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Abstract
In this paper, we proposed a dual-polarized bidirectional three-dimensional metamaterial absorber (3D-MA) with transmission windows. This 3D-MA can achieve a broadband absorption in the range of 3.45-4.82 GHz for the forward incident wave. Meanwhile, it possesses another absorption band in the range of 1.89-3.84 GHz for backward incident waves. Due to its hollow 3D lattice structure, it also has two additional transmission windows at low frequency and high frequency bands. The design is insensitive to polarization and maintains good angular stability for oblique incidence up to 40°. In order to verify the performance of the design, a prototype was manufactured and measured. The measurement results agree well with the simulation. By studying normalized equivalent impedance and surface current distribution of the 3D-MA, the physical mechanism of the MA is clarified. The MA breaks the symmetrical transmission through the delicate designed 3D unit cell. The asymmetric absorption feature greatly expands the function of MA by providing an additional absorption band for backward incident waves. It also provides a new degree of freedom for the design of electromagnetic metamaterials. The proposed design has important application prospects in the field of radar asymmetric recognition, detection, and stealth.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Electromagnetic metamaterials are artificial structures composed of periodic or non-periodic arrangement of sub-wavelength unit cells, which can realize novel physical phenomena that do not exist in nature [1–4]. Since Landy first invented the perfect metamaterial absorber (MA) in 2008 [5], numerous MAs have already been revealed and implemented from the microwave band to the optical band [6]. Due to their exotic characteristics, MAs have been widely used for stealth [7], sensing [8], wireless communication [9], terahertz imaging [10], etc.
In the ideal case, the absorbers can absorb undesired electromagnetic (EM) waves over a wide range of frequencies for all incident angles with near unity absorptivity. They also should be ultrathin and insensitive to all polarization angles. Unfortunately, it is still very hard to simultaneously achieve all these objectives in one design [11]. Some common techniques have been provided to achieve multiband and broadband absorption. For example, in [12], it combined multiple resonances by introducing several resonators to obtain three distinctive absorption peaks. In [13] and [14], researchers achieved broadband absorption by loading lumped resistors in the unit cell. In [15] and [16], different resistive films were used to extend the absorption bandwidth of absorbers. In [17] and [18], graphene material has been introduced in the design of MAs to achieve ultrabroadband and wide-angle absorption. In addition, in [19] and [20], people proposed to build three-dimensional structure to realize broadband absorption. Due to the existence of the absorber metal ground, any incident EM wave is blocked from transmission. Later, band-pass frequency selective surface (FSS) is integrated with the MA to replace the perfect electric conducting (PEC) ground, which produces a transmission window at a certain frequency band. This kind of metamaterial is also known as frequency selective rasorber (FSR) [21,22]. In recent years, MAs and FSRs with multifunction and reconfigurable features have been proposed [23–26]. However, they can only provide absorption for the forward incident waves [27,28]. Therefore, it will be particularly interesting to explore the possibility of designing a MA that can realize distinct frequency bands absorption or transmission functionalities for both forward and backward incident waves.
In this paper, a dual-polarized bidirectional 3D-MA with transmission windows is proposed. Our work is greatly inspired by the recently proposed Janus metasurface [29]. The design in [29] can break out-of-plane symmetry, realize different functions for opposite propagation directions, and enable direction-dependent versatile functionalities. Based on this concept, we present a MA which has a 3D periodic interlocking structure. This design achieves an asymmetric absorption for the opposite incident wave. When the incident wave is incident along -z direction, the -10 dB absorption bandwidth covers the range of 3.45-4.82 GHz, corresponding to the fractional bandwidth (FBW) of 33.13%. When the incident wave is incident along +z direction, the -10 dB absorption bandwidth covers the range of 1.89-3.84 GHz, corresponding to the FBW of 68.06%. On the other hand, since the structure has hollow lattices, it provides a possibility for optically transparent. The 3D-MA provides specific transmission windows for waves incoming from both sides of the metamaterial at both low frequency and high frequency bands. The design is insensitive to polarization and has good angular stability when the incident angle changes from 0° up to 40°.
2. Design and analysis of the designed 3D-MA
The proposed 3D-MA structure is shown in Fig. 1(a). It is composed of a periodic array of hollow 3D lattices. The unit cells are arranged along the x and y directions. An enlarged view of the unit cell is depicted in Fig. 1(b). As can be seen from the figure, the unit cell is composed of five folding metallic rings which are printed on the Rogers RO4003C substrate with a thickness of 0.813 mm. The relative permittivity of the substrate is 3.38 with loss tangent of 0.0027. There are four smaller rings of equal size placed on the left side of the unit cell while another larger one is affixed nearby right. Three lumped resistors are inserted into the corresponding positions of the metal rings.
Fig. 1. (a) 3-D illustration of the proposed 3D-MA. (b) Perspective view of the proposed 3D-MA structure unit cell and the optimized geometry parameters. (p1 = 43.2 mm, p2 = 30 mm, L1 = 14.1 mm, L2 = 10.5 mm, L3 = 8.7 mm, e = 0.8 mm, c1 = 0.5 mm, c2 = 0.6 mm, c3 = 0.8 mm, f1 = 28.8 mm, f2 = 19.9 mm, w1 = 0.6 mm, w2 = 12.1 mm, w3 = 0.7 mm, w4 = 2.3 mm, w5 = 26.5 mm, R1 = 105 $\Omega$, R2 = 230 $\Omega$).
To analyze the performance of the designed 3D-MA, we use commercial software to simulate the designed 3D-MA. The co- and cross-polarized S parameters of the designed 3D-MA are shown in Fig. 2. It can be seen from the figure that when EM waves are incident along -z direction, the S11 and S21 are below -10 dB in the range of 3.45-4.82 GHz. It indicates that there is an absorption band in this frequency band. On the other hand, when EM waves are incident along +z direction, the absorption band shifts to the range of 1.89 GHz to 3.84 GHz. Since the S21 and S12 are higher than -1.5 dB in both low frequency and high frequency bands, transmission windows exist in these bands as shown in Fig. 2. To address the novelty of this work, it is important to clarify the difference between traditional absorbers, asymmetric transmission metasurface [30,31] and our design. Traditional absorbers can achieve in-band absorption and out-of-band reflection for single direction incident wave. In our design, asymmetric absorption bands are achieved under both forward and backward illumination. However, this asymmetric absorption feature is different from the so-called asymmetric metasurface which relies on the polarization manipulation of the incident wave. From the S11($r_{yx}$), S21($t_{yx}$) and S22($r_{yx}$), S12($t_{yx}$) shown in Fig. 2, it can be deduced that polarization remains conserved in our design. In addition, since the proposed 3D-MA is symmetrical in the x and y directions, it has good polarization stability under the normal incidence for both TE and TM polarization.
Fig. 2. S-parameters of the designed 3D-MA when the waves incident along with different directions (a) along the -z direction, (b) along the +z direction.
In order to clarify the absorption mechanism of the designed 3D-MA, the normalized equivalent impedance of the MA is analyzed. Although equivalent impedance theory has been successfully used to study the absorption mechanism of traditional MA, it has not been fully applied to analyze metamaterial with bidirectional absorption. Since the absorption performance is different in two opposite directions, we can assume that the absorber has two distinct equivalent impedance under forward and backward incidence. These two different impedances are defined as Z$_{1}$ and Z$_{2}$, which can be extracted from S parameters [32]. In this case, when the incident wave is incident along -z direction, the equivalent impedance is defined as $Z_1=\sqrt {\frac {\left (1+S_{11}\right )^{2}-S_{21}^{2}}{\left (1-S_{11}\right )^{2}-S_{21}^{2}}}$. When the incident wave is incident along +z direction, the equivalent impedance is defined as $Z_2=\sqrt {\frac {\left (1+S_{22}\right )^{2}-S_{12}^{2}}{\left (1-S_{22}\right )^{2}-S_{12}^{2}}}$. The normalized impedances of the designed 3D-MA when the wave is incident in different directions are illustrated in Fig. 3. It can be seen from Fig. 3(a) that when the wave is incident along -z direction, the real part is close to 1 and the imaginary part is close to 0 in the absorption band. This means that the designed 3D-MA has good impedance matching with free space. Similarly, it can be seen from Fig. 3(b) that when the wave is incident along +z direction, the designed 3D-MA achieves good impedance matching with free space in the absorption band.
Fig. 3. The normalized impedance of the designed 3D-MA when the wave is incident in different directions. (a) along the -z direction, (b) along the +z direction.
To better understand the physical mechanism of the designed 3D-MA, we also study the surface current distribution at the different resonance frequencies. According to S-parameter curve shown in Fig. 2, we have selected three resonance frequencies which are 2.07 GHz, 3.65 GHz and 4.28 GHz. This multiple resonance originates from the mutual coupling between the metallic rings and their neighborhoods. Fig. 4 shows the surface current distribution at these frequencies. It can be seen that there is a strong coupling between the small metal rings and the large metal ring. In this case, the maximum value of the current appears in this region. This phenomenon can be equated to the short circuit case. Thus, we claim that a virtual ground is produced in this region. The surface current distribution when the wave is incident along -z direction is shown in Fig. 4(a). At 2.07 GHz, strong resonance occurs on the large metal ring. The current is mainly concentrated between the small metal rings and the large metal ring. Most of the energy is reflected to the +z direction. Since the current on the small rings is quite weak, the energy is not absorbed by the lumped resistors but radiated to the upper space. Moreover, at 3.65 GHz and 4.28 GHz, the resonance between the small metal rings is strengthened. The current is concentrated on the two lumped resistors which means the energy is absorbed by the lumped resistors. When the absorber is under backward illumination, the working mechanism is quite similar to the forward incidence case. As shown in Fig. 4(b), the current on the lumped resistor is strong at 2.07 GHz and 3.65 GHz. This shows that the energy at these two resonances is absorbed. At 4.28 GHz, since the current between the large metal rings is weakened, the wave is reflected to the incident direction.
Fig. 4. The surface current distribution at the three resonance points of the designed 3D-MA when the wave is incident in different directions (a) along the -z direction, (b) along the +z direction.
From the above analysis, it can be noted that the absorption and reflection of waves are manipulated by the coupling resonance between the metallic loops. When the wave is incident, a virtual ground is produced in the structure, and the incident EM waves are reflected. Moreover, by adding lumped resistors at appropriate positions, the impedance of the 3D-MA is matched with the free space. The incoming energy is effectively absorbed by the lumped resistors. It breaks the symmetry in z direction and realizes asymmetric bidirectional EM absorption.
When the EM wave is at normal incidence, the absorptivity is calculated using the formula, $A(\omega )=1-R(\omega )-T(\omega )=1-\left |S_{11}(\omega )\right |^{2}-\left |S_{21}(\omega )\right |^{2}$. Similarly, when the EM wave is incident from the opposite direction, the absorptivity is expressed as, $A(\omega )=1-\left |S_{22}(\omega )\right |^{2}-\left |S_{12}(\omega )\right |^{2}$ [33]. To maximize the absorptivity, the transmittance $T(\omega )$ and reflectance $R(\omega )$ should be minimized. By changing the geometric parameters of the metal pattern and the value of the loaded lumped resistors, the absorption bandwidth of the designed 3D-MA can be adjusted. We first study the influence of resistance (R1 and R2) of the loaded lumped resistors. As shown in Fig. 5(a) and Fig. 5(b), it can be noticed that R1 mainly affects the absorption band of the MA under the forward incidence, and R2 is mainly related to the absorption band under the backward incidence wave. When the MA is under forward incidence, the first resonant peak of MA shifts to higher frequencies with the increase of resistor R1 and the absorptivity will decrease. When the MA is under backward incidence, the absorption bandwidth is narrowed with the value of resistor R2 increases. Fig. 5(c) shows that the coupling resonance between the structures can be adjusted by changing the geometric parameters, which will lead to optimized impedance matching in the entire absorption band. The optimized geometric and material parameters are determined as follows: R1 = 105 $\Omega$, R2 = 230 $\Omega$, L2 = 11.5 mm.
Fig. 5. The absorptivity of the designed 3D-MA with varied geometric and material parameters when the wave is incident in different directions. (a)R1. (b)R2. (c)L2.
The angle stability of the designed 3D-MA under TE polarization and TM polarization for either incident direction is shown in Fig. 6 and Fig. 7, respectively. It can be seen from Fig. 6 that when the wave is incident along the -z direction, with the increase of incident angle, the absorptivity and absorption bandwidth of the designed 3D-MA become deteriorate for TE polarization. Under TM polarization, there is almost no change in the operating frequency band. This is due to the fact that the incident wave impedance is different under different polarizations [34]. When the incident angle is large, the impedance mismatch causes the absorption performance to decrease. Similarly, as shown in Fig. 7, when the wave is incident along the +z direction, as the incident angle increases, the absorptivity of 3D-MA gradually decreases under TE polarization. Under TM polarization, the fluctuation of the absorptivity in the operating frequency band is small. At the same time, when the incident angle is less than 40°, the absorptivity is still above 80% which means the designed 3D-MA has good angular stability.
Fig. 6. The absorptivity under -z incidence of the 3D-MA with different incident angles for (a) TE polarization and (b) TM polarization.
Fig. 7. The absorptivity under +z incidence of the 3D-MA with different incident angles for (a) TE polarization and (b) TM polarization.
3. Experimental result
In order to verify the performance of the designed 3D-MA, a prototype was manufactured and measured. As shown in Fig. 8(a), the total dimension of the fabricated sample is 420$\times$420$\times$43.2 mm$^{3}$ and it consists of 14$\times$14 unit cells. Each unit was printed on 0.813 mm thick Rogers RO4003C and the metal pattern along the x- and y-axis. Its relative permittivity and loss tangent are 3.38 and 0.0027, respectively. The substrate is cut and assembled into interlocking lattices without metal backed ground.
As shown in Fig. 8(b), the 3D-MA prototype was measured in the microwave chamber. A pair of horn antennas connected to a vector network analyzer (Agilent N5230A) is used to measure the reflection and transmission coefficients of the prototype. The operation frequency of the horn antenna is 1 to 18 GHz. We tested the S parameters of the prototype under forward and backward incidence respectively. The comparison between the measured and simulated S-parameters is shown in Fig. 9. It can be observed that the measured results are in good agreement with the simulation results. Some of the differences between the measurement and simulation results may be due to the tolerances in fabricating the MA samples, the unstable relative permittivity of the substrate, and other manufacturing errors.
Fig. 9. Comparison between measured and simulated S-parameters when the waves propagate along with different directions of the z-axis (a) along the -z direction (b) along the +z direction.
Finally, in order to better illustrate the advantages of the proposed 3D-MA in this article. Table 1 shows the performance comparison between the proposed 3D-MA and the structure reported in the literature. It can be observed that most of the previous designs can only achieve single direction or single polarization symmetrical absorption due to the existence of metal backed ground. However, in this article, the proposed dual-polarization bidirectional 3D-MA achieves asymmetric broadband absorption along with transmission windows at low frequencies and high frequencies.
Table 1. Performance comparisons between the proposed 3D-MA and the references.
4. Conclusion
In this paper, a dual-polarized bidirectional 3D-MA with transmission windows is proposed. The 3D-MA is composed of a periodic array of hollow 3D lattices without metal backed ground. According to simulation and measurement, the proposed 3D-MA achieves asymmetric broadband absorption. Moreover, due to its hollow 3D lattice structure, it also has two additional transmission windows at low frequency and high frequency bands. In order to set forth its absorption mechanism, we studied the normalized equivalent impedance and surface current distribution of the 3D-MA. The virtual ground is produced when the wave is incident in different directions, and the incident EM waves are reflected. The design is insensitive to polarization and it still maintains good angular stability for oblique incidence up to 40°. The MA breaks the symmetrical transmission through delicate designed 3D unit cell. The asymmetric absorption feature greatly expands the function of MA by providing an additional absorption band for backward incident waves. The exotic characteristic is based on the coupling effect between layered meta-structures. This concept provides a new degree of freedom for the design of EM metamaterials which have a prosperous application future in the field of radar asymmetric recognition, detection, and stealth.
Funding
Fundamental Research Funds for the Central Universities (CCNU19TS073, CCNU20GF004); Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing, Guilin University of Electronic Technology (GXKL06190202); Open fund of China Ship Development and Design Centre (XM0120190196); National Natural Science Foundation of China (41974195).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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