Zero Index Metamaterial for Designing High-Gain Patch Antenna

A planar wideband zero-index metamaterial (ZIM) based on mesh grid structure is studied. It is demonstrated that the real part of the index approaches zero at the wideband covering from 9.9GHz to 11.4GHz. Two conventional patch antennas whose operating frequencies are both in the range of zero-index frequencies are designed and fabricated. And then, the ZIM is placed in the presence of the conventional patch antennas to form the proposed antennas. The distance between the antenna and the ZIM cover is investigated. Antenna performances are studied with simulations and measurements. The results show that the more directional and higher gain patch antennas can be obtained. The measured results are in good agreement with the simulations. Compared to the conventional patch antenna without the ZIM, it is shown that the beamwidth of antenna with the ZIM cover becomes more convergent and the gain is much higher.

Recent studies show that ZIM may have paved a new way for designing novel high-gain antennas due to its unique properties.Based on Snell's law, it is considered an incident ray on an interface of the ZIM with grazing incidence that comes from a source inside ZIM.A near-zero index ray in the media will be refracted in a direction that is very close to the normal.The lower the optical index is, the closer the normal direction is.Enoch et al. [15] is the first to realize high directive radiation by employing monopole source embedded in ZIM, thus confining the radiated energy to a small solid angle.After the work of Enoch, Wu et al. [16] proposed a lefthanded metamaterial as a substrate for designing directional radiation.Through the control of the structure's geometry, the zero index frequency can be tuned to the desired specification to produce directional emission.In addition, other works about directive radiations employing ZIM were also studied [17][18][19].However, in the previous references, the directive antennas based on ZIM operate at a single frequency or a narrowband frequency.

International Journal of Antennas and Propagation
Inspired by Enoch, in this paper, a planar wideband ZIM is fabricated firstly.The resonant electromagnetic properties present in the bandwidth of the planar ZIM can be up to 1.5 GHz.And then, two high-gain patch antennas (narrowband patch antenna and wideband patch antenna) based on the ZIM cover are studied.The antennas' performances are studied with simulations and measurements.It is demonstrated that gain and directivity of the proposed antennas can be improved at the wideband frequencies compared to the conventional patch antennas without the ZIM.In addition, the electric field distributions are presented for explaining physically the improvement of antenna performance.A simple method for achieving a wideband high-gain patch antenna is provided in the present work.

Zero Index Metamaterial
2.1.ZIM Design Principle.Pendry discovered that electromagnetic behaviors of arrays of periodical wires are similar to those of metal [1].Plasma is a system composed of a large number of charged particles, which shows neutral.The effective permittivity can be expressed as where   is the plasma frequency and  is the frequency of the propagating electromagnetic wave.The plasma frequency   of the metal can be expressed as where   is the charge density,  is the electric quantity,  eff is the effective mass, and  0 is the permittivity in free space.
The plasma frequency   of the metal is in the frequency of ultraviolet.Pendry proposed a mechanism for the depression of the plasma frequency   to microwave by employing arrays of wires.Wires can depress   and increase  eff , resulting in lowering the plasma frequency   .The plasma frequency   of the wires can be expressed as where  is the radius of the wires,  is the lattice constant, and  0 is the speed of light in the free space.From (3), the plasma frequency   can be lowered by optimizing the lattice constant  and the radius  of the wires.It can be concluded that the permittivity is negative when the frequency is below the plasma frequency.
Based on Pendry's thought, we design the mesh grid structure whose plasma frequency can be in the microwave band by optimizing the parameters of the mesh grid structure.When operating at the plasma frequency, the effective permittivity is zero, and hence it yields a zero index.

Fabrication and Experiment.
Figure 1 shows the planar ZIM consisting of arrays of mesh grid on each side of the substrate with the thickness of 1.5 mm and the effective dielectric constant   of 2.65 ( = 0.009).The design idea is inspired by [15].However, in the present paper, we utilize single-layer microstrip technology for realizing the planar ZIM.Geometrical dimension of the unit cell presented in Figure 1(a) are line width  and lattice constant .Zero index frequency can be controlled by constructing the parameters  and .In the present paper, the simulations were employed by using German commercial software package CST Microwave Studio on the basis of the finite integration method.Electromagnetic resonant behaviors of the planar ZIM for different parameters  and  are studied.Figure 2 shows the resonant behaviors for  = 0.2 mm, 0.4 mm, 06 mm, and 0.8 mm with constant  = 14 mm.Figures 2(a) and 2(b) show the transmission spectrums and reflection spectrums.The calculated permeability, permittivity, and index by using -parameters retrieval method [23] are presented in Figures 2(c), 2(d), 2(e), 2(f), 2(g), and 2(h).It is presented that the cutoff nearzero index is 9.9 GHz, 10.9 GHz, 11.7 GHz, and 12.39 GHz corresponding to  = 0.2 mm, 0.4 mm, 06 mm, and 0.8 mm.The near-zero index shifts the higher frequency with the increase of the parameter .Meanwhile, the results show that the imaginary parts of the permeability, permittivity, and index are all small at the near-zero index.The electromagnetic behaviors of the planar ZIM versus the parameter  are also investigated.The study shows that the near-zero index shifts the lower frequency with the increase of  (not shown here).
The planar ZIM structure was fabricated by using a shadow mask/etching technique in this paper.The geometrical dimensions of the unit cell are chosen as follows: line width  = 0.6 mm and lattice constant  = 14 mm.Deposited copper thickness is 35 m.The fabricated planar ZIM sample is shown in Figure 1(b).The experiments composed of two standard horn antennas (8.2-12.4GHz) were carried out with an AV3618 network analyzer (50 MHz-20 GHz) in an anechoic chamber.The measured refractive index is shown in Figure 2(g), where the real part of the index is near-zero at the wideband frequencies.Frequency (GHz) Frequency (GHz) from 9.914 GHz to 10.76 GHz, with the relative bandwidth of 8.184%.Whereas the measured −10 dB bandwidth is 0.8 GHz covering from 10.14 GHz to 10.94 GHz, with the relative bandwidth of 7.6%.The measured frequency is slightly higher than the simulated one.This discrepancy may be due to the fabrication tolerance and the substrate material where the actual dielectric constant is a little different from the value used in the simulations.

High-Gain Patch Antennas with the ZIM Cover
In order to broaden antenna bandwidth, four parasitic patches [24] with the dimension of 2.3 mm × 7.8 mm surrounded by the radiation patch are added.The wideband patch antenna prototype is shown in Figure 3(b).The simulated −10 dB bandwidth is 1.212 GHz covering from 9.884 GHz to 11.096 GHz, with the relative bandwidth of 11.55%.Whereas the measured −10 dB bandwidth is 1.2 GHz covering from 10.05 GHz to 11.25 GHz, with the relative bandwidth of 11.3%.The antenna bandwidth is wider by 0.4 GHz than that of the narrowband patch antenna.The operation frequency of the wideband antenna is still in the range of zero index of the ZIM.
The prototype of the proposed antenna with the ZIM cover is shown in Figure 4.It is demonstrated that  the distance ℎ between the patch antenna and ZIM cover influences the antenna performances.Figure 5 gives the simulated performances of the narrowband patch antenna with the ZIM cover, which presents the optimum distance ℎ = 9mm.The average gain of the narrowband antenna with the ZIM is 10.17 dB at the working frequencies, and the peak gain can be up to 10.59 dB at 10.5 GHz. Figure 6 gives the simulated performances of the wideband antenna with the ZIM cover.The optimum distance is also ℎ = 9 mm.The average gain of the proposed wideband antenna with ZIM is 10.9 dB at the working frequencies, and the peak gain is 11.6 dB at 10.9 GHz.Therefore, in the present paper, we fabricate the antenna samples with the optimum distance ℎ = 9 mm.In addition, the number of the ZIM layers versus antenna performances is also investigated.The antenna performances are listed in Table 1.The results show that the antenna gain is improved with the increase of the ZIM layers.When one layer ZIM is placed above the conventional patch antenna, antenna beamwidth is convergent and the gain is improved greatly.When two layers ZIM or much more layers International Journal of Antennas and Propagation ZIM are utilized, antenna gain is improved slowly.When the ZIM cover is increased to seven layers, the antenna gain is almost stable.In order to design the antenna with compact volume and improved gain, the antenna based on one layer ZIM with the optimum distance ℎ = 9 mm is fabricated in the present paper.To demonstrate the ZIM cover for improving antenna performance, the comparative radiation patterns between the conventional patch antenna and the proposed antenna are presented in Figure 8.It shows that the measured HPBW in the  plane is reduced by 42 ∘ , and HPBW in the  plane is reduced by 15 ∘ compared to the conventional patch antenna without the ZIM.The side lobe is reduced and the forward radiation is enhanced.As a result, the gain is improved.The comparative gains are shows in Figure 9, which presents that the measured average gain is improved by 4.23 dB compared to the conventional antenna without the ZIM.The comparative antenna radiation patterns between the conventional wideband patch antenna and the proposed antenna are presented in Figure 11.The radiation patterns at the frequencies of 10.15 GHz, 10.6 GHz, 10.8 GHz, and 11.3 GHz are all given in order to demonstrate that the antenna performs good performances at the wideband frequencies.It shows that HPBW in the  plane is reduced by 49 ∘ and HPBW in the  plane is reduced by 22 ∘ compared to the conventional wideband patch antenna without the ZIM cover.The comparative gains are presented in Figure 12, which shows that the measured average gain is improved by 4.37 dB compared to the conventional wideband antenna without the ZIM cover.

Discussion.
In order to explore physically the improvement of antenna performance, simulated electric field distributions for the conventional wideband antenna and the antenna with the ZIM cover at the lower frequency (10 GHz) and the upper frequency (11.1 GHz) are given in Figure 13.The electromagnetic wave front presents a spherical wave for the conventional antenna without the ZIM cover at these two frequencies.However, the electromagnetic wave front shows a plane wave for the antenna with the ZIM cover.The planar ZIM cover plays a role in controlling the electromagnetic wave propagation direction, changing the spherical wave radiated by the conventional antenna to the plane wave.In the far-field view, the sideward radiation will be reduced, and forward radiation can be enhanced in the radiation patterns.As a result, a more directional and higher gain antenna can be obtained.The similar electric field distributions can be obtained for the conventional narrowband antenna and the antenna with the ZIM cover.
It is known that the propagation phase can be defined as Δ =  0  when the electromagnetic wave transmits the distance  in the medium.For the ZIM, the index is zero.Therefore, propagation phase is independent of propagation distance.It is expected that the propagation phase is the same at the interface between the medium and the free space whenever excitation of radiation source in the ZIM is the spherical wave or the plane wave.Hence, the form of the electromagnetic wave front depends on the curvature of the emergent surface when the electromagnetic wave transmits through the ZIM.In this paper, the planar ZIM can be employed for changing the spherical wave radiated by the conventional antenna to the plane wave.As a result, the directivity and gain of the antenna with the ZIM cover can be enhanced.
In the present paper, the high-gain patch antennas based on the ZIM cover are proposed.The planar ZIM structure in our paper is fabricated by using a single-layer shadow mask/etching microstrip technology, resulting in the merits of simple and planar structure, low profile, low weight, compact size, and easy fabrication.In addition, compared to the reported patch antennas [25,26], our proposed patch antenna has the compact volume and a much better aperture efficiency.In summary, the proposed antenna has the advantages of more compact volume, better gain, and higher aperture efficiency.Hence, we provide a method to solve some limitations (low gain, low radiation efficiency) of the conventional patch antenna.It is regarded that using the planar ZIM to improve the gain of the conventional patch antenna is significant in this paper.

Conclusions
In this work, a wideband planar ZIM is investigated.According to the zero index, two high-gain patch antennas based on the ZIM cover are designed and fabricated.The optimal distance between the patch and the ZIM cover and the number of the ZIM layers are demonstrated.The antenna performances are studied with simulations and measurements.The results show that the energy radiated by the ZIM cover antennas becomes more concentrate.As a result, the more directional and higher gain antennas are obtained.The average gain for the narrowband proposed antenna is improved by 4.23 dB.Besides the narrowband antenna, the antenna performance is improved at the wideband frequencies when the ZIM cover is placed above the wideband patch antenna.
The average gain for the proposed wideband antenna is improved by 4.37 dB as compared with the antenna without the ZIM cover.
It is significant that the wideband high-gain planar patch antenna based on the ZIM cover is realized.It is expected that the proposed high-gain antenna can be applied in the fields of high-rate data transmission, high-resolution radar systems, and among other fields.In addition, the ZIM has the merits of simple structure, compact size, and most importantly it can improve the antenna performances greatly at the wideband frequency.Furthermore, the planar ZIM cover can also be used with the other antennas such as monopoles, dipole antennas, leak-wave antennas, and aperture antennas.

Figure 2 :
Figure2: The results for  = 0.2 mm, 0.4 mm, 0.6 mm, and 0.8 mm with  = 14 mm, (a) the simulated transmission spectrums, (b) the simulated reflection spectrums, (c) the simulated real parts of the permeability, (d) the simulated imaginary parts of the permeability, (e) the simulated real parts of the permittivity, (f) the simulated imaginary parts of the permittivity, (g) the simulated and measured real parts of the index, and (h) the simulated imaginary parts of the index.

Figure 3 :Figure 4 : 6 InternationalFigure 5 :
Figure 3: The conventional patch antennas, (a) the prototype of the conventional narrowband antenna, (b) the prototype of the conventional wideband antenna, and (c) the reflection coefficients.

Figure 6 :
Figure 6: The performance of the proposed wideband antenna with the ZIM cover for different distances ℎ, (a) the reflection coefficients and (b) the antenna gains.

Figure 7 :Figure 8 :
Figure 7: The performances of the proposed narrowband antenna with the ZIM cover, (a) the reflection coefficients and (b) the radiation patterns.

FrequencyFigure 9 :
Figure 9: The comparative gains of the conventional narrowband antenna and the proposed antenna, (a) simulations and (b) measurements.

Figure 10 :
Figure 10: The performances of the proposed wideband antenna with the ZIM cover, (a) the reflection coefficients and (b) the radiation patterns.

Table 1 :
The performances of the antenna based on the different ZIM layers.