1. Introduction

The field of metamaterial research has attracted considerable attention in recent years following the fabrication of metallic structures with both negative permittivity and permeability at certain resonant frequencies [1, 2]. The potential applications of such metamolecules are numerous, owing to the unique ability to engineer the material’s refractive index, including negative refractive indices. While most metamaterials research has been focused on potential applications in free space, metamolecules loaded on to microwave waveguides have also been demonstrated [3, 4], allowing their easy incorporation into microwave circuits. Such applications of metamaterials in the microwave region include band-stop and band-pass filters [5–8] and antennae [9, 10].

In this paper, we report on a metamaterial-inspired passive antenna incorporating both the fish-scale [11, 12] and split ring resonator (SRR) designs [1, 13, 14]. We refer to this structure henceforth as a ‘metamolecule’, in order to avoid the term ‘metamaterial’ which usually refers to large arrays consisting of hundreds of elements. By coupling SRRs to a modified fish-scale, a hybrid structure was developed with a greater absorption than either component taken in isolation when loaded on a coplanar waveguide (CPW). We fabricated one sample that has only the fishscale design and one sample that has the hybrid metamolecule which incorporates the combination of the fishscale and the SRRs. The designs were first probed using the finite element method (FEM) using the commercial software package COMSOL Multiphysics and then tested experimentally using a vector network analyser (VNA). We show that there is excellent agreement between the simulations and the experimental measurements of the frequency response of the system. This permits us to use COMSOL to extract and compare the electric fields generated by the fishscale and those generated by the hybrid design. Furthermore, using COMSOL we show how varying the size of the strucure affects the resonances of the SRR and the fishscale. COMSOL also predicts that at resonance the launched power is emitted and the hybrid metamolecule design acts as an antenna. To confirm this behaviour we compare its results with the experimental difference in losses between the fishscale and the hybrid sample finding very good agreement. Finally, COMSOL was used to extract the antenna gain of the hybrid design as a function of direction and as a function of frequency.

2. Metamolecule design

The metamolecule design under investigation and its dimensions are detailed in Fig. 1. The hybrid metamolecule was designed to incorporate aspects of both the concentric double SRR and fish-scale designs. The fishscale pattern was modified by replacing the ‘U’ shape with a ring of sector angle 270° with inner and outer radii 1.7 mm and 1.9 mm (Fig. 1(a)), creating a structure that resonates at microwave frequencies. An inner split ring was placed inside the fishscale structure, as shown in Fig. 1(b), this arrangement creates the hybrid metamolecule. It was hoped that the outer radii of the modified fishscale pattern would act as an outer split ring when used in this geometry. A segment of 40° was removed from the inner ring to produce the SRR gap for the inner ring. When the structure is reflected vertically and the split ends are spliced together, a ‘zip-like’ structure is created as seen in in Fig. 1(c). It was decided that the metamolecule design should incorporate multiple SRRs in order to introduce an element of periodicity, and two were used. More were not used so as to simplify the structure, both for ease of analysis and to decrease the time taken to compute the model by decreasing the number of fine mesh elements required.

 

Fig. 1 (a) The geometry and dimensions of one unit segment of the modified fish-scale structure. (b) The geometry of a fish-scale segment complete with inner ring to form a SRR. The angular gap θ used for the inner split ring is 40°. (c) The final hybrid fishscale/SRR metamolecule. In the finalised design, r_o = 1.1 mm and r_i = 0.9 mm.

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The fishscale was chosen to be located centrally over one of the gaps of the CPW, this placement prevents a symmetric driving field over the metamolecule in the y direction. Figure 2(a) shows the placement of the metamolecule relative to the dimensions of the CPW. Inner split rings were only placed on one half of the structure so as to allow its placement asymmetrically on a CPW while ensuring all SRRs experience the same driving fields. Due to the high symmetry of the fishscale structure, asymmetric placement was chosen so as to avoid the excitation of currents of equal magnitude in opposite directions, thereby maximising the overall net current. The final placement was checked using COMSOL to verify good coupling between the CPW and hybrid metamolecule. The metamolecule consisted of a 0.07 mm layer of Cu and was separated from the CPW with a 0.7 mm thick layer of FR4 (Fig. 2(b)). The CPW was 0.07 mm of Cu with gaps of 0.2 mm separated by 1.1 mm (shown in Fig. 2(a)). No line-feeding is required from the CPW to the antenna, instead the design is based on the coupling between the CPW, fishscale and SRRs. As mentioned in the introduction, we fabricated and tested one sample with only the fishscale design and another with the hybrid metamolecule.

 

Fig. 2 (a) Top-down view of the hybrid structure on the CPW with placement relative to the CPW gaps (shown in red). (b) View from the side of the same sample showing the dimensions of the device layers.

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3. Numerical investigations

Before the device was fabricated, the metamolecule design was studied in COMSOL to identify appropriate dimensions for the device with a view to enable coupling between the fishscale and SRR structures. The final dimensions are shown in Fig. 1 and Fig. 2. The sample, complete with CPW was ‘wrapped’ in two cylinders to define perfectly matched layers (PMLs) surrounding the system. All cylinder ends were defined as scattering boundary conditions, and both ends were excited with an SMA end launch connectors identical in size and geometry to those which would be used on the physical sample. Half the length of the SMA connector was enclosed within the PML cylinders. Outside the PMLs, all metal on the SMA connectors was set to be a perfect electric conductor, and the exposed dielectrics at each end were used as ports in to and out of the system. In this way, it was possible to excite one port at a certain frequency, and use both ports to extract the scattering matrix parameters (S-parameters) of the system. In this way, the numerical model matches the physical system as closely as possible. The investigation predicted that the fishscale would exhibit a resonant frequency at around 16 GHz. It was discovered that SRRs of inner radius 0.9 mm and outer radius 1.1 mm would, when coupled with the fishscale, produce a stronger resonance than either of the individual components. Three different systems were simulated, one only with SRRs, one only with fishscale and one with the hybrid metamolecule. As shown in Fig. 3 the SRRs exhibit two resonances at around 15.2 GHz when placed in isolation on the CPW. This level repulsion between the two resonances of the SRRs indicate that the two are coupled. When these SRRs are introduced to the modified fish-scale, which itself exhibits a resonance at 15.7 GHz, a far stronger resonance is observed, but still at 15.7 GHz. This suggests a hybrid mode is produced by the coupling between the SRRs and modified fish scale.

 

Fig. 3 The calculated S₂₁ for the SRRs (blue), the fishscale (green), and the hybrid SRR and fishscale structure (red). Coupling beteen the two SRRs can be observed through the presence of two resonances in close proximity to one another in the red line.

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To understand how the SRRs couple with the fishscale, the simulated electric fields generated by both structures at their resonances are presented in Fig. 4. The electric field map for the CPW loaded fishscale is presented in Fig. 4(a), and that of the hybrid structure in Fig. 4(b). The polarisation of the electric field profile plotted is perpendicular to the propagation axis, y-axis according to Fig. 1. This polarisation was chosen as it effectively shows the coupling between the two SRRs and fishscale.

 

Fig. 4 Electric field maps produced by the CPW-loaded structures determined using COMSOL simulation. The y-polarized electric fields (according to the geometry of Fig. 1 and perpendicular to the propagation axis) for both the isolated fishscale (a) and hybrid structure (b) are shown. The structures were excited by a coaxial port from the right hand side of the figure.

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Evidence of coupling between the structures is apparent from the change in electric field present around the fishscale in the region surrounding the SRR closest to the excitation port that is located on the right hand side of Fig. 4(b). The electric field present around the inner edge of the fishscale in this region deviates from that of the isolated fishscale as the polarisation changes to match that of the SRR. Furthermore, the polarity of the electric field generated along the outer edge of the fishscale in this region is opposite to the polarity of that region when the isolated fishscale is excited. This can be observed by the change of the right hand region of the fishscale between Figs. 4(a) and 4(b). By contrast, however, the fields produced by the segment of fishscale surrounding the SRR further away from the input (left hand side of Fig. 4(b)) appear much the same as those from the isolated fishscale. The SRR in this region, however, demonstrates a much weaker field than that of its counterpart. It is probable that the weaker coupling is due to the phase of the EM wave, which is changed by the first SRR it encounters. When the input and output ports are swapped the simulation produces a mirror image to the ones in Fig. 4.

4. Experimental results

As mentioned, physical samples of both the fishscale and hybrid structures were created on the underside of ungrounded CPWs. The dimensions of the waveguide structures are those shown in Fig. 1, which were modelled in COMSOL. Physical testing of the samples was performed with a vector network analyzer (VNA) as outlined in [3]. The sample was connected to both ports of the VNA with coaxial cables attached to the SMA connectors. The sample was placed between two Helmholtz coils which could be used to place the sample within a DC magnetic field. The VNA was then able to extract the S-parameters of the system both as a function of field and frequency. A comparison of the S₂₁ for both the physical and numerical results is shown in Fig. 5(a) and (b), where it can be seen that the enhancement of the fish-scale resonance is verified experimentally. There is an approximately 0.4 GHz shift between simulation and experiment in the position of each resonance, perhaps due to the limitations of the mesh size in COMSOL, slight inaccuracies in the dimensions of the physical sample, or slightly innacurate material parameters. Both the absorption of the isolated fishscale mode and hybrid mode are not as prominent in the experimental investigations when compared with the numerical results. This may be attributed to the presence of much greater resistive losses in the experimental setup. The percentage decrease in transmission between the experimental results is around −4 dB, whereas between the computational results it is around −9.5 dB as seen in Fig. 5(c).

 

Fig. 5 Comparison of computational results (green) with experimental results (blue). The S₂₁ for the fishscale is shown in (a) and that of the hybrid structure is shown in (b). The difference in transmission between the hybrid structure and the fishscale for both the experimental and computational results is shown in (c).

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5. Effect of SRR size on resonant properties

A further numerical investigation was performed to determine how changes in the sizes of the SRRs affect the coupling of the SRRs to the fishscale mode and the resonant properties of the hybrid structure. In COMSOL, the radii of the SRRs were altered whilst maintaining the SRR’s track width at 0.2 mm. The fishscale size was kept constant and the overall absorption of the hybrid metamolecule for each size is presented in Fig. 6(a). The strength of the resonance is affected by tuning the size of the SRRs, the greatest absorption is obtained with SRRs 0.99 times the original size. In Fig. 6(a) two separate modes of the hybrid metamolecule around the area of interest can be observed. For example, for SRR sizes of 0.98 times the original size, the lower frequency resonance of the hybrid metamolecule present at 15.5 GHz is dominated by the fishscale mode and it is present when the SRRs are removed. The resonance of the hybrid metamolecule present at around 15.9 GHz is linked to the presence of the SRRs. In Fig. 7, we show the y-polarization of the electric fields in the hybrid metamolecule with SRRs 0.98 times those used to obtain Fig. 4(b). Note the large increase of the electric field strength, in Fig. 7 in relation to Fig. 4(b). The concentration of the electric fields generated at this frequency surrounding the SRRs further demonstrates that this mode is dominated by the SRRs. Evidence of coupling between these two modes of the hybrid metamolecule is apparent in Fig. 6 by the shift in frequency of the fishscale mode as the size of the SRRs is altered. The shift of these resonances can be more clearly observed from Fig. 6(b). The shift is specified in relation to the original inner radius that is 0.9 mm. For the smaller SRR size (0.9 mm × 0.975), shown in blue, the SRR mode is observable on the right while the fishscale mode is observable in the centre. For the larger SRR size (0.9 mm × 1.125), the fishscale mode can be observed in approximately the same place, though the SRR mode has started to appear on the left. It is hoped that by extending the length of the structure, it would be possible to tailor SRR sizes to produce stronger resonances. As shown, size variation of the SRR structure in the order of 10 μm greatly affects the strength and frequency of the metamaterial response. It is possible that the geometry of the fabricated structure was slightly different to that designed leading to small discrepancies in absorption and frequency between the experimental and computational results shown in Fig. 5.

 

Fig. 6 Absorption as a function of frequency and SRR size, normalised to the inner radius of the original SRR dimension, which is 0.9 mm is shown in (a). At smaller SRR sizes, both the original fishscale resonance and SRR introduced resonance can be identified separately. For the smallest geometry geometry, the fishscale resonance can be seen on the left while that of the SRRs is seen on the right. Absorption as a function of frequency for the two most extreme SRR sizes are presented as linescans in (b).

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Fig. 7 The y-polarization of the electric fields produced by the hybrid structure with SRRs 0.98 times the original size at the resonance around 15.9 GHz.

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6. Use as a radiative antenna

To demonstrate its properties as a radiative antenna, the radial emission from the metamolecule-CPW structure was analyzed as a function of frequency in COMSOL. The predicted radial emission from the structure was greatest at the frequency of the hybrid mode. We could not measure the radiative power directly, therefore, to verify this behaviour using the experimental data, the ratio of the total losses across the CPW to the input power as a function of frequency were calculated using P_lost = 1 − |S₂₁| − |S₁₁|. Then, by subtracting the losses for the fishscale from those of the hybrid stucture, the change in overall loss when the SRRs are introduced can be examined. This experimental value can be compared with an equivalent P_lost taken from the COMSOL model. The difference in P_lost is calculated for the model by subtracting the radial power outflow of the fishscale from that of the hybrid structure as a function of frequency. The experimental and simulation results are in good agreement with each other Fig. 8(a), albeit with a shift in frequency consistent with the previous comparisons of computational and experimental data, shown in Fig. 5.

 

Fig. 8 The comparison between the differences between P_lost for the hybrid structure and that of the fishscale is shown in (a). The experimental results are in blue while the computational results are in red. The frequency shift (about 0.5 GHz) of the resonance between the two sets of results is consistent with the previous computational results shown in Fig. 5. The computational far field emission profile at resonance is shown in (b), and is presented in terms of far-field antenna gain in dBi. On the far field plot, the x-axis goes into the page, and the y and z axes point towards 0° and 90° respectively. The slice is taken at the centre of the metamolecule.

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While we were unable to measure the far-field antenna gain directly, it could be probed using COMSOL. This can be done by examining the electric far-field generated by the structure and calculating the far field gain in dBi with respect to a hypothetical isotropic radiator. COMSOL predicts peak values of 5.9 dBi at resonance, though due to the losses incurred in the experimental setup not present in the computational model, the real values are likely lower. The far-field profile at resonance is shown in Fig. 8(b) and is presented in terms of antenna gain. As can be seen, it exhibits a bidirectional emission pattern, emitting perpendicular to the plane of the metamolecule.

7. Conclusions

A novel metamolecule antenna has been presented and discussed. Its properties have been examined theoretically, using COMSOL, and experimentally, using a VNA in conjunction with a CPW. Unlike most CPW base antenna designs, no line feeding is required. The antenna is driven via the mutual coupling which exists between fish-scale/SRR combination and the CPW. This feature, offers the prospect of rapidly interchangeable frequency dependent antennae. In practice it should be possible to optimize antenna gain by increasing the quality factor Q of the fish-scale/SRR combination. The angular profile of the emission can be tuned by changing the number of metamolecules used for the design and of course the shape of the hybrid metamolecule. In addition, it should also be possible to increase the mutual coupling by (i) decreasing the distance between the antenna and CPW, and (ii) finding the optimum placement of the CPW gaps with respect to the fish-scale/SRR combination. Furthermore, it could be possible to tune and affect the absorptive and emission properties via coupling to the FMR resonance of magnetic materials, as outlined in [3].