Abstract

Based on Maxwell’s equations and Mie theory, strong sub-wavelength artificial magnetic and electric dipole resonances can be excited within dielectric resonators, and their resonant frequencies can be tailored simply by scaling the size of the dielectric resonators. Therefore, in this work we hybridize commercially available zirconia and alumina structures to harvest their individual artificial magnetic and electric response simultaneously, presenting a negative refractive index medium (NRIM). Comparing with the conventional NRIM constructed by metallic structures, the demonstrated all-dielectric NRIM possesses low-loss and high-symmetry advantages, thus benefiting practical applications in communication components, perfect lenses, invisible cloaking and other novel electromagnetic devices.

© 2012 OSA

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  1. 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]
  2. N. Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science 302(5650), 1537–1540 (2003).
    [CrossRef] [PubMed]
  3. J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pacheco, B. I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11(7), 723–734 (2003).
    [CrossRef] [PubMed]
  4. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
    [CrossRef] [PubMed]
  5. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
    [CrossRef]
  6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  7. Q. Q. Gan, Y. J. Ding, and F. J. Bartoli, “Rainbow’ trapping and releasing at telecommunication wavelength,” Phys. Rev. Lett. 102(5), 056801 (2009).
    [CrossRef]
  8. M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variation,” Phys. Rev. B 75(23), 235114 (2007).
    [CrossRef]
  9. J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004).
    [CrossRef] [PubMed]
  10. T.-C. Yang, Y.-H. Yang, and T.-J. Yen, “An anisotropic negative refractive index medium operated at multiple-angle incidences,” Opt. Express 17(26), 24189–24197 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. Y. J. Lai, C. K. Chen, and T. J. Yen, “Creating negative refractive identity via single-dielectric resonators,” Opt. Express 17(15), 12960–12970 (2009).
    [CrossRef] [PubMed]
  14. Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008).
    [CrossRef]
  15. O. G. Vendik and M. S. Gashinova, “Artificial double negative (DNG) media composed by two different dielectric sphere lattices embedded in a dielectric matrix,” in Proceedings of the 34 European Microwave Conference (2004), pp. 1209–1212.
  16. J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
    [CrossRef]
  17. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
    [CrossRef]
  18. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler. Metallösungen,” Ann. Phys. 25(4), 377–445 (1908).
    [CrossRef]
  19. T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, D. C. Schmadel, and R. J. Phaneuf, “Optical plasmonic resonances in split-ring resonator structures: an improved LC model,” Opt. Express 16(24), 19850–19864 (2008).
    [CrossRef] [PubMed]

2011

J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
[CrossRef]

2009

2008

Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008).
[CrossRef]

T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, D. C. Schmadel, and R. J. Phaneuf, “Optical plasmonic resonances in split-ring resonator structures: an improved LC model,” Opt. Express 16(24), 19850–19864 (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(15), 157403 (2007).
[CrossRef] [PubMed]

M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variation,” Phys. Rev. B 75(23), 235114 (2007).
[CrossRef]

2004

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

2003

2002

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. 14(15), 4035–4044 (2002).

2001

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]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1999

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1996

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

1908

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler. Metallösungen,” Ann. Phys. 25(4), 377–445 (1908).
[CrossRef]

Bartoli, F. J.

Q. Q. Gan, Y. J. Ding, and F. J. Bartoli, “Rainbow’ trapping and releasing at telecommunication wavelength,” Phys. Rev. Lett. 102(5), 056801 (2009).
[CrossRef]

Bearpark, T.

N. Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science 302(5650), 1537–1540 (2003).
[CrossRef] [PubMed]

Chen, C. K.

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(15), 157403 (2007).
[CrossRef] [PubMed]

Chen, M.

Corrigan, T. D.

Ding, Y. J.

Q. Q. Gan, Y. J. Ding, and F. J. Bartoli, “Rainbow’ trapping and releasing at telecommunication wavelength,” Phys. Rev. Lett. 102(5), 056801 (2009).
[CrossRef]

Drew, H. D.

Economou, E. N.

M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variation,” Phys. Rev. B 75(23), 235114 (2007).
[CrossRef]

Gan, Q. Q.

Q. Q. Gan, Y. J. Ding, and F. J. Bartoli, “Rainbow’ trapping and releasing at telecommunication wavelength,” Phys. Rev. Lett. 102(5), 056801 (2009).
[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(15), 157403 (2007).
[CrossRef] [PubMed]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pacheco, B. I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11(7), 723–734 (2003).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Kafesaki, M.

M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variation,” Phys. Rev. B 75(23), 235114 (2007).
[CrossRef]

Katsarakis, N.

M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variation,” Phys. Rev. B 75(23), 235114 (2007).
[CrossRef]

Kolb, P. W.

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(15), 157403 (2007).
[CrossRef] [PubMed]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pacheco, B. I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11(7), 723–734 (2003).
[CrossRef] [PubMed]

Koschny, Th.

M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variation,” Phys. Rev. B 75(23), 235114 (2007).
[CrossRef]

Lai, Y. J.

Lu, J.

Ma, Y. G.

Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008).
[CrossRef]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler. Metallösungen,” Ann. Phys. 25(4), 377–445 (1908).
[CrossRef]

O’Brien, S.

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. 14(15), 4035–4044 (2002).

Ong, C. K.

Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008).
[CrossRef]

Pacheco, J.

Pendry, J. B.

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

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. 14(15), 4035–4044 (2002).

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[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(15), 157403 (2007).
[CrossRef] [PubMed]

Phaneuf, R. J.

Qu, S.

J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
[CrossRef]

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(15), 157403 (2007).
[CrossRef] [PubMed]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Schmadel, D. C.

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[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]

Seddon, N.

N. Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science 302(5650), 1537–1540 (2003).
[CrossRef] [PubMed]

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]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[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.

M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variation,” Phys. Rev. B 75(23), 235114 (2007).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Sushkov, A. B.

Tsiapa, I.

M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variation,” Phys. Rev. B 75(23), 235114 (2007).
[CrossRef]

Wang, J.

J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
[CrossRef]

J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
[CrossRef]

Wang, P.

Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008).
[CrossRef]

Wei, X.

J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
[CrossRef]

Wu, B. I.

Xu, Z.

J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
[CrossRef]

Yang, T.-C.

Yang, Y.

J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
[CrossRef]

Yang, Y.-H.

Yen, T. J.

Yen, T.-J.

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Yu, Z.

J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
[CrossRef]

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(15), 157403 (2007).
[CrossRef] [PubMed]

Zhang, Y.

Zhao, L.

Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008).
[CrossRef]

Ann. Phys.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler. Metallösungen,” Ann. Phys. 25(4), 377–445 (1908).
[CrossRef]

Appl. Phys. Lett.

Y. G. Ma, L. Zhao, P. Wang, and C. K. Ong, “Fabrication of negative index materials using dielectric and metallic composite route,” Appl. Phys. Lett. 93(18), 184103 (2008).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. Appl. Phys.

J. Wang, Z. Xu, Z. Yu, X. Wei, Y. Yang, J. Wang, and S. Qu, “Experimental realization of all-dielectric composit cubes/rods left-handed metamaterial,” J. Appl. Phys. 109(8), 084918 (2011).
[CrossRef]

J. Phys.

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. 14(15), 4035–4044 (2002).

Opt. Express

Phys. Rev. B

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variation,” Phys. Rev. B 75(23), 235114 (2007).
[CrossRef]

Phys. Rev. Lett.

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(15), 157403 (2007).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Q. Q. Gan, Y. J. Ding, and F. J. Bartoli, “Rainbow’ trapping and releasing at telecommunication wavelength,” Phys. Rev. Lett. 102(5), 056801 (2009).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Science

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]

N. Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science 302(5650), 1537–1540 (2003).
[CrossRef] [PubMed]

Other

O. G. Vendik and M. S. Gashinova, “Artificial double negative (DNG) media composed by two different dielectric sphere lattices embedded in a dielectric matrix,” in Proceedings of the 34 European Microwave Conference (2004), pp. 1209–1212.

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Figures (3)

Fig. 1
Fig. 1

(a) Measured scattering coefficients and phase of transmission for one unit of ZrO2 and Al2O3 sample in the WR-137 rectangular waveguide. (b) Simulated scattering coefficients and phase of transmission for one unit of ZrO2 and Al2O3 sample in the WR-137 rectangular waveguide. The dimensional parameter of unit cell for ZrO2 cuboid (Al2O3 cube) is 5.5 × 5.5 × 10 mm3 (9x9x9mm3) with the boundary condition of PEC along the x and y directions as shown in the inset. Both results are in good agreement to indicate magnetic resonance of Al2O3 particle and electric resonances of ZrO2 particle at 7.79 GHz.

Fig. 2
Fig. 2

(a) Spectra of effective material parameters (permeability and permittivity) of ZrO2 and Al2O3 particles arrays calculated by retrieval method, showing negative permittivity and negative permeability at 7.79 GHz, respectively. (b) Electric and magnetic field distributions for ZrO2 particle at electric resonance frequency (at 7.79 GHz) and those for Al2O3 particle at magnetic resonance frequency (at 7.79 GHz). Notice a magnetic dipole oriented along the y-direction at 7.79 GHz for Al2O3 particle, and an electric dipole oriented along y-direction at 7.79 GHz for ZrO2 particle.

Fig. 3
Fig. 3

(a) Measurement and (b) simulation of transmittance magnitude and phase spectra of scattering coefficients for one unit of ZrO2 (black) and Al2O3 (red) samples in the WR-137 rectangular waveguide. Green curve is that simulated transmittance magnitude and phase for one pair of ZrO2 and Al2O3 sample hybridized in the WR-137 rectangular waveguide. (c) Effective material parameters (permeability and permittivity) of integration of ZrO2 and Al2O3 particles arrays calculated by retrieval method, showing negative refractive index at 7.79 GHz.

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