Multiband Negative Permittivity Metamaterials and Absorbers

Design and characteristics of multiband negative permittivity metamaterial and its absorber configuration are presented in this paper. The proposed multiband metamaterial is composed of a novel multibranch resonator which can possess four electric resonance frequencies. It is shown that, by controlling the length of the main branches of such resonator, the resonant frequencies and corresponding absorbing bands of metamaterial absorber can be shifted in a large frequency band.


Introduction
Metamaterials, defined as artificial structures not found in nature, possess interesting properties, for example, negative refraction, perfect image, backward-wave radiation, reversals of both Doppler shift and Cherenkov radiation, and so forth [1][2][3][4].It has recently shown that metamaterials can be used in various areas including microwave and optical components, absorbers, invisible cloaks, and so forth [5][6][7][8][9].Due to these exciting properties and applications of metamaterials, in the past decade, various types of metamaterial configurations have been reported, operating at very wide frequency spectra ranged from microwave, THz, and even optical frequencies [10][11][12][13].
On another hand, in our previous research results [7], we have experimentally and numerically demonstrated a snowflake-shaped metamaterial absorber and obtained a well agreement between the measured and simulated results.
The snowflake-shaped metamaterial resonator was composed of equal three main branches and six side branches.However, we found that it could achieve multiresonance frequencies when the main branches were not equal.In this paper, we firstly propose a simple design of negative permittivity metamaterial by using a multibranch resonator which can possess four electric resonance frequencies.The transmission and reflection characteristics are firstly investigated and then the effective electromagnetic parameters retrieved from the -parameters are determined.The tuning effects of the four operating frequencies by altering the main branches are discussed.Due to the fact that most of the single negative permittivity metamaterials are used to design the metamaterial absorbers in such research area, the multiband metamaterial absorber constructed by the proposed resonators is also discussed in this paper.

Model Design
The unit cell of the proposed multiband negative permittivity metamaterial is presented in Figure 1.There are four mainbranches with different lengths that intercrossed each other and eight pair of subbranches with equal length  = 0.86 mm located on the main branches with angle of 60 ∘ between the main and subbranches.To obtain four electronic resonance points, the proposed resonator should be at least  2 symmetry to meet that there are two current routes with equal magnitudes and outphase flow orientations [24,25].
The subbranches in the resonator are used to enhance the capacitance, resulting in the enhancement of electronic resonance strength, and also can reduce the size of resonator.The widths of the main and subbranches are  1 = 0.3 mm and  2 = 0.2 mm, respectively, and the distance between the center of the resonator and the locations of subbranches is fixed as  = 1.45 mm.The length of each main branch can be changed and will affect the operating frequencies, which will be discussed later.
We firstly demonstrate the multiresonance and transmission characteristics of the proposed negative permittivity metamaterials.For simply, the resonator with copper thickness of 0.017 mm is placed on a Rogers Ro4003 dielectric substrate with thickness of 1 mm (the relative permittivity is 3.55 and dielectric loss tangent is 0.0027).The other parameters of the resonator are defined as  = 4.1 mm,  = 3.2 mm,  = 3.3 mm, and  = 2.5 mm, by using finite-element-methodbased commercial electromagnetic simulator (Ansoft HFSS V14).The period spaces between the resonators along the field and -field are 9 mm (as shown in Figure 1).

Simulation and Results
For simulations, the unit cell is paced in a hollow waveguide with cross-section of 9 × 9 mm 2 .The side walls of the waveguide perpendicular to the -field are defined as perfect electric boundaries and those perpendicular to the -field are defined as perfect magnetic boundaries to simulate an infinite period situation.The front and back planes parallel to the plane of the resonator are set as wave ports.
By using the previously mentioned dimensional parameters, we obtain the numerical transmission and reflection results of the proposed multibranch resonator by HFSS software, as show in Figure 2. It can be seen that there are clearly four transmission dips that appeared in the frequency range of 10-17.5 GHz; that is, four resonances are obtained at 11.55 GHz, 13.58 GHz, 15.22 GHz, and 16.82 GHz.
To demonstrate the negative permittivity properties, we retrieve the effective electromagnetic parameters from the simulated -parameters by using the retrieving method mentioned by Smith et al. [26].The results are illustrated in Figure 3, and it is shown that, near the reflection dips as presented in Figure 2, the multiband metamaterial possesses high impedance characteristics (see Figure 3 frequencies, but all of them cannot lead to the negative permeability properties.This is due to the fact that, in the last two resonant frequencies, the bianisotropy properties occurred [27].

Discussions
The advantage of the proposed multiband resonator is that its four resonant frequencies can be adjusted by changing the corresponding main branches, respectively.In this section, we numerically discuss the tuning effects of the multiband metamaterial by altering each main branch.Firstly, by changing the length of main branch  cannot be affected significantly.This means that the first transmission dip can be decided by the longest main branch with length .
Secondly, when the length of another main branch  was shortened from 3.2 mm to 2.4 mm, the simulated tuning characteristics of the transmission results of the multiband metamaterial can be found in Figure 4(b).It is seen that the third transmission dip blue-shifts from 15.22 GHz to 16.22 GHz and the other three transmission dips do not change.Therefore, this branch mainly contributes to the control of the third transmission dip.
By using the same method, we obtain the other two tuning properties for the second and forth transmission dips by changing the lengths of the main branches c and d from 3.7 mm to 2.9 mm and from 2.9 mm to 2.1 mm, respectively.The numerical results are shown in Figures 4(c) and 4(d), and it can be found that the corresponding transmission dips blue-shift from 13.02 GHz to 13.95 GHz and from 15.67 GHz to 17.03 GHz, respectively.Also, in each tuning condition, the other three transmission dips cannot be affected significantly.
These tuning properties provide a simple way to control the four operating frequencies and keep the whole period space unchanged.So it possesses the advantages in design of practical double negative metamaterials or metamaterial absorbers.In next section, we will design a multiband planar metamaterial absorber by using the previously discussed multibranch electric resonator.

Multiband Absorber
To construct the multiband metamaterial absorber, we just add another full-size copper plane with thickness of 0.017 mm on the other side of the dielectric substrate, with the similar method as shown in [20].And in the numerical simulation setup, due to the full-size ground plane, there is not any EM wave which can be transmitted through the metamaterial absorber.So only one wave port is needed in simulations as shown in Figure 5.
In simulations, the other dimensional parameters of the metal resonator and dielectric substrate (except the thickness of the substrate) have the same values as mentioned in previous section.The absorptivity can be defined as () = 1 − () = 1 − | 11 | 2 due to the ground plane, where the () is the simulated reflectivity.As analyzed in [20], the critical parameters to achieve the higher absorptivity are the thickness of the substrate, so in this paper, it is needed to optimize the value of the substrate thickness.
After optimizations, we get the near-equal four absorption peaks by setting the thickness of the substrate as 0.85 mm.The simulated absorptivity property of the multiband metamaterial absorber composed of the proposed multibranch resonator is illustrated in Figure 6.It clearly shows that there are four absorption peaks located at 9.91 GHz, 11.08 GHz, 14.26 GHz, and 15.76 GHz, respectively.However, the four absorption peaks are correspondingly lower than the transmission dips as shown in Figure 2.This is due to fact that the added ground plane would increase the inductances and capacitances between the metallic resonance and such ground plane, which would significantly reduce the resonance frequencies.Moreover, the surface current distributions in the multibranch resonator and ground plane at each absorbing peaks are presented in Figure 7 to understand the absorbing mechanism of the proposed multiband metamaterial absorber.As can be seen, this kind of metamaterial absorber exhibits typical electric resonance and magnetic resonance (due to the antiparallel currents between the resonator and ground plane) characteristics at all the four absorption peaks, similar to the conventional metamaterial absorbers [20].
Moreover, the absorption strength at the four absorbing frequencies of the proposed multiband metamaterial absorber can be enhanced separately and/or simultaneously by altering the thicknesses and the kinds (with different dielectric loss) of the substrate, the period space, and the kinds of the metal materials (not discussed in this paper).Some of the optimizing methods can be found in recently developed research paper such as in [20][21][22].

Conclusion
In this paper, we have demonstrated a novel kind of multiband negative permittivity metamaterial composed of multibranch electric resonator.The proposed metamaterial can exhibit four electric resonant frequencies, that resulted in four negative permittivity bands.Moreover, the four electric resonant frequencies can be tuned by changing the main branches.Also, we designed a multiband metamaterial absorber by using the proposed multibranch resonator and numerically demonstrated its absorptivities and surface current distributions.These results can enlarge the design categories of the band-enhanced metamaterials and the multiband applications.

Figure 2 :
Figure 2: Simulated transmission and reflection results of the proposed multiband metamaterial (color online).

Figure 3 :
Figure 3: Retrieved effective electromagnetic parameters from the simulated -parameters (color online).
(a)), and the effective refractive index in the whole frequency band is positive (see Figure 3(b)).As shown in Figure 3(c), four typical electric resonances are obtained, and correspondingly four negative permittivity bands appeared at 11.55-11.75GHz, 13.58-14.85GHz, 15.22-15.62GHz, and 16.82-16.96GHz.Moreover, the retrieved effective permeability as shown in Figure 3(d) indicates that two antimagnetic resonances appear at first two resonance frequencies, and contrarily there are two typical magnetic resonances for the last two resonant

Figure 4 :
Figure 4: Simulated transmission properties of the proposed multiband metamaterial in different lengths for the four main branches (color online).

Figure 5 :
Figure 5: Numerical simulation setup of the metamaterial absorber composed of the multibranch resonator (color online).

Figure 7 :
Figure 7: Surface current distributions in the resonator and the ground plane at the absorbing frequency: (a) 9.91 GHz, (b) 11.08 GHz, (c) 14.26 GHz, and (d) 15.76 GHz (color online).