1. Introduction

The concept of metamaterials describes sub-wavelength media whose collective responses arise mainly from their structures rather than their constitutions. Based on such effective media, rare and even unprecedented electromagnetic properties can be tailored at the desired frequencies. For example, recently two distinct sets of artificially constructed metamaterials, split-ring resonators (SRRs) [1,2] as well as plasmonic wires (PWs) [3,4] were introduced to present negative magnetic permeability and negative electric permittivity, respectively. By further integrating these two metamaterials together, soon later the theoretically proposed negative refractive index medium (NRIM) [5] was realized to demonstrate the inverse Snell’s Law in the microwave region under a grazing-angle excitation [6]. In addition to the inverse Snell’s law, the striking NRIM revises more electromagnetic rules like inverse Doppler shift [7], inverse Cherenkov radiation [8] and superlensing effect [9,10] to instantly attract researchers’ attention.

More recently, other metamaterials like H-shaped metallic wires [11], short-wire pairs [12,13], two-handed metamaterials [14] and pairs of metallic crosses [15] were also proposed to exhibit negative refraction based on a normal incident excitation instead. These metamaterials do promise negative refraction, but they all strongly depend on the incident angles and the polarized directions of external excitations [6,11–13,15,16] and such anisotropic behaviors obviously, limit the implementation of NRIM for practical devices. As a consequence, here we develop a new class of metamaterials to display negative refraction under multiple angle incidences (MAI). An overlapped allowed band with respect to negative refractive indices is revealed at different incident angles. In addition, the opposite directions of group and phase velocities are also demonstrated for grazing-angle, normal and 45-degree incidences while electromagnetic waves propagate inside this structure at its resonant state, indicating that the designed structure indeed possesses anisotropic negative refractive index for MAI.

2. Structure design and numerical simulation

To ease the strong anisotropic burden from conventional NRIM aforementioned [6,11–13,15,16], in this study we develop a structure responding to multiple-angle incident excitations. As shown in Fig. 1 , the designed structure is comprised of two overlapped copper plates with two opposing “U” rings sandwiching a ROGER 5880 board (ε_r=1.98), whose dimension of a unit cell and other detailed parameters are listed in Table 1. The designed structure is simulated by CST microwave studio, a commercial electromagnetic solver, to compute the complex reflectance and transmittance coefficients (i.e., S-parameters) [14] to allow us retrieving the corresponding electric permittivity, magnetic permeability, and refractive index [17,18]. In addition, we also plot the distribution of induced currents in order to elucidate the mechanism of these MAI responses. Furthermore, we also demonstrate the calculated negative phase velocity with snapshots of E-field distribution. Note that we assume there is no strong coupling between electric and magnetic fields so that one can ignore the bi-anisotropic issue [19,20].

 

Fig. 1 The design of structure and its perspective. The yellow parts are two copper plates composed by U rings and rectangular plates on a Roger 5880 substrate. All the parameters are tabulated in Table 1

Download Full Size | PDF

Table 1. The detailed parameters of the structure.

View Table

3. Simulation and Measured Results

3.1 NRIM operated at grazing-angle incidence

In the case of grazing-angle incidence, the applied electromagnetic wave (k) is parallel to the plane of the structure and the external electric field (E) is along the sidebars of U-ring structures as shown in the inset of Fig. 2 . Based on this configuration, we can tune the artificial plasma frequencies to the desired frequencies by adjusting the spacing between the unit cell to achieve negative permittivity [3,4]; meanwhile, the U-ring structure also allows resonant magnetic dipole moments excited by the external magnetic field (H) to enable negative permeability, and eventually leads to negative refractive index of the designed structure. Our measured samples are fabricated by commercial print circuit board process and whose parameters are as same as those in simulation. Fig. 2(a) presents the simulated transmittance (S21) and reflectance (S11) in the range of 9-10 GHz by the red and blue curves, respectively. The black curve is the measurement result by using Aglient E8364A network analyzer connected with broadband horn antennas. The fabricated sample and the details of the setup configuration are shown in Fig. 3 . We clearly observe a transmittance peak centered at 9.68 GHz to indicate an allowed band in this structure and the measurement results have consistency with simulation both for transmittance and its phase change in Fig.2. Next, we further retrieve the corresponding electric permittivity, magnetic permeability and refractive index of this NRIM structure.

 

Fig. 2 (a) The simulated transmittance (red), reflectance (blue) and measured transmittance (black) curves in dB scale at grazing-angle incidence. One can observe a transmittance peak at about 9.68 GHz, indicating an allowed band in this frequency region. Inset shows the configuration of the excited electric and magnetic fields for grazing-angle incidence. (b): the transmittance phase change of both measurement (black) and simulation (red).

Download Full Size | PDF

 

Fig. 3 The fabricated sample, the measurement setup and its configuration. Two broadband horn antennas are connected to the vector network analyzer (Aglient E8364A) to obtain the transmittance (S21). The receiver horn (port 2) is enclosed by microwave absorber and the measured samples are placed on the Styrofoam stage. We arrange our samples for two distinct incident angle in order to consist with the simulation. The inset shows the photograph of the real fabricated sample.

Download Full Size | PDF

First of all, as shown in Fig. 4 negative effective permittivity occurs because the external electric field parallel to the discontinuous wire-like sidebars drives flowing currents from bound electrons rather than free ones [21], so that a Lorentz resonance appears at lower frequency region (not shown) resulting in negative permittivity above its resonant frequency [22]. At the meantime, the retrieved effective magnetic permeability also exhibits a Lorentz resonance in the nonmagnetic copper structure, in which the artificial magnetic response is excited by the external time-varying magnetic field. According to the dynamical Maxwell’s equations, the external time-varying magnetic field induces circulating currents in the copper bars of the two opposing “Us” regions, then generating magnetic dipole moments. Evidenced by the inset of Fig. 4, the induced circulating current is strongly localized at the ends of the rectangular part, which introduces equivalent LC-resonance [1] inside the structure and further enhances the generated artificial magnetic response. Therefore, the effective permeability turns to negative about 9.35 GHz and simultaneously overlaps with the negative permittivity. Accordingly, the refractive index of the structure indeed becomes negative from 9 to 9.45 GHz as shown in Fig. 4.

 

Fig. 4 Calculated material parameters (ε_eff , μ_eff and RI) at grazing-angle incidence (solid and dotted lines represent for real and imaginary parts, respectively). (a): retrieved effective permittivity (blue lines) and effective permeability (red lines). Lorentz resonance of permittivity is excited by the electric field due to the discontinuous conductor in the structure and ε_eff turns into negative above the resonance frequency. A magnetic resonance appears at 9.3 GHz and ε_eff exhibite an anti-resonance stemmed from magnetic resonance. (b): negative refractive index occurs near the region both ε_eff and μ_eff are negative. NRI is from 9.0 to 9.45 GHz and the value is down to -0.75. The induced currents are shown by arrows in the inset, indicating the induced currents are strongly localized at the ends of the rectangular plates where the artificial magnetic dipole mainly arises from.

Download Full Size | PDF

3.2 NRIM operated at normal incidence

More recently, several new designed metamaterials such as the H-shaped metallic wires [11], the short-wire pairs [12,13], and pairs of metallic crosses [15] have been reported to demonstrated negative refractive indices operated under the normal incidence excitation. Among those designs, the common rationale of attaining the negative magnetic response stems from the excitation of the anti-parallel currents occurring in their double-layered conductive plates, leading to the induced magnetic dipole moments [11,23,24]. Likewise, in our design the overlapped copper plates also contribute the negative magnetic permeability from the induced anti-parallel current indicated in the Fig. 5 and the inset of Fig. 6 . In Fig. 5, we observe that both transmittance and reflectance are similar to those at grazing-angle incidence except a slight variation in amplitudes and frequencies, meeting our demand to design an NRIM for MAI. Meanwhile, the electric field remains parallel to the wire-like sidebars (y-axis) so that sidebars play the same role as the previous case of grazing-angle incidence. Hence, the effective permittivity exhibits a Lorentz resonance and remains negative in the vicinity of 9.8 GHz. All the retrieved results following the same computation process aforementioned are shown in Fig. 6. In addition, we find out in both cases of grazing-angle and normal incidences, there are anti-resonance behaviors of permittivity corresponding to magnetic resonance. The anti-resonance mechanism [25,26] discussed by T. Koschny et al. is due to the reason that the refractive index must be bounded in the structures which possess finite spatial periodicity. Comparing to retrieved results, the refraction index of the structure is centered at 9.35 GHz for grazing-angle incidence while at 9.78 GHz with a bandwidth of about 1 GHz for normal incidence and NRI region overlap partially by comparing the retrieved results in Fig. 4 and Fig. 6.

 

Fig. 5 S-parameters (a) and transmittance phase change (b) at normal incidence. The similar transmittance behavior as in the case of grazing angle incidence appears. The transmittance peak indicates the negative refractive index with the smallest imaginary part. The inset depicts the polarization of incident wave.

Download Full Size | PDF

 

Fig. 6 Calculated material parameters (ε_eff, μ_eff and RI) at normal incidence (solid and dotted lines represent for real and imaginary parts, respectively). (a): Resonance and anti-resonance in permittivity (blue) and their mechanisms are discussed in the content. Strong magnetic resonance in permeability (red) at about 9.8 GHz. (b): The refractive index is negative centered at 9.78 GHz and the region is from 9.2 GHz to 10 GHz. The inset is the induced current flows around the two copper plates, generating a magnetic resonance. The red arrows point out the direction of current flow.

Download Full Size | PDF

3.3 Multiple-angle responses and negative phase velocities

To further verify that this structure exhibits negative refraction for multiple-angle incidences, we plot the E-field distribution of wave fronts to examine the change of phase velocities while normal, grazing-angle and 45-degree incident waves propagate across the structure at its resonant frequency. The detailed results of this demonstration are presented in a series of snapshots in Figs. 7(a) , 7(b) and 7(c) for grazing-angle, normal and 45-degree incidence respectively, and the more detailed behaviors are also provided by animations [27]. As shown in Fig. 7, we locate our designed structures in the center of the whole calculation region (free space) and the incident wave propagates from the right hand side of boundary. For the sake of saving calculation time, we apply PEC (top & bottom sides) and PMC (front & rear sides) as the boundaries and one repetition exists in PMC boundary direction. We choose y= 52.5 mm (two and half unit cell height from the bottom) as our monitor plane to observe the propagation of the phase. The height as well as the color both indicate the intensity and the direction of E field along y axis. Clearly, the wave fronts inside the structure turn to the opposite direction, indicating a negative phase velocity resulting from the negative refractive index inside the structure. To sum up, these calculation results demonstrate that our designed structure indeed exhibit the negative index for MAI.

 

Fig. 7 Negative phase velocities shown by the animations of electric-field distributions. In this simulation, we rotate our structure a certain angle for the corresponding case (0, 45, 90 degree for grazing-angle, normal and 45 degree incidences, respectively.) (a) Phase velocity at grazing-angle incidence (Media 1). (b), (c) Phase velocity at normal (Media 2) and 45 degree (Media 3) incidence respectively. The black arrows indicate the peak of the wave inside the structure while the red ones specify the direction of incident wave The standing waves appear in the right of the structure because of the interface impedance mismatch. However, we observe the phase velocity of the transmittance wave is opposite to the wave in the structure. Therefore the phase velocity is negative in our designed structure.

Download Full Size | PDF

4. Conclusions

In this work, we have successfully designed an anisotropic negative refractive index medium operating at a variety of incident angles, verified by measured S-parameters, retrieved material properties and simulated negative phase velocities. The key of such exceptional properties is to realize negative artificial magnetic response under both grazing-angle and normal incident cases, which can be completed by combining a U-ring resonator for grazing-angle incidence and a double-layered metallic structure for normal incidence. Different from other conventional NRIM that demand to integrate two building blocks for providing negative permittivity and negative permeability concurrently [6,28], our monolithic pattern possesses double negative material properties itself. This new designed structure eases the burden of strong anisotropic responses in conventional metamaterials and widely increases the feasibility of practical applications.