique for surface and interface electronic properties,” Phys. Rev. B 40(18), 12164–12175 (1989).
[Crossref]

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007).
[Crossref]

Phys. Rev. E (4)

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71(3), 036617 (2005).
[Crossref]

S. L. Prosvirnin and N. I. Zheludev, “Polarization effects in the diffraction of light by a planar chiral structure,” Phys. Rev. E 71(3), 037603 (2005).
[Crossref]

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, “Retrieval of the effective constitutive parameters of bianisotropic metamaterials,” Phys. Rev. E 71(4), 046610 (2005).
[Crossref]

Z. Li, K. Aydin, and E. Ozbay, “Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients,” Phys. Rev. E 79(2), 026610 (2009).
[Crossref]

Phys. Rev. Lett. (5)

V. A. Fedotov, P. L. Mladyonov, S. L. prosvirnin, A. V. Rogacheva, Y. Chan, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref] [PubMed]

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. O. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[Crossref] [PubMed]

S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. 102(2), 023901 (2009).
[Crossref] [PubMed]

C. Wu, H. Li, Z. Wei, X. Yu, and C. T. Chan, “Theory and experimental realization of negative refraction in a metallic helix array,” Phys. Rev. Lett. 105(24), 247401 (2010).
[Crossref]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Science (3)

B. Yang, Q. Guo, B. Tremain, R. Liu, L. E. Barr, Q. Yan, W. Gao, H. Liu, Y. Xiang, J. Chen, C. Fang, A. Hibbins, L. Lu, and S. Zhang, “Ideal Weyl points and helicoid surface states in artificial photonic crystal structures,” Science 359(6379), 1013–1016 (2018).
[Crossref] [PubMed]

J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[Crossref] [PubMed]

Other (7)

T. C. Choy, Effective Medium Theory: Principles and Applications (Oxford University, 1999).

J.A. Kong, Electromagnetic Wave Theory (Cambridge University, 2008).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley and Sons, 1983).

G.W. Milton, The Theory of Composites (Cambridge University, 2002).
[Crossref]

A. Priou, A. Sihvola, and S. Tretyakow, Advances in Complex Electromagnetic Materials (Springer Science & Business Media, 2012).

www.comsol.com .

A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bi-Anisotropic Materials: Theory and Applications (Gordon and Breach Science, 2001).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Top view of the bianisotropic metamaterial with parallel cylindrical inclusions arranged in either (a) regular or (b) random lattice in the xy plane. The in-plane and out-of-plane directions are along xy and z directions, respectively.
Fig. 2
Fig. 2 The spatially averaged electric field and displacement field of each layer inside the metamaterials having the square lattice structure for the incident angle (a) θ = π/6 and (b) θ = π/3 are noted by circles, while the electric field and displacement field along the x direction in corresponding effective continuous medium under the same incidence are shown by lines. The effective medium slab (photonic crystal) region is between the dotted lines. The incident beam is Ez polarized with amplitude E0. The constitutive parameters of the cylinder are εt = 2,εz = 5,µt = µz = 1,κt = 0.5,κz = 0.3,κk = 0.4, and the radius is r0 = 0.3a.
Fig. 3
Fig. 3 The spatially averaged electric field and displacement field of each layer inside the metamaterials having the triangular lattice structure for the incident angle (a) θ = π/6 and (b) θ = π/3 are noted by circles, while the electric field and displacement field along the x direction in corresponding effective continuous medium under the same incidence are shown by lines. The effective medium slab (photonic crystal) region is between the dotted lines. The incident beam is Ez polarized with amplitude E0. The constitutive parameters of the cylinder are εt = 8,εz = 3, µt = µz = 1, κt = 0.3, κz = 0.4, κk = 0.5, and the radius is r0 = 0.3a.
Fig. 4
Fig. 4 Comparison between the refractive indices obtained from the formulas (lines) and those from the slopes of band dispersion (circles). (a) The chirality tensor of the cylinder has no off-diagonal terms (κk = 0) and κz = 0.5. (b) The chirality tensor of the cylinder has no diagonal terms (κt = κz = 0). The other constitutive parameters of the cylinder are εt = 10, εz = 5, µt = µz = 1 and the radius is r0 = 0.35a.
Fig. 5
Fig. 5 Comparison between the refractive indices obtained from the formulas (lines) and those from the slopes of band dispersion (circles). (a) The chirality tensor of the cylinder has no off-diagonal and out-of-plane terms (κk = κz = 0). (b) The chirality tensor of the cylinder has no diagonal terms (κt = κz = 0). The other constitutive parameters of the cylinder are εt = εz = −1.5, µt = µz = 1 and the radius is r0 = 0.3a.

Equations (34)

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

D = ε 0 ε ¯ ¯ E + i c κ ¯ ¯ H , B = μ 0 μ ¯ ¯ H i c κ ¯ ¯ T E ,
ε ¯ ¯ = ε t x ^ x ^ + ε t y ^ y ^ + ε z z ^ z ^ , μ ¯ ¯ = μ t x ^ x ^ + μ t y ^ y ^ + μ z z ^ z ^ ,
κ ¯ ¯ = κ t x ^ x ^ + κ t y ^ y ^ + κ z z ^ z ^ + κ k x ^ y ^ κ k y ^ x ^ .
D = ( ε ¯ ¯ E + i κ ¯ ¯ H ) = ε t E + i κ t H + i κ k ( × H ) z ^ = 0 , B = ( μ ¯ ¯ H i κ ¯ ¯ T H ) = μ t H i κ t E + i κ k ( × E ) z ^ = 0 , × D = × ( ε ¯ ¯ E + i κ ¯ ¯ T H ) = ε ¯ ¯ × E + i κ ¯ ¯ × H i κ k H z ^ , × B = × ( μ ¯ ¯ H i κ ¯ ¯ T H ) = μ ¯ ¯ × H i κ ¯ ¯ × E i κ k E z ^ ,
ε ¯ ¯ = ε z ( x ^ x ^ + y ^ y ^ ) + ε t z ^ z ^ , μ ¯ ¯ = μ z ( x ^ x ^ + y ^ y ^ ) + μ t z ^ z ^ , κ ¯ ¯ = κ z ( x ^ x ^ + y ^ y ^ ) + κ t z ^ z ^ .
E = i k 0 κ k ( κ t B z i μ t D z ) ε t μ t κ t 2 , H = i k 0 κ k ( κ t D z i ε t B z ) ε t μ t κ t 2 .
× D = k 0 ( M ¯ ¯ 1 D + i M ¯ ¯ 2 B ) , × B = k 0 ( M ¯ ¯ 1 B i M ¯ ¯ 3 D ) ,
M ¯ ¯ 1 = κ z ( x ^ x ^ + y ^ y ^ ) + ε t μ t κ t 2 κ k 2 ε t μ t κ t 2 κ t z ^ z ^ , M ¯ ¯ 2 = ε z ( x ^ x ^ + y ^ y ^ ) + ε t μ t κ t 2 κ k 2 ε t μ t κ t 2 ε t z ^ z ^ , M ¯ ¯ 3 = μ z ( x ^ x ^ + y ^ y ^ ) + ε t μ t κ t 2 κ k 2 ε t μ t κ t 2 μ t z ^ z ^ .
× D = 2 D = k 0 2 ( M ˜ 1 M ¯ ¯ 1 + M ˜ 2 M ¯ ¯ 3 ) D + i k 0 2 ( M ˜ 1 M ¯ ¯ 2 + M ˜ 2 M ¯ ¯ 1 ) B , × B = 2 B = k 0 2 ( M ˜ 1 M ¯ ¯ 1 + M ˜ 3 M ¯ ¯ 2 ) B i k 0 2 ( M ˜ 1 M ¯ ¯ 3 + M ˜ 3 M ¯ ¯ 1 ) D ,
M ˜ 1 = ε t μ t κ t 2 κ k 2 ε t μ t κ t 2 κ t ( x ^ x ^ + y ^ y ^ ) + κ z z ^ z ^ , M ˜ 2 = ε t μ t κ t 2 κ k 2 ε t μ t κ t 2 ε t ( x ^ x ^ + y ^ y ^ ) + ε z z ^ z ^ , M ˜ 3 = ε t μ t κ t 2 κ k 2 ε t μ t κ t 2 μ t ( x ^ x ^ + y ^ y ^ ) + μ z z ^ z ^ .
2 ( D B ) + k 0 2 ( M ˜ 1 M ¯ ¯ 1 + M ˜ 2 M ¯ ¯ 3 i ( M ˜ 1 M ¯ ¯ 2 + M ˜ 2 M ¯ ¯ 1 ) M ˜ 1 M ¯ ¯ 1 + M ˜ 3 M ¯ ¯ 3 i ( M ˜ 1 M ¯ ¯ 3 + M ˜ 3 M ¯ ¯ 1 ) ) ( D B ) = 0 ,
k 2 ( E z H z ) = k 0 2 ( ε z μ t + κ z κ t i μ t κ z + i μ z κ t i ε t κ z i ε z κ t ε t μ z + κ z κ t ) ( E z H z ) .
2 ( k ± / k 0 ) 2 = ε z μ t + ε t μ z + 2 κ z κ t ± Δ , Δ = ( ε z μ t ε t μ z ) 2 + 4 κ z κ t ( ε z μ t + ε t μ z ) + 4 κ z 2 ε t μ t + 4 κ t 2 ε z μ z ,
( E z H z ) ( i ( ε z μ t ε t μ z ± Δ ) 2 ( κ z μ t + κ t μ z ) 1 ) = ( i v ± 1 ) .
E i n s ( r ) = n [ c n N n ( 1 ) ( k + , r ) + c n M n ( 1 ) ( k + , r ) + d n N n ( 1 ) ( k , r ) + d n M n ( 1 ) ( k , r ) ] ,
L n ( J ) = [ i n ρ z n ( J ) ( ρ ) ϕ ^ + z n ( J ) ( ρ ) r ^ ] e i n ϕ , M n ( J ) = [ i n ρ z n ( J ) ( ρ ) r ^ + z n ( J ) ( ρ ) ϕ ^ ] e i n ϕ , N n ( J ) = z n ( J ) ( ρ ) e i n ϕ z ^ ,
× L n ( J ) = M n ( J ) = N n ( J ) = 0 , × M n ( J ) = L n ( J ) z ^ = k N n ( J ) , × N n ( J ) = k M n ( J ) .
× E i n s = i ω B i n s = i ω ( μ ¯ ¯ H i n s i κ ¯ ¯ E i n s ) ,
H i n s = i μ t n [ k + c n κ t c n ) M n ( 1 ) ( k + , r ) + ( k d n κ t d n ) M n ( 1 ) ( k , r ) + ( k + c n κ z c n ) N n ( 1 ) ( k + , r ) + ( k d n κ z d n ) N n ( 1 ) ( k , r ) ] .
i μ z c n = i v + ( k + c n κ z c n ) i μ z d n = i v ( k d n κ z d n ) .
E i = n [ q n N n ( 1 ) ( k 0 , r ) + p n M n ( 1 ) ( k 0 , r ) ] , H i = i n [ p n N n ( 1 ) ( k 0 , r ) + q n M n ( 1 ) ( k 0 , r ) ] , E s = n [ b n N n ( 3 ) ( k 0 , r ) + a n M n ( 3 ) ( k 0 , r ) ] , H s = i n [ a n N n ( 3 ) ( k 0 , r ) + b n M n ( 3 ) ( k 0 , r ) ] ,
a n = A n p n + C n q n , b n = D n p n + B n q n .
q n J n ( x 0 ) b n H n ( 1 ) ( x 0 ) = c n J n ( x + ) + d n J n ( x ) , p n J n ( x 0 ) a n H n ( 1 ) ( x 0 ) = c n J n ( x + ) d n J n ( x ) , p n J n ( x 0 ) a n H n ( 1 ) ( x 0 ) = μ z 1 [ ( k + c n κ z c n ) J n ( x + ) + ( k d n κ z d n ) J n ( x ) ] , q n J n ( x 0 ) b n H n ( 1 ) ( x 0 ) = μ t 1 [ ( k + c n κ t c n ) J n ( x + ) + ( k d n κ t d n ) J n ( x ) ] ,
A 0 = i 4 ( μ z 1 ) π x 0 2 , A ± 1 = i 4 ( 1 ε t ) ( 1 + μ t ) + κ t 2 ( 1 + ε t ) ( 1 + μ t ) κ t 2 π x 0 2 , B 0 = i 4 ( ε z 1 ) π x 0 2 , B ± 1 = i 4 ( 1 + ε t ) ( 1 μ t ) + κ t 2 ( 1 + ε t ) ( 1 + μ t ) κ t 2 π x 0 2 , C 0 = D 0 = i 4 κ z π x 0 2 , C ± = D ± 1 = i 2 κ t ( 1 + ε t ) ( 1 + μ t ) κ t 2 π x 0 2 .
( k 1 / k 0 ) 2 = ε z ε t 1 ( ε t μ t κ k 2 ) , ( k 2 / k 0 ) 2 = μ z μ t 1 ( ε t μ t κ k 2 ) ,
D i n s = n [ d n N n ( 1 ) ( k 1 , r ) + e n M n ( 1 ) ( k 2 , r ) , B i n s = n [ c n M n ( 1 ) ( k 1 , r ) + f n N n ( 1 ) ( k 2 , r ) ,
d n k 1 = i ε z c n , e n k 2 = i ( ε t κ k 2 μ t ) f n ,
E i n s = n d n ε z N n ( 1 ) ( k 1 , r ) + μ t e n ε t μ t κ k 2 M n ( 1 ) ( k 2 , r ) + i κ k c n ε t μ t κ k 2 L n ( 1 ) ( k 1 , r ) , H i n s = n f n μ z N n ( 1 ) ( k 2 , r ) + ε t e n ε t μ t κ k 2 M n ( 1 ) ( k 1 , r ) + i κ k e n ε t μ t κ k 2 L n ( 1 ) ( k 2 , r ) .
q n J n ( x 0 ) b n H n ( 1 ) ( x 0 ) = ε z 1 d n J n ( x 1 ) , i p n J n ( x 0 ) + i a n H n ( 1 ) ( x 0 ) = μ z 1 f n J n ( x 2 ) , p n J n ( x 0 ) a n H n ( 1 ) ( x 0 ) = μ t e n ε t μ t κ k 2 J n ( x 2 ) + κ k c n ε t μ t κ k 2 n x 1 J n ( x 1 ) , i q n J n ( x 0 ) + i b n H n ( 1 ) ( x 0 ) = ε t c n ε t μ t κ k 2 J n ( x 1 ) + κ k e n ε t μ t κ k 2 n x 2 J n ( x 2 ) ,
A 0 = i 4 ( μ z 1 ) π x 0 2 , A ± 1 = i 4 ( 1 ε t ) ( 1 + μ t ) + κ k 2 ( ε t + 1 ) ( μ t + 1 ) κ k 2 π x 0 2 , B 0 = i 4 ( ε z 1 ) π x 0 2 , B ± 1 = i 4 ( 1 + ε t ) ( 1 μ t ) + κ k 2 ( ε t + 1 ) ( μ t + 1 ) κ k 2 π x 0 2 , C 0 = D 0 = 0 , C ± 1 = D ± 1 = ± 1 2 κ k ( ε t + 1 ) ( μ t + 1 ) κ k 2 π x 0 2 .
A 0 = i 4 ( μ z 1 ) π x 0 2 , A ± 1 = i 4 ( 1 ε t ) ( 1 + μ t ) + κ k 2 ( ε t + 1 ) ( μ t + 1 ) κ k 2 π x 0 2 , B 0 = i 4 ( ε z 1 ) π x 0 2 , B ± 1 = i 4 ( 1 + ε t ) ( 1 μ t ) + κ k 2 ( ε t + 1 ) ( μ t + 1 ) κ k 2 π x 0 2 , C 0 = D 0 = i 4 κ z π x 0 2 , C ± 1 = D ± 1 = 1 2 i κ t ± κ k ( ε t + 1 ) ( μ t + 1 ) κ k 2 π x 0 2 .
A i e = A i , B i e = B i , C i e = C i , D i e = D i , i = 1 , 0 , 1
ε e z = 1 + i Λ B 0 , μ e z = 1 + i Λ A 0 , κ e z = i Λ C 0 , ε e t = ( i Λ A 1 ) ( i + Λ B 1 ) + Λ 2 C 1 D 1 ( i + Λ A 1 ) ( i + Λ B 1 ) Λ 2 C 1 D 1 , μ e t = ( i + Λ A 1 ) ( i Λ B 1 ) + Λ 2 C 1 D 1 ( i + Λ A 1 ) ( i + Λ B 1 ) Λ 2 C 1 D 1 , κ e t = i Λ 2 ( C 1 D 1 ) ( i + Λ A 1 ) ( i + Λ B 1 ) Λ 2 C 1 D 1 , κ e k = Λ ( C 1 D 1 ) ( i + Λ A 1 ) ( i + Λ B 1 ) Λ 2 C 1 D 1 ,
ε e z = ( ε z 1 ) p + 1 , μ e z = ( μ z 1 ) p + 1 , κ e z = κ z p , ε e t = ( 1 + ε t ) ( 1 + μ t ) κ t 2 κ k 2 + 2 ( ε t μ t ) p [ ( 1 ε t ) ( 1 μ t ) κ t 2 κ k 2 ] p 2 ( 1 + ε t ) ( 1 + μ t ) κ t 2 κ k 2 + 2 ( 1 ε t μ t + κ t 2 + κ t 2 ) p + [ ( 1 ε t ) ( 1 μ t ) κ t 2 κ k 2 ] p 2 , μ e t = ( 1 + ε t ) ( 1 + μ t ) κ t 2 κ k 2 + 2 ( ε t μ t ) p [ ( 1 ε t ) ( 1 μ t ) κ t 2 κ k 2 ] p 2 ( 1 + ε t ) ( 1 + μ t ) κ t 2 κ k 2 + 2 ( 1 ε t μ t + κ t 2 + κ t 2 ) p + [ ( 1 ε t ) ( 1 μ t ) κ t 2 κ k 2 ] p 2 , κ e t = 4 κ t p ( 1 + ε t ) ( 1 + μ t ) κ t 2 κ k 2 + 2 ( 1 ε t μ t + κ t 2 + κ t 2 ) p + [ ( 1 ε t ) ( 1 μ t ) κ t 2 κ k 2 ] p 2 κ e k = 4 κ k p ( 1 + ε t ) ( 1 + μ t ) κ t 2 κ k 2 + 2 ( 1 ε t μ t + κ t 2 + κ t 2 ) p + [ ( 1 ε t ) ( 1 μ t ) κ t 2 κ k 2 ] p 2 ,

Metrics