1. Introduction

The 5G mobile communication is rapidly developing at a faster-than-expected pace. Among all frequency bands of 5G mobile communication, the low-frequency band has been widely used in 2/3/4G mobile communications, and the high-frequency band in the millimeter range is still mainly under experimental exploration, so the mid-frequency band or the so-called sub-6G band, roughly in the (3-6) GHz range, is the most notable one of the 5G mobile communication. In November 2017, the Ministry of Industry and Information Technology (MIIT) of China formally announced that the (3,300-3,600) MHz and (4,800-5,000) MHz bands were assigned to the 5G mobile communication application. Also, most countries and regions have announced plans of commercial 5G operation by 2020 [1,2]. However, traditional design of absorbers such as Salisbury absorption screens and Jaumann absorber layers have certain drawbacks, including relatively large thickness (generally no less than 1/4 of the wavelength of the incident electromagnetic wave) [3] and narrow bandwidth [4–8]. These drawbacks have greatly hampered the practical use of microwave absorbers. So the design of ultra-thin and ultra-broadband absorbers has become an urgent need at present.

Metamaterial absorbers (MMAs) are considered to be a good choice for the design of ultra-thin, and ultra-broadband absorbers [9–13]. However, related researches are currently focused on high-frequency bands above 6 GHz. In 2014, T. Jang [14] printed a butterfly-shape pattern on the polydimethylsiloxane (PDMS) substrate with an aluminum wire mesh on the bottom as the ground layer to obtain a partially transparent broadband absorber in (5.8-12.2) GHz. In 2016, M. Grande [7] et al. used a graphene layer as the backplane and fabricated a transparent absorber in (8.3-11.2) GHz. In 2016, I.G. Lee et al. reported transparent absorbers with indium tin oxide (ITO) as the backplane in (9.6-13.9) GHz [15]. In 2018, our group reported a flexible and transparent absorber with only 1.1 mm thickness in (19.9-51.8) GHz using polyethylene terephthalate (PET) as the medium layer [16]. In general, these MMAs are above 6 GHz and do not match the mid-frequency band of the 5G mobile communication system, partly because of the fact that lower frequency leads to higher wavelength so the thickness of the absorbers can hardly be made thin enough for meaningful practical applications. At the same time, it is difficult to achieve both optical transparency and microwave absorption due to the limit of material properties [8,17,18]. Therefore, in-depth study of transparent MMA to cover the sub-6G band of the 5G mobile communication is imminent.

In this paper, sandwich-structure MMAs using PET and PET-PDMS-PET as the medium layer were designed and tested, respectively. Both samples were transparent in the visible light range and featured >80% broadband absorption suitable for applications in the sub-6G band of 5G mobile communication.

2. Methods and designs

According to the EM field theory, the absorption of the EM wave by the absorber can be expressed by Eq. (1):

Here $R\left(\omega \right)={\left|S_{11}\right|}^2$represents the reflectance and $T\left(\omega \right)={\left|S_{21}\right|}^2$represents the transmittance. $S_{11}$ and $S_{21}$ characterize the reflection and transmission coefficients of the electric field, respectively. Usually, a nearly perfect electrical conducting material will be used as the ground layer to guarantee zero transmission, so the transmittance $T\left(\omega \right)={\left|S_{21}\right|}^2=0$. Therefore, the absorption efficiency of the absorber can be written as Eq. (2):

Here $\left|S_{11}\right|=\left[Z\left(\omega \right)-Z_0\right]/\left[Z\left(\omega \right)+Z_0\right]$, Z(ω) is the equivalent impedance of the absorber, and $Z_0$ is the characteristic impedance of the free space. By optimizing the parameters of the cell structure to make $Z\left(\omega \right)=Z_0$, perfect absorption can be achieved with the reflection coefficient $S_{11}=0$.

In this paper, two optically transparent, flexible, and broadband microwave MMAs are demonstrated, with PET or PET-PDMS-PET as the medium layer, respectively. A conductor-dielectric-conductor sandwich structure as shown in Fig. 1 is used, which consists of three layers: the ITO resonant structure array as the top layer, the middle dielectric media layer (PET or PET-PDMS-PET) and the ITO ground backplane. It is worthy to point out that one important characteristic of ITO is that it should be treated as a good conductor with finite conductivity, substantially different from metals, which is usually treated as PEC, or perfect electric conductor. In the absorber design, the ITO layer introduces distributed resistance automatically, which is beneficial, yet lumped resistors must be used for metals wherever needed. Detailed discussion and comparison will be given in a following paper.

 

Fig. 1 Schematic of the structure of the broadband microwave MMA

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The microwave absorption spectra were simulated and optimized using the Ansoft High Frequency Structure Simulator (HFSS). The master-slave boundary conditions were set to simulate periodic structures. The “solution frequency”, or adaptive mesh division frequency in the simulation was set to 8 GHz. ITO was set as the impedance boundary.

The top resonant structure design is the key to the MMA performance. Many structures were simulated and optimized, and the final choice is shown in Fig. 1. One cell structure of the top resonant structure array is composed of two pairs of double rings with same width and gap size but different directions of gap opening. The optimized cell structure has a periodic size of p*2p, where p = 20 mm. The thickness of ITO on the top and the bottom layer was h = 185 ± 5 nm, with a sheet resistance of 8 Ω/square. The resonant structure was a 180° rotational-symmetric structure with the geometrical parameter as follows: the side length a = 16 mm, the spacing between double rings d = 1 mm, the width of a ring w = 1 mm, and the gap size e = 2 mm. The cell structure was periodically repeated, and the size of the final prepared MMA sample was (310*290) mm².

3. The PET-medium MMA

The PET-medium MMA was studied first. The optimized thickness of the PET layer was t = 6.25 mm, which is commercially available. The ITO layer was coated to the PET substrate by the well-known low temperature sputtering technology, and then went through a laser dry-etching process to obtain the designed pattern. In the experiments, two 1-18 GHz standard horn antennas were used for signal transmitting and receiving, which perpendicularly faced the absorber sample for normal incidence. The distance between the horn antennas and the absorber was kept greater than $2*D^2/\lambda$ to satisfy the far-field condition, where D is the maximum physical size of the absorber (310mm for our sample), λ is the operating wavelength. The reflection spectrum of the absorber was measured by the vector network analyzer (Agilent N5244A), then the absorption of the absorber was calculated accordingly, assuming zero transmission [19]. Mainly due to the high conductance of the bottom layer, simulation results showed that the transmittance of the MMA was <-50dB in the whole band, and the actual measured transmitted signal power was also below the measurement limit, so the zero transmission assumption is reasonable. The reflection spectrum of a reference copper plate was measured in advance for spatial normalization purpose [20]. Comparison between simulation results and experimental results is shown in Fig. 2(a). The simulation results show that the absorption of the absorber in (3.0-10.0) GHz is >80%. The experimental results were in agreement with it, actually a bit better, and the difference could come from sample fabrication errors as well as measurement errors. The cross-polarization effect was considered and calculated in the simulation results, which did not impact much though. Figure 2(b) shows a picture of the PET-medium absorber, which was placed on top of a piece of white paper printed with the university name and logo, showing excellent transparency in the visible light band.

 

Fig. 2 (a) Comparison of the simulation and experiment results of the MMA using PET as the medium layer. (b) Picture of the PET-medium MMA on top of a piece of paper printed with the university name and logo.

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From the simulation curve of the MMA using PET medium layer, it can be clearly seen that there are three absorption peaks, at 3.7 GHz, 6.5 GHz, and 9.0 GHz, respectively. Figure 3(a)-3(c) show the surface electric fields at the three peak frequencies, respectively; Fig. 3(d)-3(f) show the surface current density distribution profiles at the three peak frequencies, respectively. As we know, a perfect MMA can be realized with simultaneous electric and magnetic resonances [9]. It is observed in Fig. 3(a)-3(c) that electric fields are concentrated strongly in the gaps, the right-angled corners and the area between two rings. From the current density distribution shown in Fig. 3(d)-3(f), it can be seen that there were high current thus high magnetic field areas appeared especially near the gaps. The absorption peaks appeared at the frequencies where strong electric field resonance was formed at the top layer, and at the same time, strong magnetic field resonance was formed by the anti-parallel surface currents in the top and bottom layers. Therefore at these three frequencies, both electric and magnetic fields showed strong resonance, which led to high absorption of the electromagnetic energy.

 

Fig. 3 The surface electric field (a-c) and surface current density (d-f) distribution profiles at the three absorption peaks of the MMA using PET as the medium layer.

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4. The PDMS-medium MMA

The PET-medium MMA showed excellent microwave absorption and optical transparency. However, the Young's modulus of PET is still relatively large, about 3,000 MPa or even higher, and the bending radius of a 6 mm thick PET film is usually not less than 50 cm. To obtain better flexibility, we changed the major dielectric medium from PET to PDMS, whose Young's modulus is usually 0.5 MPa only. To make use of the mature ITO-PET coating technique, a relatively complex sandwich structure of ITO-PET-PDMS-PET-ITO was used in practice. Here, the PET film was 125 μm thick with ITO coated on it, and the PDMS layer was 6 mm thick, and all other parameters were the same with the PET-medium MMA. The PDMS layer was fabricated in the laboratory using the commercially available precursor (Sylgard184) from Dow Corning Company, which includes two ingredients. The two ingredients were mixed at 10:1 mass ratio at room temperature and stirred for 1 hour to ensure complete mixing. The mixture was slowly poured into a cuboid mould, and heated at 150°C for 10 minutes to obtain the PDMS film. The thickness of the film could be accurately controlled by carefully adjusting the volume of the mixture poured into the mould. Then two ITO-PET thin films were carefully stuck to the top and bottom surface of the PDMS film, to obtain the PDMS-medium MMA sample.

The simulation results considering the cross-polarization effect show that the absorption was >80% between 3.2 GHz and 11.0 GHz, with three absorption peaks, as shown in Fig. 4(a). The experiment results showed slightly wider absorption band than the simulation but was generally consistent with it. The bending radius of PET-PDMS-PET-medium MMA could easily reach ~2 cm, with even better optical transparency than the PET-medium MMA, as shown in Fig. 4(b). Figure 4(c)-4(h) show the simulated surface electric field and current density distribution profiles at the three peak frequencies (4.4 GHz/ 6.8 GHz/10 GHz) of the PET-PDMS-PET-medium MMA, respectively. Similar to the PET-medium MMA, strong electric fields also focus in the gaps, the right-angled corners and the area between two rings. Strong magnetic resonance is also observed from the surface current density distribution profiles shown in Fig. 4(f)-4(h).

 

Fig. 4 (a) Comparison of the simulation and experiment results of the MMA using PET-PDMS-PET as the medium layer. (b) Picture of the transparent PET-PDMS-PET-medium MMA bent by hand. (c-e) Surface electric field and (f-h) current density distribution profiles at the three absorption peaks of the MMA using PET-PDMS-PET as the medium layer.

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The absorption spectrum of the PET-PDMS-PET sample was measured at a bending radius of r = 10 cm, and compared to the no-bending measurement result, as shown in Fig. 5(a). It can be seen that in general the absorption will decrease when the absorber is bent. This can be explained by the absorption decrease at oblique incidence. As shown in Fig. 5(b), when the incident angle becomes larger, the absorption spectrum decreases quickly. When the absorber sample was bent, the incident angle changed from normal incidence to oblique incidence for most areas of the sample, so the total absorption would decrease.

 

Fig. 5 (a) The measured absorption curve (red) when the MMA sample was bent at a curvature radius of r = 10 cm, compared to the no-bending absorption curve (black). (b) Simulated absorption curves at different incident angles when the MMA sample is flat.

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Careful comparison of the simulation curves of the PET-medium MMA and the PET-PDMS-PET-medium MMA, as shown in Fig. 6(a), shows that the former features (3.0~10.0) GHz high absorption band, and the latter features (3.2~11.0) GHz high absorption band, so the PET-PDMS-PET design has slightly wider absorption. It is worthwhile to point out that the electric field intensity of the PET-PDMS-PET-medium MMA is one order of magnitude stronger than that of the PET-PDMS-PET-medium MMA, which could explain the reason why it has slightly higher absorption and broader bandwidth.

 

Fig. 6 (a) Comparison of the absorption spectra for the MMAs using PDMS and PET as the dielectric layer. (b) Comparison of the optical transmission spectra of the MMAs using PDMS and PET as the dielectric layer.

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The optical transmission spectra of two samples were also measured and compared, as shown in Fig. 6(b). As can be seen, both samples were transparent in the visible light range, yet the PDMS sample showed higher light transmittance than the PET sample.

Both MMAs can be used for the mid frequency band of 5G mobile communication, and both are optically transparent, yet PET-PDMS-PET features better flexibility. The flexible and transparent properties make it more versatile in shielding applications of Sub-6G Band of 5G Mobile Communication. For example, the absorber can be used to shield mobile phone signals in some specific situations.

To better compare the relative bandwidth as well as the relative thickness of broadband MMAs, the main results of some related work are listed in Table 1. The relative bandwidth in Table 1 is defined as the ratio of the highest frequency to the lowest frequency in the frequency band when the absorption is higher than 80% [8]; the relative thickness is defined as the ratio of the real thickness of the absorber to the wavelength corresponding to the lowest absorption frequency when the absorption rate is higher than 80% [8]. From Table 1, we can see that the MMA using PDMS medium has the largest relative bandwidth, but its relative thickness is a litter larger than the absorber using PET. With additional advantages of excellent flexibility and transparency, absorbers made in the paper have a wider range of practical applications.

Table 1. The relative bandwidth and the relative thickness of different microwave MMAs

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5. Conclusion

To summarize, we proposed and demonstrated a PET-medium MMA with an absorption bandwidth from 3.0 GHz to 10.0 GHz, and a PET-PDMS-PET-medium MMA with absorption bandwidth from 3.2 GHz to 11.0 GHz, both were 6.25 mm thick. The relative thickness of the absorbers were 0.0625 or 0.067 only. Simulation and experiment results complied with each other. The absorbers also show advantages of optically transparent and mechanically flexible. This result will echo the arrival of the 5G mobile communication and can have extensive practical applications.