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Radiation Effects and Defects in Solids:Incorporating Plasma Science andPlasma TechnologyPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/grad20

Effect of spiral left-handed materialwith near-zero index on rectangularmicrostrip antennaYan-Rong Zhanga, Ji-Jun Wanga, Lei-Lei Gonga & Zhi-Pan Zhua

a Department of Physics, Jiangsu University, Zhenjiang 212013,People's Republic of ChinaPublished online: 18 Sep 2014.

To cite this article: Yan-Rong Zhang, Ji-Jun Wang, Lei-Lei Gong & Zhi-Pan Zhu (2014) Effect ofspiral left-handed material with near-zero index on rectangular microstrip antenna, RadiationEffects and Defects in Solids: Incorporating Plasma Science and Plasma Technology, 169:9, 808-815,DOI: 10.1080/10420150.2014.954576

To link to this article: http://dx.doi.org/10.1080/10420150.2014.954576

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Radiation Effects & Defects in Solids, 2014Vol. 169, No. 9, 808–815, http://dx.doi.org/10.1080/10420150.2014.954576

Effect of spiral left-handed material with near-zero index onrectangular microstrip antenna

Yan-Rong Zhang∗, Ji-Jun Wang, Lei-Lei Gong and Zhi-Pan Zhu

Department of Physics, Jiangsu University, Zhenjiang 212013, People’s Republic of China

(Received 22 March 2014; final version received 11 August 2014)

In this paper, spirals are arranged periodically on the surface of the substrate, making a left-handed mate-rial (LHM) with a near-zero index of refraction. A radiation patch is etched on the surface of this substrate,making an antenna. The finite difference time domain method is used to study the effect of this LHM witha near-zero index of refraction on the microstrip. At f = 13.78 GHz, the equivalent permittivity and per-meability of the proposed spiral materials are both negative; at f = 28.02 GHz, the equivalent permittivityand permeability are both negative and the refraction index is near zero. Compared with conventionalmicrostrip antenna, the radiation gain of the antenna is much higher and the return loss is much lower dueto the near-zero-index effect.

Keywords: near-zero index; LHM; gain

1. Introduction

Left-handed material (LHM) is a novel periodic artificial electromagnetic (EM) structure. It hasnegative permittivity and negative permeability simultaneously. When the EM wave propagatesthrough the material, the electric field, magnetic field, and wave vector of the EM wave will forma left-handed triad. As early as 1968, Veselago investigated the abnormal EM phenomenon ofthe LHM in theory (1). In 2000, the first artificial LHM was fabricated by Smith and Kroll (2) bycombining split resonant rings and continuous wires. LHM has many wonderful optical and EMcharacteristics, such as reversed Doppler effect, reversed Vavilov–Cerenkov effect, and unusualSnell phenomenon (1), making LHM promising in these fields.

Now a novel material with a zero index or a near-zero index attracts our great attention dueto its ability to realize high-directivity radiation with high gain (3). A near-zero-index materialcan obtain high-power beam (4) and can be applied in controlling wave directivity (5–7) andradiation pattern (8). The phase variation of the EM waves entering these types of structures isvery small (6). The phase of the wave ‘freezes’ inside a zero-index material, suggesting that thephase front of the wave exiting the structure always conforms with the material interface. If theexiting material interface is flat, then the refracted wave is focused along the direction perpendic-ular to the interface. Among different kinds of metamaterials, the zero-index metamaterial wasdeveloped by designing subwavelength elements working within a frequency range where eitherthe effective permittivity or the permeability of the structure is close to zero (5, 6). Enoch and

∗Corresponding author. Email: 592020574@qq.com

c© 2014 Taylor & Francis

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his group have attempted the numerical and experimental endeavor to study its method to realizethis radiation (3).

In this paper, we insert the spirals on the surface of the substrate, making a LHM with a near-zero index of refraction. A radiation patch is etched on the surface of this substrate, making anantenna. The finite difference time domain (FDTD) method is used to analyze the characteristics

Figure 1. A view of the composite spiral antenna: (a) the first layer and (b) the second layer, (c) the spiral structure,and (d) the stereochemical structure.

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of the composite spiral antenna based on the near-zero-index metamaterial. It achieves a muchlower return loss and a higher gain than the conventional antenna.

2. Computing model of the composite spiral antenna based on near-zero index

2.1. The theory of FDTD

The FDTD method (9–11) is much more suitable in dealing with such complicated processesamong many algorithms used to compute and analyze microstrip antennas owing to its manyadvantages. Maxwell equations can be transformed into a scalar field model during calculationand then a numerical difference coefficient in the second rank precision is used instead of a dif-ferential quotient, discretizing the differential equations in space-time using the method proposedby Yee, and making composite spiral antenna meshed (9). Then difference equations in the scalarfield model can be obtained, and Maxwell equations can be transformed into FDTD equations initerative formulation.

A perfectly matched layer (10–12) is taken as the boundary condition toward x, y directionwhile computing, and a cell is divided by 20 × 20 discretization, then the time step is chosen as4000, and finally the composite spiral antenna with source is simulated by the FDTD numericalmethod.

The Gauss pulse is chosen as the excitation source due to its smoothness in the time domain,and the bandwidth is easy to choose. Its frequency ranges from 0 to 40 GHz.

Figure 2. A top view of conventional microstrip antenna.

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2.2. Geometric model of the composite spiral antenna

The composite spiral antenna has two layers of substrate with the dimension 120 mm × 120 mm,the first substrate has a thickness of 3 mm with permittivity 10.0, and the second substrate hasa thickness of 2 mm with permittivity 2.2, in the back of it is a ground plane. In the first sub-strate, the dimension of the rectangular microstrip antenna is 100 mm × 100 mm, and its frameis 3 mm wide, the periodic structure is composed of a circle array and a triangular array. Theexcitation source is a Gaussian discrete source, fed by a microstrip measuring 2 mm × 10 mm,as shown in Figure 1(a). In the second substrate, the rectangular structure is the same as in thefirst substrate. The composite structure is shown in Figure 1(b), the parameter of the spiral isshown in Figure 1(c), and the stereochemical structure of the composite spiral antenna is shownin Figure 1(d).

The conventional rectangular microstrip antenna is shown in Figure 2. The permittivity of thesubstrate is 10.0.

3. Simulation results and analysis

The FDTD simulator is applied to analyze the two antennas. Return loss s11, voltage standingwave ratio (VSWR), and gain of two couples are obtained, as shown in Figures 3–5.

Figure 3 shows that return loss s11 of the composite spiral antenna is −39.67 dB, 34.30 dBless than that of the conventional antenna at f = 13.78 GHz. At f = 28.02 GHz, return loss s11

Figure 3. Return loss s11 of the composite spiral antenna (a) and the conventional microstrip antenna (b) near atf = 13.78 GHz, the composite spiral antenna (c), and the conventional microstrip antenna (d) near at f = 28.02 GHz.

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Figure 4. VSWR of the composite spiral antenna (a) and the conventional microstrip antenna (b) near atf = 13.78 GHz, the composite spiral antenna (c), and the conventional microstrip antenna (d) near at f = 28.02 GHz.

is −31.92, 28.11 dB less than that of the conventional antenna. This indicates that the compositespiral antenna can obtain much lower return loss. Their characteristic parameters are listed inTables 1 and 2.

As is shown in Figure 4, VSWRs of the composite spiral antenna are 1.02 and 1.05 at f =13.78 and 28.02 GHz, respectively, and they are exceedingly near to 1, while the conventionalantenna’s VSWRs are 3.33 and 4.62, respectively.

Figure 5 shows that the conventional antenna’s maximum gain is 4.17 dB at 13.78 GHz, whilethe composite spiral antenna’s maximum gain reaches 7.95 dB at 13.78 GHz, improved about 1time. The conventional antenna’s maximum gain is 2.86 dB at 28.11 GHz, while the compositespiral antenna reaches 10.12 dB at 28.02 GHz, improved about 2.54 times. The simulated resultsare listed in Tables 1 and 2.

Here, the Nicolson–Ross–Weir transmission/reflection method (13) is introduced to get theequivalent refraction index n, equivalent permittivity εr, and equivalent permeability μr of thismetamaterial from S parameters containing return loss and transmission coefficient.

The equivalent refraction index n, equivalent permittivity εr, and equivalent permeability μr

of the composite spiral antenna are shown in Figure 6.The extracted results are shown in Figure 6. At the resonant frequency f = 13.78 GHz,

Figure 6(a) shows that εr = −1.75, μr = −1.78, n = −1.77, and n is not near zero. At the res-onant frequency f = 28.02 GHz, Figure 6(b) shows that εr = −0.36, μr = −0.50, n = −0.42,and n is near zero. At f = 13.78 GHz, compared with the conventional rectangular microstripantenna, the gain of the antenna based on a left-handed effect is improved about 1 time, whileat f = 28.02 GHz, the gain of the antenna based on a left-handed effect with a near-zero index

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Figure 5. Gain of the composite spiral antenna (a) and the conventional microstrip antenna (b) near at f = 13.78 GHz,the composite spiral antenna (c), and the conventional microstrip antenna (d) near at f = 28.02 GHz.

Table 1. Parameters of the two antennas near at f = 13.78 GHz.

Resonant Return Maximumfrequency (GHz) loss s11 (dB) VSWR gain (dB)

The conventional antenna 13.78 −5.37 3.33 4.17The composite spiral antenna 13.78 −39.67 1.02 7.95

Table 2. Parameters of the two antennas near at f = 28.02 GHz.

Resonant Return Maximumfrequency (GHz) loss s11 (dB) VSWR gain (dB)

The conventional antenna 28.11 −3.81 4.62 2.86The composite spiral antenna 28.02 −31.92 1.05 10.12

is improved about 2.54 times. It indicates that a near-zero index can improve the antenna’s gainand a left-handed effect with a near-zero index can improve the antenna’s gain much more thana left-handed effect (improving about 2.17 dB). It is explained that the left-handed metamate-rial can enhance the EM wave’s tunnel effect (14), and the boundary plane between the positiverefraction and the medium of the composite spiral system with negative refraction dielectricsupports the surface wave of the EM wave’s tunnel traverse model (12). These surface wavespropagate through the boundary plane according to the evanescent waves’ coupling effect. Thepower density near the boundary plane increases rapidly (15), indicating that the equivalent nega-tive refraction structures possess the ability of amplifying evanescent waves, so the transmission

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Figure 6. Equivalent permittivity εr , permeability μr , and refraction index n of the composite spiral antenna: (a) atf = 13.78 GHz and (b) at f = 28.02 GHz.

of surface waves in these models can be enhanced obviously, and since the directivity of theantenna is effectively enhanced based on the zero refraction characteristics (7). Such effects canimprove the antenna’s radiation gain and its matching condition, so the antenna’s return lossis much lower compared with that of a conventional antenna. It can be seen that a left-handedmetamaterial with a near-zero index can improve an antenna’s gain compared with a left-handedmetamaterial.

4. Conclusion

In this paper, the effect of a near-zero-index metamaterial on an antenna is studied. We insertedspirals on the surface of the substrate, making a LHM with a near-zero index of refraction.

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A radiation patch was etched on the surface of this substrate, making an antenna. The FDTDmethod was used to analyze the characteristics of the composite spiral antenna based on thenear-zero-index metamaterial. Simulation results show a double frequency effect. The EM waveresonance occurred at f = 13.78 GHz and f = 28.02 GHz. At f = 13.78 GHz, the equivalentpermittivity εr and permeability μr are both negative. At f = 28.02 GHz, the composite antennaalso satisfies that n is near zero, realizing a double frequency effect. By comparing the charac-teristics of the antennas, the left-handed metamaterial with a near-zero index and the left-handedmetamaterial both can improve the antenna’s gain; the former can improve the gain of the con-ventional antenna much more. It also indicates that and the evanescent waves’ enhancing effectare formed, improving the localization level of the EM wave’s energy obviously. Moreover,waves can be converged in the near-zero-index metamaterial, improving the antenna’s directiv-ity and its matching condition. Due to these advantages, this antenna will be extended to mobilecommunication, satellite communication, aviation, etc.

Acknowledgements

The Students’ Scientific Research Item of Jiangsu University in 2013 (No. 12A417).

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