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Abstract
Traditional microwave absorbers usually use the epoxy resin dielectric board, which is neither flexible nor optically transparent, so cannot be used in certain applications. In this work, a flexible and optical-transparent broadband absorber is reported, which is based on the indium tin oxide (ITO) and polyethylene terephthalate (PET) material system with an ITO-PET-ITO structure. It showed more than 75% transmittance in the visible light range. The microwave absorption was above 0.8 from 19.9 GHz to 51.8 GHz. The absorption decreased when the absorber was bent, though the variation was not big. Further analysis pointed out that the absorption decrease could be attributed to the change of the incident angle. Theoretical simulation results agreed well with the measured absorption spectra.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Because of the high absorbance [1], broad absorbing band [2,3], and wide incident angle [4], metamaterial absorbers have important applications in radar stealth systems [5], electromagnetic (EM) screening [6], infrared detection [7], THz imaging [8], and other areas. However, the traditional epoxy resin board is rigid and non-transparent, which limits its applications in flexible electronics [3,9,10]. Flexible broadband absorbers based on different material systems have attracted more and more attentions in recent years [9–12]. For example, Jang et al. proposed a flexible microwave absorber from 5.8 GHz to 12.2 GHz, using aluminum on polyethylene terephthalate (PET) and polydimethylsiloxane (PDMS) substrates [11]; Singh et al. designed a single frequency flexible absorber at 77 GHz on top of the polyimide (PI) substrate [12].
With the help of indium-tin-oxide (ITO), a conducting oxide with good optical transparency, a flexible microwave broadband absorber based on the ITO-PET-ITO structure has been designed and tested. Through careful material selection and structure design, the absorber could achieve wide absorption bandwidth from 19.9 GHz to 51.8 GHz (absorption > 0.8), with a remarkable thickness of only 1.1 mm. What is more, the absorber is optically transparent in the whole area, instead of partially transparent when aluminum or other metals are used as the conducting material in the absorbers.
2. Methods
This paper proposes to use ITO as the conducting material and PET as the dielectric material to form the ITO-PET-ITO sandwich structure of the absorber. In this design, the top layer is an array of periodic ITO patterns, the middle layer is a PET dielectric film, and the bottom layer is a continuous ITO film as the ground. The absorption coefficient A(ω), as a function of the angular frequency ω, can be calculated from the S parameters:
where T(ω) is the transmission coefficient and R(ω) is the reflection coefficient.As can be seen from Eq. (1), the perfect absorption requires minimization of both the reflection and transmission. The reflection coefficient R(ω) can be calculated from Eq. (2):
Here Z(ω) is the impedance of the absorption structure given by Eq. (3), and Z0 is the characteristic impedance of the free space given by Eq. (4): where µ0 is the vacuum permeability, ɛ0 is the vacuum permittivity, µr is the relative permeability, and ɛr is the relative permittivity. Adjusting the geometric shape and size of the top periodic pattern can optimize the µr and ɛr so that the impedance Z(ω) equals to Z0, and thus the reflection R(ω) approaches 0 or gets minimized. On the other hand, because the bottom ITO ground layer has a good conductivity close to the perfect electric conductor (PEC), the transmission T(ω) is almost 0, or S21 = 0. So the absorption coefficient can be rewritten as:Details of the structure design is shown in Fig. 1. For clarity, only one unit of the periodic array is illustrated and pictured.
Fig. 1 Illustration of the structure unit: (a) the ITO-PET-ITO sandwich structure; (b) top view of the ITO pattern unit; (c) a microscope picture of one unit of the fabricated sample (the white part is ITO and the dark part is PET). Scale bar: 100 μm.
The optimized structure parameters were found as follows: D1 = 1000 μm, D2 = 2000 μm, W1 = 100 μm, W2 = 400 μm, P = 4000 μm. The thickness of the PET film was 1.1 mm, with the relative permittivity εr = 3. The thickness of the ITO film was 185 nm, with a surface resistance of 8 Ω/square. ADS software was used for the equivalent circuit and absorption spectrum simulation, and compared to the simulation result of HFSS software, as shown in Fig. 2. The two curves agreed reasonably well with each other. As can be seen from Fig. 2, the deep absorption band (absorption >0.8) ranged from 19.9 GHz to 51.8 GHz, with an ultra-broad bandwidth of 31.9 GHz. Within this band, the absorption between 21.0 GHz to 42.5 GHz reached 0.9 and above. There were three absorption peaks close to perfect absorption within this band, at 23.8 GHz (absorption = 0.99756), 36.8 GHz (absorption = 0.99084), and 50.2 GHz (absorption = 0.97928), respectively.
The normalized structure impedance Z can be calculated by Eq. (6) [11-12], and the results are illustrated in Fig. 3.
Because of the bottom ITO ground layer, |S21| always equals to 0. The three points where the absorption was close to 1 were labeled in Fig. 3, and it can be seen that at each of these three frequencies, the real part of the normalized impedance was close to 1 and the imaginary part was close to 0, i. e., the structure impedance Z matched very well with the free space impedance Z0. So almost perfect absorption could be achieved.
The polarization angle φ is an important parameter for the absorption characteristics. The polarization angle φ = 0 was defined as the direction parallel to one side of the rectangular open ring, as illustrated by Fig. 4(a). The absorption spectra at different polarization angles were simulated by HFSS at normal incidence, as shown in Fig. 4(b). As can be seen from Fig. 4(b), the variation of the polarization angle caused a decent drop of the absorption spectrum around 45 GHz, but was negligible at frequencies below 35 GHz or above 50 GHz. Due to the frequency limitation of our measurement system, the interested frequency range is below 40 GHz, where the variation caused by the polarization angle could be neglected.
Fig. 4 (a) Illustration of the polarization angle φ, where φ = 0 was defined as the direction parallel to one side of the rectangular open ring. (b) Absorption spectra at different polarization angles at normal incidence.
The incident angle is another important parameter that may impact the absorption characteristics. Here the normal incidence was defined as θ = 0, as illustrated by Fig. 5(a). The absorption spectra at different incident angles were simulated by HFSS and shown in Fig. 5(b). It can be seen that the incident angle can cause decent change of the absorption spectra. In general, the bigger the incident angle is, the lower the absorption spectrum would be.
Fig. 5 (a) Illustration of the incident angle definition, where normal incidence was defined as θ = 0; (b) The absorption spectra at different incident angles.
3. Results
A picture of the fabricated absorber sample is shown in Fig. 6(a), where the sample was placed on top of a printed logo of the School of Electronic and Optical Engineering at Nanjing University of Science and Technology, showing that the sample was transparent everywhere. As shown in Fig. 6(b), the average transmittance in the visible light range was about 75%. In principle the visible light transmittance of the ITO-PET-ITO film can reach 90% or so. But part of the PET film was burned off during the laser lithography procedure of the sample fabrication, which caused the decrease of light transmission.
Fig. 6 (a) The flexible absorber sample placed on top of a piece of white paper with printed logo. (b) The optical transmittance spectrum of the absorber sample.
The absorption measurement system and method were the same as described before [13,14]. A piece of copper foil was used as the PEC reference reflection plane for calibration [14], and the measured S11 spectrum was used as the reference signal of total reflection. The difference between the measured reflection signal from the sample and from the reference copper foil was calculated as the sample reflection S11 signal. The absorption can be calculated from the S11 values using Eq. (5). The measured absorption spectrum from 18 GHz to 40 GHz is shown in Fig. 7, agreeing pretty well with the HFSS simulation results. Possible error origins include the noise during testing as well as the sample fabrication error.
Fig. 7 The measured absorption spectrum of the absorber sample, agreeing well with the HFSS simulation results.
The 1.1 mm thick ITO-PET-ITO absorber sample has good flexibility, and can be easily bent, as shown in Fig. 8(a). The sample was bent along cylinders with different radii, and the absorption spectra were measured respectively. The results are shown in Fig. 8(b). Please note that each and every time the reference copper foil was also bent along the same cylinder to obtain the reference PEC reflection spectrum at this curvature radius.
Fig. 8 (a) The ITO-PET-ITO absorber sample can be easily bent. (b) The absorption spectra of the sample at different curvature radii: r = 6 cm, 12 cm, and ∞ (flat surface).
4. Discussion
The variation of the absorption spectra with the bending curvature probably can be attributed to the impact of the incident angle change. As described above, the absorption spectra were calculated from the measured reflection spectra by Eq. (1), and the reflection of the curved surface can be treated as the integration of the reflection from discrete parts of the surface, which correspond to different incident angles and thus different absorption spectra, as illustrated by Fig. 5. Details of the deduction are as follows:
where A(θ) is the absorption coefficient, Pr(θ) is the reflected power, and Pi(θ) is the incident power. For simplicity, the reflected power Pr(θ)) can be normalized to the incident power Pi(θ), and be calculated from S11(θ) given by the HFSS simulation. Assume infinitely long cylinder and take advantage of the axis symmetry, the incident angle calculation can be simplified to a 2D geometric question. The sample surface is simplified into a circle, which can be divided into a group of equal-length arcs, and each arc has a length L and corresponds to a central angle α, as illustrated in Fig. 9. As an approximation, we can assume that each arc corresponds to a unique and constant incident angle θ, thus the integration turns into a summation. Then the reflected power Pr(θ) and thus A(θ) can be calculated from Eq. (7). Thus the total reflected power from the ITO-PET-ITO sample and the reference copper foil at all incident angles can be calculated respectively, as shown below:The net total reflected power from the bent ITO-PET-ITO sample can be calculated by Eq. (9):And the total absorption of the bent sample can be calculated by Eq. (10):Note that Eq. (10) is valid for all frequencies, so the absorption spectra at different bending curvatures can be calculated accordingly.For comparison with the experiment data, the sample surface was virtually divided into seven arcs with different incident angles, as shown in Fig. 9. So we have ,,,,,,, and . The absorption spectra at each incident angle was obtained from HFSS simulation. Then the absorption spectra at different curvature radii can be calculated using Eq. (8)-Eq. (10). The calculation results were compared to the experiment data in Fig. 10, for r = 6 cm and r = 12 cm, respectively. It can be seen that the calculation results agree reasonably well with the experiment data, implying that the bending characteristics can be explained by the variation of the incident angle.
Fig. 10 Comparison of the simulation results and experiment data at different curvature radii r: (a) r = 6 cm, (b) r = 12 cm.
5. Conclusion
To summarize, an optically transparent flexible broadband microwave absorber was reported, which achieved 31.9 GHz wide deep-absorption (absorption >0.8) from 19.9 GHz to 51.8 GHz. The polarization angle did not impact the absorption much, yet the incident angle could cause decent absorption decrease. While bent, the absorption decreased, and the absorption bandwidth shrunk, which was attributed to the incident angle variation at different parts of the sample surface. Theoretical analysis agreed reasonably well with the experiment data. This transparent flexible broadband absorber can be useful in flexible stealth systems, microwave screening, and other applications.
Funding
National Natural Science Foundation of China (NSFC) (61627802); The Fundamental Research Funds for the Central Universities (30917012202); Aeronautical Science Foundation of China (2017ZF59005); Innovation Talent Program of Jiangsu Province.
Acknowledgments
The authors would like to thank Prof. Shilong Pan’s group from Nanjing University of Aeronautics and Astronautics for help in the microwave absorption measurement.
References and links
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