High-gain composite microstrip patch antenna with the near-zero-refractive-index metamaterial

Optik 125 (2014) 6491–6495

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High-gain composite microstrip patch antenna with the near-zero-refractive-index metamaterial Ji-jun Wang a , Lei-lei Gong a,∗ , Yu-xin Sun b , Zhi-pan Zhu a , Yan-rong Zhang a a b

Department of Physics, Jiangsu University, Zhenjiang 212013, China School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China

a r t i c l e

i n f o

Article history: Received 20 November 2013 Accepted 19 June 2014 Keywords: MTM Near zero refractive index Gain FEM FDTD

a b s t r a c t A high-gain rectangular microstrip patch antenna which is covered by a single layer metamaterial (MTM) superstrate with the near zero refractive index is proposed. The refraction of the metamaterial at frequency 3.51 GHz–3.57 GHz is very close to zero. The metamaterial with the near zero refractive index is placed 42 mm above an ordinary rectangular microstrip patch antenna. The effectively zero refractive index behavior of metamaterial superstrate can gather the wave emitted from the microstrip patch antenna and collimate it toward the normal direction of the antenna. The finite element method (FEM) and the finite difference time domain (FDTD) method are used to study the characteristics of this antenna. The results of the two methods indicate that the realized gain of the proposed antenna is increased by more than 6 dB, and the antenna has a flatness high gain in the predicted frequency band, where the proposed MTM is designed to have a near zero index of refraction. Therefore, the high-gain antenna is effectively enhanced based on the near-zero-refractive-index metamaterial. © 2014 Elsevier GmbH. All rights reserved.

1. Introduction Since Veselago [1] has investigated various properties of MTMs with the negative permittivity and permeability, numerous applications of MTMs such as high-directive antennas and superlens have been continuously explored [2,3]. MTM can occur in corresponding resonance to electric and magnetic fields based on the different structure unit cell, which can easily control the effective permittivity and effective permeability. Based on this idea, the MTM with the effective permittivity and effective permeability are negative or zero can be designed in microwaves [4]. Moreover, as a branch of the artificial electromagnetic effects, zero-refractiveindex MTM caused public concern widely, which can be used to achieve high-gain directional radiation. According to Snell’s law (n1 sin  1 = n2 sin  2 ), when the ray is incident from inside the zerorefractive-index MTM (n1 = 0) into free space (n2 > 0), no matter how much angle of incidence ( 1 ), the angle of refraction ( 2) will be close to zero, so the refracted rays will be normal to the interface. This property provides a unique method of controlling the direction of emission. Enoch et al. [5] experimentally demonstrated for the first time that energy radiated by a source embedded in

a slab of zero index MTM will be concentrated in a narrow cone in the surrounding media, so a great improvement of directivity was potentially obtained. Wu et al. [6] studied the performances of the dipole antenna embedded in different low/zero index MTM structures. Recently, high-gain microstrip patch antenna had been realized by increasing radiation patch or using antenna array, and mostly high-gain antennas are achieved by embedding antenna into the near-zero-refractive-index MTM. But these methods will increase the size and complexity of the antenna. In this letter, we have presented the microstrip patch antenna structure covered with a planar thin MTM superstrate based on a near zero refractive index over a wide frequency range. The design is simple and the antenna has a simple feed system. Its concerned parameters are obtained by the FEM and FDTD method to simulation and analysis. The results of the two methods have good consistency. Comparing to the ordinary microstrip patch antenna, the proposed antenna with near-zero-index MTM shows large improvement in a realized gain with excellent flatness in a wide frequency band.

2. Computing model of antenna

∗ Corresponding author. E-mail address: [email protected] (L.-l. Gong). http://dx.doi.org/10.1016/j.ijleo.2014.06.158 0030-4026/© 2014 Elsevier GmbH. All rights reserved.

At present, the electromagnetic methods of solving and analysing antenna mainly included method of moment (MOM), FEM, FDTD, etc. These numerical methods can provide high

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accuracy in the analysis of the radiation and scattering problems of metal conductor. In this paper, we use the FEM and FDTD to analyze the high-gain microstrip patch antenna. 2.1. The theory of FDTD The FDTD method [7–9] has been widely used to calculate the problems in electromagnetics such as antennas, waveguide propagation, and scattering. Maxwell equations can be transformed into scalar field model by calculating. Then we use the numerical difference quotient in the second rank precision instead of differential quotient. We discrete the differential equations in space-time using the method proposed by Yee, and make the rectangular microstrip patch antenna meshed [7]. We assume that x and y are space steps toward x and y direction, respectively, t is time step, then we can get difference equations in scalar field model, and Maxwell equations can be transformed into FDTD equations in iteration formulation when it is in transverse electric (TE) model. n+1/2

Exn+1 (i, j) = Exn (i, j) +

Hz

Eyn+1 (i, j) = Eyn (i, j) +

Hz

n+1/2

Hz

−

n−1/2

(i, j) = Hz

n+1/2

(i, j) +

n+1/2

(i, j + 1/2) − Hz y

n+1/2

(i + 1/2, j) − Hz x

(i, j − 1/2)

(i − 1/2, j)

·

·

t ε(i, j) (1)

t ε(i, j) (2)

Exn (i, j + 1/2) − Exn (i, j − 1/2) t ·  y

Exn (i + 1/2, j) − Exn (i − 1/2, j) t ·  x

(3) Fig. 1. (a) Geometry of the unit cell; (b) geometry of proposed MTM structure.

To ensure steady results in iteration constringency, x, y, and t must satisfy these steady conditions [10] t ≤ c



1 (x)

−2

+ (y)

(4)

−2

The calculating formulation for Hx , Hy , and Ez in TM model can be attained by the same way. In the process of calculation, we take perfectly matched layer (PML) [9] as the boundary condition and take the Gauss pulse as the excitation source. 4000 time steps are chosen for calculation. By using the method of FDTD numerical calculation, the microwave active antenna structure is simulated. 2.2. The theory of FEM Three-dimensional Maxwell equation is the governing equation of three-dimensional electromagnetic field. . The FEM used in the governing equation is:In order to model and calculate conveniently, we select the first two curl equation of Maxwell equations, and the vector Helmholtz equation of electric field intensity have been derived. We let this vector Helmholtz equation be the governing equations. ×

1

r



∇ × E − k0 2 εr E = 0

(5)

Here, E(x,y,z) is harmonic field corresponding to the vector, k0 is wave number in free space, r is permeability, and εr is permittivity. According to the variational principle, function of (5) can be written as:



1

F(E) = ˝

r

2

(∇ × E) · (∇ × E) − k0 εr E · E



d˝

(6)

The finite element method (FEM) is a numerical analysis method which is based on variational principle and the numerical analysis. The basic ideas of solving the electromagnetic field with FEM need several steps. Dividing the solution domain into a series of unit area and using local function to replace each subdomain of the field, the field of each subdomain is associated by the nodes, and the entire field can form the grid by the subdomain nodes; the link between the node correlation equations can be built by the equilibrium relationship and the energy equation, and the general algebraic equations are composed of each cell equation. Each node of the field distribution can be obtained by certain incentives and the boundary constraint, so as to get the full wave solution of the problem, and then get S parameter, characteristic impedance, antenna pattern and related results [11]. 3. The design and testing of near-zero-refractive-index MTM The near-zero-refractive-index MTM is realized by etching the periodic rectangular-shaped box unit cell on the one side of the dielectric-slab. Fig. 1a is the periodic rectangular-shaped box unit cell, and it is realized by slotting cross-shaped and four small rectangles on the center of rectangular patch; the detailed dimension is shown in Fig. 1a. Fig. 1b is the geometry of proposed MTM structure, and it is composed of 6 × 6 unit cells that are placed 42 mm above the patch antenna. The structure is based on Rogers 5880 substrate with the periodic unit cell printed on its one surface. The Rogers 5880 substrate has a thickness of 2 mm and a dielectric constant of 2.2, and the size of the substrate is 120 mm × 120 mm. The distance between unit cell and the dielectric substrate edge is 5 mm, and 4 mm spacing between each unit cell.

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Fig. 2. Effective index of refraction n of MTM.

Pendry et al. [12] proposed that the arrays of metal mesh are characterized by a plasma frequency, and its equivalent permittivity is: εeff = 1 −

ωp 2

(7)

ω2

Fω2 ω2

− ω02 + iω

(8)

where F is the fractional area of the unit cell occupied by √ interior of the split ring,  is the dissipation factor, and ω0 = 1/ LC is the resonant frequency. The refractive index n is defined as: n=

√

eff εeff

(9)

That is to say, when ω approaches ωp , the refractive index n is close to zero. Based on this theory, the periodic rectangular-shaped box unit cell is designed by the MTM in this paper. When the frequency of the electromagnetic wave is close to the plasma frequency, the equivalent permittivity εeff of MTM is close to zero, so the near zero refractive index is realized, which can gather the wave emitted from the microstrip patch antenna and collimate it toward the normal direction of the antenna. According to the S parameter inversion algorithm in Ref. [13], the S parameters of the MTM can be obtained from simulation, so we can calculate the refraction of MTM. The inversion formula is: cos (nkd) =

4. The design and simulation of antenna 4.1. The design of antenna

where ωp is the plasma frequency and ω is the frequency of the electromagnetic wave, when ω approaches ωp , the equivalent permittivity εeff is close to zero. And its equivalent permeability has the form below: eff = 1 −

Fig. 3. A top view of ordinary antenna.

2 + S2 1 − S11 21

2S21

According to the design formula of rectangular microstrip patch antenna and the simulation optimization of FEM, we have designed the ordinary rectangular microstrip patch antenna of the center frequency at 5.57 GHz. The dielectric substrate of the antenna is FR4 epoxy glass fiber board with the relative dielectric constant being 4.4, and thickness being 5.0 mm. The radiation patch, microstrip feed and ground plate are the perfect electric conductors. The size of radiation patch is 22 mm × 18 mm, and the size of the ground plate and substrate are 120 mm × 120 mm, and use microstrip line to feed antenna. The microstrip line’s size is 51 mm × 2 mm. The microstrip patch antenna structure is shown in Fig. 3. The MTM is placed right above the ordinary antenna with the distance of 42 mm, which can make the performance of the antenna meet optimization. In order to verify the correctness of the analysis and design, the antenna is simulated by two methods (Fig. 4). The FEM is used to simulate the far field radiation gain of ordinary antenna and the proposed antenna respectively. Fig. 5a and b shows the gain in E-plane. From the simulation results, we can see that the conventional antenna’s maximum gain is 3.96 dB, while the gain of antenna with MTM is 10.66 dB at 3.57 GHz, which improves 6.7 dB compared to the conventional antenna’s one, showing that the antenna with MTM can improve antennas’ gain obviously in a certain frequency band. From Fig. 5c, we can see that the gain in the predicted frequency band, where the proposed MTM is designed to have a near zero index of refraction, is flatness and no more than 1 dB.

(10)

Here d is the length of the waveguide, k is the phase constant, and S11 and S21 are the scattering parameters of the waveguide port 1. We use MATLAB language to program, and by importing the S parameters to MATLAB language, we can obtain the refraction diagram, which is shown in Fig. 2. From Fig. 2, we can see that the refractive index of the MTM is very close to 0 in frequency band of 3.51 GHz–3.57 GHz, showing good characteristics of zero refractive index. As is mentioned earlier, we can control the plasma frequency readily by varying construction parameters shown in Fig. 1. Consequently, it means that the size, height, and periodicity of the unit cell can be adjusted to obtain zero n at a required frequency band. In this paper, we have obtained the refractive index of 0.02 at 3.57 GHz.

Fig. 4. A view of the composite antenna with MTM.

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Fig. 5. The radiation patterns by FEM: (a) ordinary antenna;(b) the antenna with MTM; (c) realized gain with MTM of near zero refractive index.

Using FDTD method to simulate the proposed antenna and ordinary antenna, the gain of the antenna in E-plane is shown in Fig. 6. From Fig. 6a, we can see that the ordinary antenna’s maximum gain is 6.2 dB at 3.57 GHz, and in Fig. 6b the gain of the proposed antenna is 12.4 dB, which improves 6.2 dB than the ordinary antenna’s one. Fig. 6c shows that the antenna has a high gain in frequency band where the refraction is near zero. From the simulation results above, we can see that the antenna with MTM has higher gain than ordinary microstrip antenna. The simulation results of FEM and FDTD show that the increase amplitude of the gain is basically identical, which is about 6 dB. These results prove that the two methods are reliable.

Fig. 6. The simulation diagram of antenna gain by FDTD: (a) ordinary antenna;(b) the antenna with MTM; (c) realized gain with MTM of near zero refractive index.

5. Conclusion In this paper, we have designed a near-zero-refractive-index high-gain rectangular microstrip antenna with the MTM substrate, which can be used to gather electromagnetic beam. The refraction of MTM in 3.51 GHz–3.57 GHz is near zero and the radiation beam can be converged in this frequency range, which can improve the antenna’s gain significantly. The simulation results show that the realized gain of the proposed antenna is increased by more than

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6 dB, and the antenna has a high gain in frequency band where the refraction is near zero. References [1] V.G. Veselago, The electrodynamics of substances with simultaneously negative values of ε and , Sov. Phys. Usp. 10 (1968) 509–514. [2] J.B. Pendry, Negative refraction make a perfect lens, Phys. Rev. Lett. 85 (2000) 3966–3969. [3] B.L. Wu, W. Wang, J. Pacheco, X. Chen, J. Lu, T.M. Grzegroczyk, J.A. Kong, P. Kao, P.A. Theophelakes, M.J. Hogan, Anistropic metamaterials as antenna substrate to enhance directivity, Microw. Opt. Technol. Lett. 48 (2006) 680–683. [4] J.B. Pendry, D. Schurig, D.R. Smith, Controlling electromagnetic fields, Science 312 (2006) 1780–1782. [5] S. Enoch, G. Tayeb, P. Sabouroux, P. Vincont, A metamaterial for directive emission, Phys. Rev. Lett. 89 (2002), 213902-1–213902-4.

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