Abstract

From a periodic array of commercially available zirconia cubes, we demonstrate artificial magnetic and electric dipoles due to the combination of displacement currents and Mie resonance. By scaling the size and periodicity of these dielectric resonators, the corresponding magnetic and electric responses are shifted to the desired frequencies. To further overlap the magnetic and electric resonances in the same frequency, we create a negative refractive index medium (NRIM) from single-dielectric resonators. Comparing with the conventional NRIM comprised of metallic or two-dielectric resonators, these single-dielectric structures present the low-loss and isotropic characteristics, and possess a further advantage to facilitate practical applications.

© 2009 OSA

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2008 (6)

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930–930 (2008).
[CrossRef] [PubMed]

A. Ahmadi and H. Mosallaei, “Physical configuration and performance modeling of all-dielectric metamaterials,” Phys. Rev. B 77(4), 045104 (2008).
[CrossRef]

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]

Y. J. Chiang and T. J. Yen, “A highly symmetric two-handed metamaterial spontaneously matching the wave impedance,” Opt. Express 16(17), 12764–12770 (2008).
[PubMed]

D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Cut-wire-pair structures as two-dimensional magnetic metamaterials,” Opt. Express 16(19), 15185–15190 (2008).
[CrossRef] [PubMed]

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 (4)

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

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]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

2006 (2)

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (2)

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

2001 (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]

2000 (1)

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

1999 (1)

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 (1)

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]

1968 (1)

G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

1947 (1)

L. Lewin, “The electrical constants of a material loaded with spherical particles,” Proc. Inst. Electr. Eng. 94, 65–68 (1947).

Ahmadi, A.

A. Ahmadi and H. Mosallaei, “Physical configuration and performance modeling of all-dielectric metamaterials,” Phys. Rev. B 77(4), 045104 (2008).
[CrossRef]

Atwater, H. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930–930 (2008).
[CrossRef] [PubMed]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Bearpark, T.

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

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Brueck, S. R. J.

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.

Chiang, Y. J.

Corrigan, T. D.

Dionne, J. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

Dolling, G.

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]

Enkrich, C.

Fan, W.

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

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]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[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]

Kivshar, Y. S.

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, T.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[CrossRef]

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]

Lewin, L.

L. Lewin, “The electrical constants of a material loaded with spherical particles,” Proc. Inst. Electr. Eng. 94, 65–68 (1947).

Lezec, H. J.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007).
[CrossRef] [PubMed]

Linden, S.

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930–930 (2008).
[CrossRef] [PubMed]

Liu, Z.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930–930 (2008).
[CrossRef] [PubMed]

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]

Malloy, K. J.

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]

Mosallaei, H.

A. Ahmadi and H. Mosallaei, “Physical configuration and performance modeling of all-dielectric metamaterials,” Phys. Rev. B 77(4), 045104 (2008).
[CrossRef]

O’Brien, S.

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. 14, 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]

Osgood, R. M.

Pacheco, J.

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Panoiu, N. C.

Pendry, J. B.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. 14, 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.

Powell, D. A.

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]

Shadrivov, I. V.

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.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

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]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[CrossRef] [PubMed]

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]

Stacy, A. M.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930–930 (2008).
[CrossRef] [PubMed]

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]

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930–930 (2008).
[CrossRef] [PubMed]

Sushkov, A. B.

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[CrossRef] [PubMed]

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]

Tuttle, G.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006).
[CrossRef]

Veselago, G.

G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

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]

Wang, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930–930 (2008).
[CrossRef] [PubMed]

Wegener, M.

Wu, B. I.

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930–930 (2008).
[CrossRef] [PubMed]

Yen, T. J.

Y. J. Chiang and T. J. Yen, “A highly symmetric two-handed metamaterial spontaneously matching the wave impedance,” Opt. Express 16(17), 12764–12770 (2008).
[PubMed]

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Figures (7)

Fig. 1
Fig. 1

(a) Schematics of the unit cell in simulation (w = 6.5-10 mm, every 0.5 mm in the space). (b) The measurement and simulation results (transmittance and phase) of the ZrO2 cubes of 10 × 10 × 10 mm3 in size. Both results are in good agreement to indicate magnetic and electric resonances at 4.51 and 5.78 GHz, respectively. (c) Effective material parameters (permeability, permittivity and refractive index) of ZrO2 cube arrays (10 mm cube) calculated by an inversion method, showing negative permeability and negative permittivity at two resonant states. (d) Electric (left part) and magnetic field (right part) distributions at magnetic resonance frequency (4.51 GHz; upper part) and those at electric resonance frequency (5.78 GHz; lower part). Notice a magnetic dipole oriented along the y-direction at 4.51 GHz, and an electric dipole oriented along x-direction at 5.78 GHz.

Fig. 2
Fig. 2

(a) The measurement results of magnetic resonance with respect to eight various sized ZrO2 resonators. (b) The simulated results of the ZrO2 resonators. In the simulation setting, εr = 33 and loss tangent = 0.002. A clear blue-shift of resonance frequencies is manifested as decreasing the size of ZrO2 resonators.

Fig. 3
Fig. 3

(a) Simulated results of two individual periodic arrays of ZrO2 resonators (εr = 33 and loss tangent = 0.002). The sizes of simulated ZrO2 resonators are 6.5mm × 6.5mm × 10mm and 9.5mm × 9.5mm × 10mm in dimensions. From the top to the bottom are transmittance and phase, effective permittivity and effective permeability respectively. Notice that the negative εr from the larger ZrO2 resonators and negative μr from the smaller ZrO2 resonators are overlapped at 5.95 GHz. (b) Simulated results of the integrated sample from the previous two individual ZrO2 resonators. From the top to the bottom are transmittance and phase (loss tangents equal to 0.002 and 0 for red and black curves), effective permittivity and effective permeability, and effective refractive index and impedance. Clearly, a negative refractive index occurs at 5.8-5.95 GHz (highlighted in yellow part).

Fig. 4
Fig. 4

The measured transmittance and phase of two individual sized ZrO2 resonators (black and red curves) and their integration (green curve). For the integrated case, there emerges a transmittance peak at 5.84 GHz rather than the previous dips from individual ZrO2 resonators, indicating the existence of the negative refractive index medium highlighted in the yellow band.

Fig. 5
Fig. 5

(a) A periodic array of single-sized dielectric resonators (ε r = 33), in which the side length of cubes equals to 2 mm and the lattice constant equals to 6.3 mm. (b) The simulated transmission and phase of the dielectric metamaterials, show that the magnetic and electric resonances at 21.7 GHz and 29.2 GHz, respectively. (c) Electric and magnetic field distributions at the magnetic and electric resonance frequencies. (d) Retrieved effective parameters based on the simulated scattering parameters.

Fig. 6
Fig. 6

Periodicity-dependent electric resonance in dielectric resonators. In this case the dielectric cubes used (ε r = 33) are identical in Fig. 5, and the periodicity e is fixed but d is varied. Eventually we find that the electric resonance only depends on d . (a) The simulated S-parameters of the dielectric metamaterials for d = 0.9-1.2 cm. A profound red-shift of electric resonance from 26.9 GHz to 22.5 GHz is observed while magnetic resonance frequency remains at 21.7 GHz. (b) The simulated S-parameters of the dielectric metamaterials for d = 1.4-1.7 cm. A profound red-shift of electric resonance from 20.7 GHz to 18.4 GHz is observed while magnetic resonance frequency remains at 21.7 GHz. (c) The transmission, phase and retrieved effective parameters for d = 1.1 cm. It shows that the magnetic and electric resonances at 21.7 GHz and 23.9 GHz. (d) The transmission, phase and retrieved effective parameters for d = 1.6 cm. It shows that the magnetic and electric resonances at 21.7 GHz and 19.1 GHz.

Fig. 7
Fig. 7

A negative refractive index medium by single-sized dielectric resonators (ε r = 33). (a) The stimulated transmission and (b) phase change corresponding to various values of d. (five cases: d = 1.20 cm, 1.29 cm, 1.30 cm, 1.31 cm and 1.40 cm) (c) The stimulated transmission corresponding to lossless case (tan δ = 0) and lossy case (tan δ = 0.002-0.008) for the parameter d equals 1.3cm. Note the scale of transmittance in (a) and (c) is much different and the yellow part is the NRIM region.

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