OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 2876–2880
« Show journal navigation

Low-loss and high-symmetry negative refractive index media by hybrid dielectric resonators

Yueh-Chun Lai, Cheng-Kuang Chen, Yu-Hang Yang, and Ta-Jen Yen  »View Author Affiliations


Optics Express, Vol. 20, Issue 3, pp. 2876-2880 (2012)
http://dx.doi.org/10.1364/OE.20.002876


View Full Text Article

Acrobat PDF (2081 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

The concept of a negative refractive index medium (NRIM), also called a left-handed materials whose electric permittivity (εr) and magnetic permeability (μr) are both negative leading to a negative refractive index and left-handed relationship among the triplet of electric field intensity (E), magnetic field intensity (H) and wave vector (k), promises to reverse the conventional electromagnetic properties, for example, Snell’s law, Doppler shift and Cerenkov effect and so on [1

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]

3

3. J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pacheco Jr, 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]

]. In fact, this revolutionary NRIM was first theoretically proposed by Veselago in 1967, but it has been labeled as a scientific “fiction” for years because one cannot discover such a material in nature. Until a decade ago, Pendry et al. proposed two sets of metallic resonators, plasmonic wires (PWs) [4

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]

] and split-ring resonators (SRRs) [5

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]

], to introduce respective exotic artificial electric and magnetic responses, respectively. By coupling these two metallic resonators, soon later, the first experimental proof of NRIM was verified at microwave frequencies [1

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]

] changing the long-standing scientific fiction into a scientific fact and further leading to various innivative applications such as superlensing effect [6

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

] and slow-light effect [7

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]

]. So far, several other designs of NRIM have also been successfully demonstrated [8

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]

10

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]

], which are all mainly based on metallic resonant scattering elements as well [4

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]

10

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]

]. Unfortunately, present metallic resonators suffer from significant intrinsic loss as well as strong anisotropic properties to destroy the performance. As a result, in this work, we hybridize two designed dielectric resonators to enable negative μr and negative εr simultaneously, yielding an NRIM with the advantages of low loss, high symmetry, compactness, high-temperature stability, and simple fabrication [10

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]

16

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]

].

As shown in Fig. 1(a)
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.
, two kinds of dielectric resonators were fabricated from commercial low-loss ceramics, including ZrO2 cuboids (purity = 94%, εr = 33, loss tangent = 0.002, and dimensions = 5.5×5.5×10 mm3) and Al2O3 cubes (purity = 99.5%, εr = 14, loss tangent = 0.001, and dimensions = 9x9x9mm3). The scattering parameters of the samples were measured by an Agilent E8364A network analyzer connected with a WR-137 rectangular waveguide (cross section: 15.799×34.849 mm2), in which the dielectric resonators were located in the center with their edges parallel to the E and H fields, and supported by a styrofoam slab with a similar dielectric constant to free space. This experiment setup, as shown in the inset of Fig. 1(a), reflects the scattering results of the one-layer array consisting of an infinite number of dielectric cubes at the excitation of the TE10 mode in accordance to the mirror theory. Besides, the measurements were numerically verified by a commercial finite-integration time-domain electromagnetic solver (CST Microwave Studio). In the simulation process, the proposed model, consisting of ZrO2 (Al2O3) cuboids (cubes), is displayed in WR-137 waveguide. The WR-137 waveguide with a cross-section of 15.799 × 34.849 mm2 works in 5.85-8.20 GHz with the boundary condition of PEC along the x and y directions, respectively, to ensure that the mode excited in the wave port is TE10 mode as shown in inset of Fig. 1(b). As the convergence condition is satisfied, the simulator can numerically calculate the scattering parameters (S21 and S11) and electromagnetic field distributions with a high accuracy.

The transmittance and phase of the fabricated dielectric resonators are presented in Fig. 1, respectively. At the resonant states, there appear two profound dips with sharp phase changes at 6.75 and 7.79 GHz for ZrO2 cuboids denoted by black curves, and similarly, one dip with a sharp phase change at 7.79 GHz for Al2O3 cubes denoted by red curves. Both the measurement and simulation results agree with each other well with a small deviation of 0.05 GHz in frequency, which may be caused by the dispersive dielectric constant of ZrO2 (Al2O3) and the uncertainty of the real sample size (~0.01 mm in the edge lengths).

Resting on the acquired scattering parameters of these single-layer dielectric resonators, we further retrieved the corresponding effective magnetic permeability (μr) and electric permittivity (εr) [17

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]

], as shown in Fig. 2(a)
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.
. These retrieved results clarify the nature of the dips aforementioned– the first dip of the ZrO2 cuboids at 6.75 GHz origins from out-of-phase magnetic dipoles (i.e., negative μr) and the second dip at 7.79 GHz is due to out-of-phase electric dipoles (i.e., negative εr); meanwhile, the dip of the Al2O3 cubes at 7.79 GHz results from out-of-phase magnetic dipoles as well. To reinforce this clarification, moreover, the field distributions of ZrO2 and Al2O3 resonators at magnetic and electric resonance are plotted in Fig. 2(b). At the resonance frequencies, a displacement current Jd is excited by time-varying electric field in the designed dielectric resonators according to Faraday’s law (Jd = εrεodE/dt), and is significantly enhanced due to the Mie resonance [18

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

]. Note that such an enhanced Jd plays an important role as the conduction current (Jc) does in the case of metallic metamaterials [19

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]

]. For example, at the resonance frequency 7.79 GHz, there induces a streamlines Jd appears along the x direction within the ZrO2 cuboids, which in turn corresponds to negative εr as shown in the upper panel of Fig. 2(a); on the other hand, a circular Jd in the Al2O3 cubes, leading to negative as shown in the lower panel of Fig. 2(b).

In summary, we have successfully constructed a low-loss and high-symmetry NRIM to ease the burden of significant intrinsic loss as well as strong anisotropic properties existing in the present metallic resonators. The key to enabling the desired magnetic and electric responses is the combination of displacement currents and Mie resonance excited within the dielectric resonators. By overlapping the frequencies of the scalable magnetic dipole resonance from ZrO2 cuboids and scalable electric dipole resonances from Al2O3 cubes together, therefore, we realize the NRIM by the hybrid dielectric resonators within microwave regimes. Both the simulated and measurement results are in good agreement, and the retrieved effective parameters verify the negative identities in the fabricated ZrO2 and Al2O3 resonators. In addition to low loss and high symmetry, this new designed hybrid dielectric NRIM possesses further advantages of compactness, high-temperature stability and simple fabrication, paving an avenue towards many potential applications such as filters, modulators, antennas, super lenses, slowing light, invisible cloaking and other novel electromagnetic devices from microwave to optical ranges in the near future.

Acknowledgments

The authors would like to gratefully acknowledge the financial support from the National Science Council (NSC98-2112-M-007-002-MY3, NSC100-2120-M-010-001, and NSC100-2120-M-002-008), and from the Ministry of Education (“Aim for the Top University Plan” for National Tsing Hua University).

References and links

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 Jr, 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]

11.

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

12.

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]

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]

OCIS Codes
(260.5740) Physical optics : Resonance
(350.4010) Other areas of optics : Microwaves
(350.3618) Other areas of optics : Left-handed materials
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: December 19, 2011
Manuscript Accepted: January 11, 2012
Published: January 23, 2012

Citation
Yueh-Chun Lai, Cheng-Kuang Chen, Yu-Hang Yang, and Ta-Jen Yen, "Low-loss and high-symmetry negative refractive index media by hybrid dielectric resonators," Opt. Express 20, 2876-2880 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2876


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001). [CrossRef] [PubMed]
  2. N. Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science302(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. Express11(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. B75(23), 235114 (2007). [CrossRef]
  9. J. B. Pendry, “A chiral route to negative refraction,” Science306(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. Express17(26), 24189–24197 (2009). [CrossRef] [PubMed]
  11. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.14(15), 4035–4044 (2002).
  12. 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]
  13. Y. J. Lai, C. K. Chen, and T. J. Yen, “Creating negative refractive identity via single-dielectric resonators,” Opt. Express17(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. B65(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. Express16(24), 19850–19864 (2008). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited