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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 Optical Society of America
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 [1–3]. 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] and split-ring resonators (SRRs) [5], 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] changing the long-standing scientific fiction into a scientific fact and further leading to various innivative applications such as superlensing effect [6] and slow-light effect [7]. So far, several other designs of NRIM have also been successfully demonstrated [8–10], which are all mainly based on metallic resonant scattering elements as well [4–10]. 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 [10–16].
As shown in Fig. 1(a) , 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.
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.
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], as shown in Fig. 2(a) . 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]. Note that such an enhanced Jd plays an important role as the conduction current (Jc) does in the case of metallic metamaterials [19]. 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).
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.
Next, by coupling the magnetic resonance from the Al2O3 particles and electric resonance from the ZrO2 particles at the same resonance frequencies, one can generate a low-loss NRIM accordingly. Figure 3(a) shows the measurement transmittance and phase spectra for the sample with combing ZrO2 and Al2O3 resonators together. As shown in Fig. 3(a), the ZrO2 resonators exhibit out-of-phase magnetic and electric resonances (i.e., negative μr and εr; the red curve) centered at 5.84 and 7.81 GHz, and the negative εr from the Al2O3 resonators is centered at 7.78 GHz (the black curve). Next, we hybridize these two sets of dielectric resonators with the periodicity of 8 mm in the waveguide to measure the transmittance. As expected, the previous transmittance dips overlapped at 7.8 GHz turn into a transmittance peak (the green curve), supporting a left-handed passband due to an effective negative refractive index from the hybrid dielectric resonators. Moreover, the transmittance of the negative refractive index region is up to −2.5 db, in which the loss stems from the inherent property of ZrO2 and Al2O3 materials, and certainly, one can choose a lower inherent loss ceramic material to obtain a better NRIM performance. Besides, a numerical verification of this low-loss and high-symmetry NRIM by hybrid dielectric resonators is also presented as shown in Fig. 3(b), in which the simulation results agree well with the measurement one in both scattering parameters and phase changes. The allowed band of combing two sets of full-dielectric resonators specifies an NRIM that are further confirmed by the retrieved material parameters presented in Fig. 3(c). Notice that the negative εr from the ZrO2 cuboids and negative μr from the Al2O3 resonators are overlapped at 7.79-7.95 GHz. Clearly, a negative refractive index occurs at 7.79-7.95GHz.
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.
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).
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