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Abstract
The absorption region of a water-based absorber was expanded by introducing tetramethylurea (TMU) into the inclusion, whose dielectric properties are tunable through the concentration of TMU. The dielectric spectroscopy of a TMU/water mixture was deconstructed using a Debye model. We designed a four-layer ultra-broadband microwave absorber with a supernatant micro-structure. Simulation and experiment results indicate that the absorber can achieve 90% perfect absorption, covering a broad frequency range of 4–40 GHz. The concentration dependence of the absorber was also studied experimentally and numerically. The concentration control provides a more practical and large frequency-region modulation of perfect absorption.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetic meta-material absorbers (MAs) with an artificial periodic structure have attracted considerable attention for application in the optical [1,2], infrared [3,4], terahertz [5,6], and microwave [7–9] regions. Many new materials have recently been introduced into MAs to realize a broad-band absorption, such as graphene [10,11]. In addition, the potential application of MAs using frequency-dispersive liquids, such as water [12], ionic liquids [13], and ethanol [14], is outstanding owing to their flexibility and easy processing. Water has been viewed as a competitive frequency-dispersive absorber inclusion [15] because it has additional advantages in terms of rich raw materials, low cost, lack of pollution, and high dielectric loss within the microwave region [16,17]. The decrease in the real part with an increase in frequency and the prominence of the imaginary part of the permittivity within the radio frequency allow water to achieve a reduced reflection with an ambient dielectric or impedance matching. Moreover, owing to the apparent temperature-dependent permittivity [18] of water, the absorption frequency region of a water-based absorber can be modulated with temperature [19,20].
Ultra-broadband microwave absorbers (UBMAs) with a periodical water structure [14,21,22] and a water inclusion have been reported [23–25]. Xie and co-authors proposed a four-layer structure with water inclusions and a resonant resin circular ring, attaining over a 90% perfect absorptivity (PA) within 12 to 29.6 GHz [26]. Zhang and Yang achieved an optical transparent micro-wave absorption within 8.3 to 17.4 GHz and 6.4 to 23.7 GHz by employing water and indium tin oxide (ITO), respectively [27,28]. Although these designs can obtain ultra-broadband absorption, it is difficult to attain absorption with a central frequency band far from 20 GHz, which is the peak frequency of the intrinsic relaxation of water. Thus, to expand the absorption region of UBMAs, an effective way is to modulate the central frequency and bandwidth of the inclusion dielectric response.
The dielectric properties of water can be effectively modulated by adding solutes, such as ions [29,30], sugar [31,32], and organic compounds [33,34]. Tetramethylurea (TMU), an amphiphilic molecule compound, contains both hydrophobic methyl groups and hydrophilic ether groups [35]. The presence of TMU can modify the dielectric relaxation process of water because various hydration shells can form around the methyl and ether groups [36]. Compared with pure water, the real part of the permittivity of a TMU solution is lower and the imaginary part is higher within a low-frequency region, making a TMU/water mixture a good option for an absorber inclusion to obtain a PA band within the low microwave band.
In this study, we focused on the concentration-dependent dielectric properties of a TMU/water solution and designed a four-layer UMBA with TMU/water inclusions to expand the absorption region to a lower frequency based on the modulated dielectric properties. The PA of the four-layer UBMA with a pure TMU inclusion was verified both numerically and experimentally. The functions of each component were investigated numerically. The impact of the concentration on the UBMA absorption performance was also considered.
2. Measurements and design
The permittivity of TMU solutions of different molar concentration ratios ω = 0, 0.01, 0.05, 0.09, 0.18, and 0.36, and pure TMU (ω = ∞) (ω = [TMU]/[water]), were measured using a vector network analyzer (VNA, PNA-X Network Analyzer N5245B, Keysight Co., Ltd) with a coaxial cable (Rosenberger LA1-C140-1000) connected probe (85070E Dielectric Probe Kit) and an electronic calibration module at 25 °C. Using the measured dielectric relaxation spectrum of pure TMU, which has a low real part of the permittivity among the solutions, we designed a UBMA containing a pure TMU solution inclusion. The dimensions of the designed absorber are illustrated in Fig. 1, where h1, h2, h3, and h4 are the upper micro-structure, upper resin layer, middle inclusion, and substrate resin, respectively. The lowermost copper with a thickness of h = 0.015 mm is used to block incident transmissions. In addition, R indicates the radius of the middle resin cylinder resonance unit, a is the length of the upper-square micro-structure, and w is the lattice periods of the absorber in both the x and y directions. A reflection characteristic simulation of the designed absorber was conducted utilizing CST Microwave Studio. No transmittance occurs with the presence of a copper sheet, and thus the absorptivity of the designed absorber can be directly obtained from A = 1 - |r|2, where A and r are the absorptivity and reflectance, respectively.
Fig. 1 (a) Oblique view of decomposed ultra-broadband absorber structure and (b) a schematic diagram of unit cell.
To obtain the widest band at over 90% perfect absorptivity, an optimization of the structure geometrical parameters was achieved through a parametric sweep. The permittivity of the included pure TMU is shown in the blue circles in Figs. 2(a) and 2(b). A resin permittivity of 2.5 (1-i0.048) is the average result obtained from a vector network analysis using a coaxial method [37], and the electric conductivity of copper is 5.96 × 107 S/m. The optimal dimensional parameters obtained are h = 0.015 mm, h1 = 4 mm, h2 = 2.4 mm, h3 = 3.1 mm, h4 = 3 mm, R = 7.7 mm, a = 6.4 mm, and w = 18 mm. Based on these dimensional parameters, the resin part of the absorber with 17 × 17 unit cells was fabricated using 3D printing. To easily inject the solution, the integral 3D-printed structure includes two parts. One part is an upper resin with a micro-structure used as a lid, and the other is a substrate resin with a middle resin cylinder used as a container.
Fig. 2 The permittivity of a TMU/water mixture with different molar ratios of ω = 0, 0.01, 0.05, 0.09, 0.18, 0.36, ∞: (a) real and (b) imaginary parts. The decomposition of permittivity of a TMU solution with a molar concentration ratio of ω = 0.18: (c) real and (d) imaginary parts.
3. Results and analysis
Figures 2(a) and 2(b) show the concentration-dependent permittivity of a TMU/water solution measured using the VNA. With an increase in ω, the amplitude of the real part gradually decreases. The imaginary part decreases and shifts first to a low frequency of approximately 2 GHz at ω = 0.36, whereas with a further increase in the concentration, the peak of the imaginary part moves back to approximately 5.4 GHz at ω = ∞. The dielectric response of water can be described using a single Debye model within the microwave region [26]. However, for a TMU/water mixture with different concentrations, the permittivity of the frequency of interest is composed of two dielectric components and can be described through two Debye models [38,39]:
where Sslow and τslow are the relaxation strength and reorientation time of a slow component, respectively. This component includes TMU molecules and their tightly bonded hydrating water molecules. In addition, Sbulk and τbulk are the relaxation strength and reorientation time of bulk-like water molecules in the outer hydration shell of the TMU, which are less affected by the solute molecules, and ε∞ is the infinite dielectric constant of the mixtures. In a TMU solution, a slow component generally provides a high dielectric loss within a low-frequency region of approximately 0–10 GHz, and the component of the bulk-like water is mainly responsible for the high dielectric loss within a frequency region of approximately 20 GHz. For instance, the decomposition of a TMU solution with ω = 0.18 is plotted in Figs. 2(c) and 2(d). The obtained parameters in Eq. (1) are Sslow = 40.7, Sbulk = 4.8, τslow = 67 ps, and τbulk = 8.4 ps. The deconstructed spectra indicate that hydrating water has been slowed by approximately 8-fold owing to the steric hinderance effect as compared with bulk water. The hydrophobic groups in the TMU molecules retard the reorientation of water and slow the component, allowing it to become the main ingredient in the solution, offering a strong dielectric loss of approximately 2.4 GHz [38].To expand the PA frequency region of the UBMA, the dielectric properties of the inclusion were modulated by introducing a TMU solute, as described above. Figure 3(a) shows the simulated absorption of the optimal UBMA with a pure TMU solution. It is clear that the UBMA can achieve 90% PA within the frequency region of 4.3–40 GHz, as shown by the black solid line in Fig. 3(a). The absorptivity of the fabricated absorber was characterized through a free-space reflection measurement in a microwave anechoic chamber, where the absorber was placed horizontally during the measurement. Two linear polarized horn antennas connected with a VNA (Agilent N5224A) were used to transmit an electromagnetic wave and receive the reflected electromagnetic wave, respectively. Three types of horn antennas covering wide frequency regions of 1–18 GHz, 17.5–26.9 GHz, and 26.5–40 GHz, respectively, were used during the measurement. The reflection measurement was calibrated by replacing the absorber with an aluminum board of the same size. The measurement results are indicated by the red circles in Fig. 3(a). The experiment results show a good agreement with the simulation results, exhibiting an 85% absorptivity from 4.6 to 40 GHz at minimum. The small difference between the simulation and experiment results from 4.5 to 10 GHz may be caused by a process error and the small angle between the two horns applied during the experiment.
Fig. 3 Absorptivity spectra of TMU meta-material absorber: (a) comparison of the simulated and experimental absorption. The inset shows a photograph of a 3D printed absorber composed of a 17 × 17 unit cell with the designed dimensions: (b) simulated results of the absorber with the absence of the upper micro-structure, middle cylinder resonator, and inclusion of pure TMU, respectively.
To analyze the function of each component of the absorber, we numerically studied its absorptivity in the absence of a pure TMU inclusion, middle cylinder resonators, or upper micro-structures, respectively. As shown in Fig. 3(b), the absorptivity of the absorber without TMU is indicated by the magenta line. Compared with the black line in Fig. 3(a), a dramatic decrease in the absorptivity, particularly within the low-frequency region, can be observed, which proves that the absorption in this region is mainly caused by the TMU solution. In the absence of a middle cylinder resonator, a distinct absorptivity gap is observed, as shown by the green line. This observation indicates that the strong absorption within a frequency of 4.3–15 GHz, shown by the black line, is likely caused by resonance occurring around the middle cylinder. The absorptivity without an upper micro-structure, where a wave-like absorptivity of below 90% emerges, as shown by the blue line, indicates that the resonance of the upper micro-structures exists within the entire frequency region. The TMU solution has a leading function in the absorption, particularly within the low-frequency region, whereas the resonances of the middle cylinder resonator and upper micro-structure modify the auxiliary loss effects.
In the simulated absorptivity, as indicated by the black curve in Fig. 3(a), five clear absorption peaks can be observed at 4.4, 9.5, 21, 30.5, and 38.2 GHz, respectively, which implies the possibility of resonances occurring at these frequencies. Figure 4 shows intuitionistic three-dimensional views of the simulated power-loss density and electric field distribution at these frequencies in the designed TMU absorber. Among all observed frequencies in Figs. 4(a)–4(e), the maximum power loss density is located in the TMU solution, particularly at 4.4 and 9.5 GHz, which matches the deconstructed peaks in the imaginary part of the permittivity, unveiling a high dielectric loss corresponding to a high power loss. The clear resonance at 4.4 GHz can be attributed to the middle cylinder in Fig. 4(f), which agrees with the simulated absorptivity with the absence of a middle cylinder (presented by the green curve in Fig. 3(b) where a large gap at below 90% appears within the low-frequency region. As shown in Figs. 4(a)–4(j), with an increase in frequency, a more localized electric field and an increased power loss in the resin structure can be observed, which indicates that the resonances in the resin structure are more pronounced at high frequencies.
Fig. 4 Power loss density of designed TMU absorber in x, y, and z directions at (a1–a3) 4.4, (b1–b3) 9.5, (c1–c3) 21, (d1–d3) 30.5, and (e1–e3) 38.2 GHz, and electric field distribution at (f) 4.4, (g) 9.5, (h) 21, (i) 30.5, and (j) 38.2 GHz.
The concentration dependence of the absorptivity of a TMU/water-solution filled absorber was studied both experimentally and numerically. Figure 5 shows the experimental and numerical absorptivity of an absorber filled with TMU solutions of different molar concentrations (ω = 0, 0.01, 0.05, 0.09, 0.18, 0.36, ∞), the dielectric relaxations of which are plotted in Fig. 2. The disagreements between the experiment and simulation results within the frequency regions of 4.5–10 GHz and 15–20 GHz might be caused by the roughness of the 3D printed structure, where the TMU solutions cannot fill the container completely or equally. The simulated absorptivity presents pronounced concentration dependences on the TMU inclusion. First, the absorption within the frequency regions of 4–10 and 15–20 GHz increases with the TMU concentration. The absorbers with a highly concentrated TMU solution have a wider and more stable absorptivity (> 80%) band than a low concentration solution and pure water. Specially, with ω 0.09, the absorbers can achieve a relatively stable high absorptivity from approximately 4 to 40 GHz. This is mainly due to the following two reasons: First, the red shift of the dielectric relaxation peak (as shown in Fig. 2(b)) increases the absorption or loss at a low frequency. Second, the low real part of the permittivity (as shown in Fig. 2(a)), which is proportional to the refraction index, reduces the reflection between the solution inclusion and surrounding resin according to Fresnel’s law. Under the premise of 90% perfect absorption in the high-frequency band, increasing the absorption in the low-frequency band simply results in a broad absorption. Second, compared with a pure TMU, the absorption bands of a solution with ω 0.09 are slightly red-shifted, which corresponds to red-shifted dielectric spectra. In Fig. 2, the central frequencies of the relaxation peaks of solutions with ω = 0.18 and 0.36 are located at approximately 2 GHz, which is lower than the central frequency of 5.6 GHz in pure TMU. However, the absorber designed in this work cannot obtain perfect absorption at 2 GHz. There are two possible reasons for this. One reason is the high reflection between the resin and TMU, leading to a lower absorption at 2 GHz. The other reason is the intrinsic structural morphology limiting the absorption spectrum. However, with a different morphology design of the structure, even with water/TMU inclusions, the absorption spectrum within a frequency region of lower than 2 GHz can be highly improved.
Fig. 5 The absorptivity of the designed absorber filled with different molar concentration ratios of a TMU/water mixture of ω = 0, 0.01, 0.05, 0.09, 0.18, 0.36, and ∞: (a) simulation and (b) experiment results.
4. Conclusion
In conclusion, the dielectric properties of a TMU solution were analyzed to design a four-layer UBMA with a supernatant micro-structure. The simulation and experiment results show that an absorber with a pure TMU inclusion can achieve a 90% PA from 4.3 to 40 GHz. The major absorption is caused by a dielectric loss of a pure TMU layer, and the auxiliary absorption is from the resonance of the middle cylinder resonator and upper micro-structure. Our absorber with a high-concentration TMU solution has a weak concentration-dependent PA band at the studied concentrations. However, compared with a pure water inclusion, an absorber with TMU can effectively expand the lower-limit frequency of the PA. Interestingly, the absorption bands of the absorber with different concentrations are still close to the relaxation peaks. The absorber with a TMU solution offers a design strategy for an ultra-broadband microwave all-dielectric absorber by modulating the dielectric properties of the inclusion with a solute.
Funding
National Natural Science Foundation of China (NSFC) (61705163, 61605213, 61735012, and 61420106006).
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