Creating negative refractive identity via single-dielectric resonators

doi:10.1364/OE.17.012960

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Creating negative refractive identity via single-dielectric resonators

Yue-Jun Lai, Cheng-Kuang Chen, and Ta-Jen Yen »View Author Affiliations

Optics Express, Vol. 17, Issue 15, pp. 12960-12970 (2009)
http://dx.doi.org/10.1364/OE.17.012960

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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.

1. Introduction

Negative refractive index media (NRIM), also called left-handed materials (LHM) that simultaneously possess negative values of electric permittivity (ε_r) and magnetic permeability (μ_r), have attracted significant attention for their potential to revise conventional electromagnetic rules involving refractive indices such as inverse optical rules [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]

–5

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

] so that the design and characterization of NRIM is an essential field of research today. In fact, the concept of NRIM was first proposed four decades ago [6

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

] but this originally proposed idea has been labeled as a scientific “fiction” because the negative ε_r can be achieved by metals but the negative μ_r is missing in nature. Until a decade ago, Pendry et al. used two sets of metallic resonators, plasmonic wires (PWs) [7

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

] and split-ring resonators (SRRs) [8

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 and soon after, the first experimental proof of NRIM was verified at microwave frequencies [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 a scientific fiction into a scientific fact.

Later studies employed these two sets of metallic resonators [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]

], and other variations [9

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]

–11

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]

], to successfully demonstrate negative refraction in microwaves. Researchers have spent considerable effort on scaling down the metallic structures toward high-frequency applications in infrared [12

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]

–14

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13(13), 4922–4930 (2005). [CrossRef] [PubMed]

] and even optical regions [15

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

,16

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]

]. Unfortunately, present metallic resonators suffer from significant conduction loss and strong anisotropic properties to tarnish the performance so that recently, dielectric resonators have emerged as alternatives for constructing NRIM due to their advantages in low loss and symmetric design [17

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

]. In fact, dielectric elements naturally have a strong electric response only, but from the viewpoint of metamaterial, artificial magnetic and electric resonances are introduced in the dielectric particles and further enhanced by the Mie resonance [17

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

,18

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]

] that is analog to LC resonance or plasmonic resonance for SRRs [8

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]

,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, O’Brien and Pendry proposed that the localized magnetic or electric resonance mode from the Mie resonance in an array of high dielectric constant dielectric particles could bring about a macroscopic bulk magnetization or polarization in the medium, giving rise to a non-zero magnetic or electric susceptibility on average [19

]. Therefore, it is possible to construct the NRIM by properly combining the negative μ_r and ε_r from two series of dielectric resonators with different dielectric constants at the same frequency region [20

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

]. An alternate approach is to integrate the negative μ_r from periodically arranged dielectric particles as well as the negative ε_r from plasmonic wires [21

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]

]. With either of these approaches, it is inconvenient to fabricate NRIM for practical devices due to the multiple-step fabrication process. In fact, Vendik and Gashinova have theoretically investigated that the effective isotropic negative refractive index medium can be achieved by using two different dielectric sphere lattices embedded in a dielectric matrix [22

O. G. Vendik, M. S. Gashinova, “Artificial double negative (DNG) media composed by two different dielectric sphere lattices embedded in a dielectric matrix,” Proc. Eur. Microw. Conf., pp.1209–1212 (2004) .

]. The underlying physic is explicit since the magnetic fundamental resonance mode and electrical resonance can be overlapped by scaling the size and lattice of the dielectric inclusions. However, the relevant experimental verification has not completed yet.

As a consequence, in this study we demonstrate an NRIM at the microwave region by periodically arranged two specific sizes of full-dielectric particles as our magnetic and electric inclusions, respectively. The size and the lattice constant of the periodically arranged dielectric particles influence the magnetic and electric resonance frequency. We experimentally designed different size of ZrO₂ periodical array to prove the red-shift of magnetic and electric resonance of larger size due to Mie resonance. The composite topology was utilized to realize left-handed material. We choose two different series ZrO₂ cube periodically arrays to realize this phenomenon. Based on investigation of resonance transmission, we experimentally overlap the magnetic resonance (come from one sized ZrO₂ array) and electric resonance (come from another sized ZrO₂ array) over the same frequency region to generate negative refractive index medium (NRIM) by appropriate periodic array of the dielectric particles. Finally, our measurement results for the negative refractive index region of transmission curve are agreed with simulation results.

2. The measurement and simulation setup

The goal of realizing electromagnetic metamaterials is to construct artificial magnetic and electric dipole moments. In contrary to magnetic and electric dipole moments in natural materials, artificial dipoles can be achieved by distinct designs, mainly metallic structures. Despite of the conventional LC-resonance interpretation for metallic metamaterials, the Mie theory is often utilized as the supporting mechanism for dielectric metamaterials instead. In the experiment here, various sized zirconia (ZrO₂) cubes were diced from commercially available bulk ZrO₂ (purity = 94%, ε_r = 33 and loss tangent = 0.002), with an uncertainty of 0.01 mm in the edge lengths. The supporting substrate was a styrofoam slab, whose dielectric constant is similar to that of air. The scattering parameters of the samples were measured by an Agilent E8364A network analyzer connected with a WR-187 rectangular waveguide (cross section: 22.149 × 47.549 mm²) in which the ZrO₂ cubes were located in the center with their edges parallel to the E and H fields as illustrated in Fig. 1(a) . This experiment setup reflects the scattering results of the one-layer array consisting of an infinite number of ZrO₂ at the excitation of the TE10 mode due to the mirror theory [21

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]

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.

Besides, the measurements are numerically verified by a commercial finite element-based electromagnetic field solver (CST Microwave Studio). For the ZrO₂ cubes of 10 × 10 × 10 mm³ in size, their results of transmittance and phase are presented by black and red lines in Fig. 1(b), respectively. At the resonant states, there appear two profound dips with sharp phase changes at 4.51 and 5.78 GHz and both the measurements and simulations agree with each other well except a small deviation of 0.1 GHz in frequency, which may be caused by the dispersive dielectric constant of ZrO₂ and the uncertainty of the real sample size. Next, according to the acquired scattering parameters the corresponding effective material parameters of this single-layer dielectric resonator, including magnetic permeability (μ_r ) and electric permittivity (ε_r ), were calculated by an inversion method [23

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]

] shown in Fig. 1(c). The retrieved results indicate the first dip at 4.51 GHz origins from negative permeability and the second dip at 5.78 GHz is due to negative permittivity whose results are reinforced by the plotted field distributions in Fig. 1(d).

3. The artificial magnetic and electric dipoles in dielectric resonators

Be specific, at 4.51 GHz a circular displacement current (J_d = ε_rε_odE/dt) is excited by time-varying magnetic field in the designed dielectric resonators as shown in the upper panel of Fig. 1(d). Such a J_d plays the similar role as the conduction current (J_c) in metal-based metamaterials [9

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]

–11

,17

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

,18

], then resulting in a significant magnetic dipole at resonance. In the lower panel of Fig. 1(d), at 5.78 GHz another displacement current along the x direction is induced opposite to its time-varying electric field excitation, which in turn corresponds to a negative effective permittivity. Both the magnetic and electric dipoles aforementioned in the dielectric particles stem from the combination of displacement currents and Mie resonance; therefore, we can engineer the resonance frequencies by scaling the sizes of dielectric resonators– the smaller sizes, the higher frequencies. Figure 2 shows the experimental and simulated results of the first mode (the second mode not shown here) from eight various sized ZrO₂ resonators. Among them, we evidently observe the blue-shifting frequency of magnetic resonance as decreasing the size of ZrO₂ resonators, which are also consistent with Levin’s model [24

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

]. Such scalable magnetic and electric resonances are valuable for application concerns, for example, constructing low-loss, isotropic, single-dielectric NRIM by properly integrating the negative μ_r and negative ε_r at the same frequency from distinct sized ZrO₂ resonators.

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, ε_r = 33 and loss tangent = 0.002. A clear blue-shift of resonance frequencies is manifested as decreasing the size of ZrO₂ resonators.

4. NRIM via two different-sized dielectric resonators

Here we design two periodic arrays of ZrO₂ resonators with 6.5mm × 6.5mm × 10mm and 9.5mm × 9.5mm × 10mm in dimensions. As shown in Fig. 3(a) , two sets of distinct sized ZrO₂ resonators exhibit respective substantial magnetic and electric resonances about 5.95 GHz, leading two transmittance dips overlapped at the same frequency region. In addition, we integrate these two sets of ZrO₂ resonators in which the distance among them is 7.1 mm as the inset in Fig. 3(b) and find out, the previous transmittance dips disappear but an allowed band surfaces in 5.8-5.95 GHz. This metamorphosed allowed band specifies an NRIM by two sized full-dielectric resonators, which is further confirmed by the retrieved material parameters presented in the middle and lower panels of Fig. 3(b). Furthermore the performance of the negative refractive index region is −1.4 db, which comes from the imaginary part of effective refractive index due to material inherent material loss. Setting the loss tangent term to zero in this simulation leads to a perfect transmission (the black curve) so that one can choose the lower inherent loss ceramic material to improve better NRIM performance.

Fig. 3 (a) Simulated results of two individual periodic arrays of ZrO₂ resonators (ε_r = 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 ε_r from the larger ZrO₂ resonators and negative μ_r 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).

In accordance with the previous simulated results, an experimental verification of NRIM by two-sized single dielectric resonators is demonstrated shown in Fig. 4 . The measured dimensions of two sets of ZrO₂ cubes are 6.5mm × 6.5mm × 10mm and 10mm × 10mm × 10mm, respectively. As shown in Fig. 4, the smaller ZrO₂ resonators exhibit magnetic and electric resonances (i.e., negative μ_r and ε_r ; the red curve) centered at 5.84 and 7.19 GHz (not shown here) and those from the larger ZrO₂ resonators are centered at 4.4 and 5.84 GHz (the black curve). Next, we integrate these two sets of ZrO₂ cubes with the periodicity of 7.5 mm in the waveguide to measure the transmittance, in which the periodicity of the integrated sample and the size of larger ZrO₂ resonators slightly differ from the simulated ones in Fig. 3 owing to the dispersive dielectric constant of ZrO₂. As expected, the previous transmittance dips overlapped at 5.84 GHz turn into a transmittance peak (the green curve), supporting a passband due to an effective negative refractive index from the integrated single dielectric resonators.

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.

5. NRIM via single-sized dielectric resonators

In the previous section, we demonstrate that both the magnetic and electric resonance frequencies can be tuned by simply manipulating the size of dielectric resonators. Now a further control of resonant frequencies is proposed by changing the lattice parameters d (the distance between dielectric cubes along H-field direction) and e (along E-field direction) in addition to the size of dielectric resonators. First, a designed array of dielectric cubes (ε_r = 33) with the size of 2 mm is presented in Fig. 5 , showing magnetic and electric resonances at 21.7 GHz and 29.2 GHz, respectively. Then, we fix the lattice parameter d but vary e to examine the corresponding scattering behaviors, revealing the same result in Fig. 5 (not shown here). Next we fix e but vary d and in contrast, as increasing d from 0.9 cm to 1.2 cm sequentially, 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 as illustrated in Fig. 6(a) . Notice that once d is larger than 1.4 cm, the red-shifting electric resonance frequency will be exceptionally lower than 21.87 GHz, leading the electric resonance frequency to being even lower than the magnetic resonance one (shown in Fig. 6(b)). The retrieval results of these two cases ( d equals 1.1 cm and 1.6 cm respectively) are also sketched in Fig. 6(c) and 6(d) to reinforce the fact of periodicity-dependent electric resonance in dielectric resonators.

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 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.

In short, the electric resonance frequency can be modulated by adjusting the size and the periodicity of the dielectric resonators due to the coupling among the induced electric dipoles, similar to the case of metallic wires in which both the radius of metallic wires and the distance along the direction perpendicular to the long axis of metallic wires substantially influence their effective plasma frequencies [7

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

,25

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]

]. In the dielectric resonators, thus, the distance normal to the induced electric dipoles is still as varying the parameter e but dissimilar as varying the parameter d . Such a periodicity-dependent property of electric resonance (i.e., highly sensitive to lattice constant along H-field direction) offers an opportunity to realize a negative refractive index medium by matching the electric and magnetic resonances over the same frequency region.

As a consequence, we gradually shift the parameter d is in the range of 1.29 cm to 1.31 cm in order to overlap the electric resonance frequency with the magnetic resonance one for creating negative refractive identity. As shown in Fig. 7(a) , 7(b), in case of the parameter d equals to 1.3 cm, indeed it evidently appears that the out-of-phase magnetic and electric resonances overlap in the shadow region, transforming the previous transmittance forbidden band into a passband centered at 21.7 GHz, in which the bandwidth is determined by electric resonance due to its smaller bandwidth than that of magnetic resonance. Besides, the transmittance of this allowed band approximates –1.1 dB and here the main factor to attenuate the transmission performance stems from the inherent dielectric loss. By simulating the transmittance about the case of d = 1.3 cm with respect to five various loss tangents, it exhibits greater efficiency with smaller dielectric loss as shown in Fig. 7(c). In particular, a perfect transmittance occur at 21.7 GHz while no inherent dielectric loss exists.

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.

6. Conclusion

In conclusion, this study demonstrates a planar negative refractive index medium (NRIM) via the single-dielectric resonators within microwave regime. The factor to enable the desired magnetic and electric responses is the combination of the displacement currents and Mie resonance excited in the dielectric resonators. We elucidate that the artificial magnetic response is merely sensitive to the size of the dielectric resonators, but the artificial electric response significantly depends on both the size and the periodicity of the dielectric resonators. Both the measured and simulated results are consistent, and the retrieved effective parameters verify the negative refractive identity in the fabricated ZrO₂ cubes. Such a new designed NRIM via the single-dielectric resonators possesses isotropic properties and less conduction loss, requires simple sample fabrication, and can be readily implemented in various applications like flat focusing lenses, band-pass and notch filters, antennas, invisible cloaking and other electromagnetic devices.

Acknowledgments

The authors gratefully acknowledge the financial support from National Science Council (NSC 95-2112-M-007 048 MY3) and Ministry of Economic Affairs (97-EC-17-A-08-S1-03) for this study.

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, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
5.	K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef] [PubMed]
6.	G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]
7.	J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]
8.	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]
9.	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]
10.	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]
11.	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]
12.	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]
13.	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]
14.	S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13(13), 4922–4930 (2005). [CrossRef] [PubMed]
15.	H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316(5823), 430–432 (2007). [CrossRef] [PubMed]
16.	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]
17.	S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. 14, 4035–4044 (2002).
18.	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]
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]
20.	A. Ahmadi and H. Mosallaei, “Physical configuration and performance modeling of all-dielectric metamaterials,” Phys. Rev. B 77(4), 045104 (2008). [CrossRef]
21.	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]
22.	O. G. Vendik, M. S. Gashinova, “Artificial double negative (DNG) media composed by two different dielectric sphere lattices embedded in a dielectric matrix,” Proc. Eur. Microw. Conf., pp.1209–1212 (2004) .
23.	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]
24.	L. Lewin, “The electrical constants of a material loaded with spherical particles,” Proc. Inst. Electr. Eng. 94, 65–68 (1947).
25.	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]

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: May 13, 2009
Revised Manuscript: June 19, 2009
Manuscript Accepted: June 19, 2009
Published: July 20, 2009

Citation
Yue-Jun Lai, Cheng-Kuang Chen, and Ta-Jen Yen, "Creating negative refractive identity via single-dielectric resonators," Opt. Express 17, 12960-12970 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12960

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References

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