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Abstract
We present a saline water-based absorber that can offer an extremely wide bandwidth of electromagnetic absorption in the microwave frequency regime. The designed absorber is a hybrid of saline water and Poly Tetra Fluoro Ethylene (PTFE) dielectric material, which exhibits an absorption level greater than 90% across the frequency band from 1.4 to 3.3 and 4.3 to 63 GHz, with a relative absorption bandwidth as high as 180%. Meanwhile, the sensitivity of the absorption against oblique incidence is studied for both TE and TM polarizations. Additionally, the absorption performance of this saline water-based absorber could be tunable by changing the salinity and the combination of different temperatures and salinity. To explain the mechanism, interference theory is employed to investigate the designed absorber, and the theoretically calculated results are well in agreement with the simulation. This design offers an effective and feasible way to construct tunable and ultra-broadband absorber in low-cost stealth technology.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past decades, electromagnetic absorbers have been widely investigated due to a vital role that they play in both civil and military applications. As one of the most concerned aspects, investigation on broadband absorption has always been the focus because of its great application. To broaden the bandwidth, various methods have been suggested. Presently, these methods can be divided into four categories. The first approach is to put all distinct narrow-band resonant frequencies together and combine them closely to form a super-unit coplanar structure [1–3]. However, some kinds of absorber unit cells would lead to inhomogeneous characteristics owing to the large cell sizes. Another method utilizes the different sections of a single structure that resonate at different frequencies to obtain multiple resonances [4,5]. The third scheme is to employ the stack of multiple layers of metal/insulator to broaden the absorption bandwidth [6–8]. The main problems with these absorbers are the devices involved very complex fabrication and realization. Therefore, it is difficult to integrate with commercial technologies and leads to a high cost. The last strategy is to insert a few of micron-sized lumped elements, such as chip resistors [9,10]. Nevertheless, these absorbers are also extremely difficult to scale up to a higher frequency such as the THz or infrared regimes.
Most of the former researches in the literature concentrated on the optimization of the subwavelength structure, and less attention is paid to the tunable absorbers. In recent years, ultra-broadband and tunable absorber are drawing considerable attention. Several methods have been reported to make absorber tunable. For example, in the microwave regime, frequency-tunable characteristics can be achieved by combining PIN diodes [11,12] or varactor diodes [13,14] into the absorber structure. However, these absorbers require a bias line and the cost of their devices is expensive. Meanwhile, the design and fabrication processes are still challenging for most researchers. In the THz regime, a tunable absorber based on micro-electro-mechanical systems (MEMS) technology has been designed [15,16]. Recently, new materials such as graphene have been used to realize tunable absorber [2,17,18]. Graphene-based absorbers can operate as tunable absorbers by changing the chemical potential or bias voltage. Despite these advantages of MEMS and graphene, the main limitation is that they are not suitable for low-frequency applications.
In the microwave regime, it would be very worthwhile to make absorbers with both tunable and ultra-broadband properties. In addition, the feasible way to achieve the material with perfect absorption via a low-cost fabrication technique for large-area structures has been long pursued. Saline water-substrate absorber can meet all these goals. Saltwater is one of the most abundant resources on earth. It is a cheap, bio-friendly, and easily deformed materials, which is a tremendous advantage over scarce and expensive materials such as barium strontium titanate [19]. The saline water has a frequency-dispersive permittivity in microwave frequencies and high transmittance characteristics [20], which can be seen as a promising candidate for designing broadband absorbers. Moreover, the permittivity of saline water can be controlled by temperature and salinity. Therefore, Saline water is an alternative substance for designing tunable absorbers. In recent years, researchers have used a dielectric layer and distilled water-substrate to achieve absorption [19,21–26]. Although a few kinds of literature about the pure water absorber with low profile have been reported [27,28], most of the literature report that the tunability of the water-based absorber is achieved by using temperature or wet [29,30] to regulate the absorbing performance. However, to the best of our knowledge, there is no literature reported saline water-based absorbers.
Motivated by the above concerns, this paper presents a saline water-based absorber in the microwave frequency range. By designing the substrate thickness and the geometry parameters, numerical results show that the broadband absorber presents an absorption level greater than 90% in the frequency range 1.4 to 3.3 and 4.3 to 63 GHz, with a relative absorption bandwidth of 180%. Additionally, the absorption performance can be tuned according to the salinity and the combination of different temperatures and salinity. We use interference theory to explore the absorption mechanisms in this absorber system and verify that the high absorption originates from the power loss and the destructive interference of the reflected waves. This design provides an effective way to construct tunable and broadband absorber with good and inexpensive products in stealth technology.
2. Permittivity and design of an absorber unit cell
2.1 Permittivity of saline water
The prominent property of saline water is that its dielectric permittivity can be described by an equation of Debye form [20]
According to Eq. (1), The dispersive dielectric permittivity of aqueous NaCl solutions at different salinity and temperatures is plotted in Fig. 1. As shown in Figs. 1(a) and 1(c), when the frequency increases from 0.1 to 100 GHz with a step of 20, it is obvious that the real part of the relative permittivity decreases gradually. While the value of the imaginary part decreases sharply, then increases lightly and decrease again, as shown in Figs. 1(b) and 1(d). The reason for this tendency is that, according to equation (a), the permittivity is inversely proportional to frequency when S or T is fixed at a certain value.
Fig. 1. Dielectric permittivity of aqueous NaCl solutions as the function of frequency using Debye formula. At the temperature T = 20℃. (a) Real (b) imaginary part; At the salinity in parts per thousand (PPT) S = 25. (c) Real (d) imaginary part.
We further studied the effect of the salinity S on the real part of the dielectric permittivity, while the frequency was fixed at a constant value. Referring to the dashed arrow in Fig. 1(a), it can be seen that the magnitude of dielectric permittivity is pushed down as S is increased. Conversely, increasing temperature pushes the real and imaginary parts of permittivity to a higher value (shown in Figs. 1(c) and 1(d)). However, according to Fig. 1(b), it can also be observed that the imaginary part of permittivity increases and then decreases slightly when S increases from 0 to 80. Similarly, according to Eqs. (1)–(7), it can be easily reduced that S is inversely proportional to the permittivity and T is proportional to the permittivity when T or S is fixed at a certain value in the high-frequency range.
Furthermore, from Fig. 1, we know that the imaginary part of the saline water provides a high value over the whole band, which indicates that the saline water-based absorber contributes to the highly effective absorption. Moreover, the real part of permittivity displays a downward trend and varies from about 80 to 10, which can provide an approach to design a saline water-based absorber with broadband absorption.
2.2 Design of an absorber unit cell
the schematic view of the proposed saline water-based absorber is shown in Fig. 2(a). The unit-cell is composed of a cylinder-shaped hole drilled in the Poly Tetra Fluoro Ethylene (PTFE) sheet backed by a copper ground plane. in the simulation, the dielectric sheet has a relative permittivity of 2.1 and loss tangent of 0.0002. On the top of the absorber unit cell, there exists a 1 mm thickness of the PTFE sheet, which is expected to prevent water from outflowing and to achieve the desired impedance matching over a broad frequency band. Figure 2(b) display the 3D view of the absorber unit, where the thickness of the substrate, saline water layer and the bottom copper layer are d, h and 0.017 mm, respectively. The upper and lower radii of the cone are r and R, respectively, and the lattice constant of each unit cell is l. Taking the water at T = 30℃ and S = 25 as an example. The optimized geometric parameters of this designed absorber are as follows (in millimeters): $r = 1.9$, $R = 7.45$, $h = 25$, $d = 26$, $l = 7.5$.
Fig. 2. (a) Schematic diagram of the saline water-based absorber structure and (b) perspective view of the unit cell.
Numerical simulation was performed using the commercial software CST Microwave Studio. In this simulation, unit cell boundaries are applied in the x and y directions and open boundary in the z-direction. In the simulation, the electric field of incidence is along the x-axis and propagates from the -z-direction normally incident on the absorber. The absorptive efficiency of this designed absorber can be calculated as $A(\omega )= 1 - R(\omega )- T(\omega )= 1 - {|{{S_{11}}} |^2} - {|{{S_{21}}} |^2}$, where $R(\omega )$ and $T(\omega )$ are the reflectance and transmittance as functions of frequency $\omega $, respectively. Owing to the copper sheet used as the backplane, the transmission coefficient is zero. Therefore, the absorption can be determined by $A(\omega )= 1 - {|{{S_{11}}} |^2}$ in this paper.
3. Simulation results and discussion
3.1 Results and analysis
Simulated reflection and absorption characteristics of the saline water-based absorber are shown in Fig. 3(a). Within the frequency range from 1.4 to 3.3 GHz and 4.3 to 63 GHz, it can be seen that the proposed absorber can achieve ultra-broadband microwave absorption with the efficiency equal or more than 90%, and the relative bandwidth can reach as high as 180%. Meanwhile, in the operating band, there are numerous peak values can be found. Moreover, since the absorption of energy is a result of power dissipation, we calculated the volume loss of the component in the proposed water-based absorber, as shown in Fig. 3(b). For a nonmagnetic dispersive medium, the time-averaged power loss density is defined by [31]: ${{d{P_{loss}}} \mathord{\left/ {\vphantom {{d{P_{loss}}} {dV = {1 \mathord{\left/ {\vphantom {1 {2{\varepsilon_0}\omega \textrm{Im}\varepsilon (\omega )}}}\right.} {2{\varepsilon_0}\omega \textrm{Im}\varepsilon (\omega )}}}}} \right.} {dV = {1 \mathord{\left/ {\vphantom {1 {2{\varepsilon_0}\omega \textrm{Im}\varepsilon (\omega )}}} \right.} {2{\varepsilon _0}\omega \textrm{Im}\varepsilon (\omega )}}}}{|E |^2}$, where ɛ0 denotes the permittivity of vacuum, ω is the angular frequency, Im(ɛ) denotes the imaginary part of relative permittivity and E is the electric field. This equation shows that a material with a large extinction coefficient (Im(ɛ)) and a strong electric intensity enhancement will result in the enhancement of absorption in this absorber. From Fig. 3(b), it is obvious that compared with PTFE, the water in the middle layer contributes to the major power loss in the entire band range considered. However, from this figure, it can be seen that water is not the only power loss source. Since the incident wave is not entirely converted into heat inside the absorber. Although the trend of the electromagnetic power loss is increasing, the PTFE substrate used here has little effect on the region of the power loss spectra, which can be ignored. Therefore, it should explore the other mechanism to explain the rest electromagnetic power dissipation. We will explore it in the next section.
Fig. 3. (a) The reflection and absorption spectra of the proposed absorber, (b) the power loss of the constitutive components in the absorber.
To qualitatively understand the physical mechanism and more clearly show the degree of electromagnetic energy dissipation behind the ultra-band absorption, the power loss density distributions inside the saline water absorber are numerically investigated for $f = 1.73,\; 30.613\; $and $50.279\ $GHz, as shown in Fig. 4. It is clear that the power loss distributions of this absorber are distributed at a different part for different frequencies. Figure 4(a) displays the distribution at the low-frequency f = 1.73 GHz. We can find that the power loss density distribution is mainly concentrating on the bottom side of the proposed absorber. As the frequency increases, the distribution moves to the top side of the cone (seen in Figs. 4(b) and 4(c)). Meanwhile, it is also seen that, in all cases, the power loss densities completely concentrate in the cone made of water, which is due to saline water itself has high absorption at microwave frequencies and the loss tangent of the parcel layer PTFE is too small.
Fig. 4. The distributions of power loss in xoz plane at different resonance frequencies: (a) 1.73 GHz, (b) 30.613 GHz and (c) 50.279 GHz, respectively.
For a perfect absorber, angular performance is an important criterion to the electromagnetic absorbers. To study the influence of the incident angle on the absorption performance, we simulated the electromagnetic waves oblique incident to the saline water-based absorber with transverse electric (TE) and transverse magnetic (TM) polarization, respectively. Figure 5 shows the calculated absorption spectra as a function of both frequency and incident angle $\theta \; $under TE and TM polarizations, where TE polarization corresponds to E parallel to the x-axis and TM polarization corresponds to the y-axis. As shown in Fig. 5(a), the absorption remains almost unchanged until the incident angle reaches 60° for the TE polarization. For the TM incident wave as presented in Fig. 5(b), the absorbing properties are almost unchanged for all of the incident angles. It means that our ultra-broadband electromagnetic wave absorber can work well over a large range of incident angles for both TE and TM polarizations.
Fig. 5. Calculated absorption spectra under different incidence angles $\theta$ for (a) TE and (b) TM polarization.
3.2 Salinity and temperature tunability
According to Eq. (1), we know that the permittivity of saline water is highly dependent on salinity and temperature. As for an absorber transferring EM energy to thermal energy, the salinity and temperature of the saline water may be changed as the ambient temperature changes during the process of application. Therefore, the absorption under different salinities and temperatures should be investigated. In general, the changes of salinity S in the range from 0 to 260 PPT and temperature T from 0 to 100 °C have a negligible effect on the absorption. Here, we first consider the change of one of the two factors and the other remains the same. Figure 6(a) presents the reflection dependence of salinity for the proposed saline water-substrate absorber optimized at T = 30℃. With the increase of the salinity from 0 to 100 PPT, not only the reflection peaks will be gradually shifted, but the reflection bandwidth will also be changed accordingly in the low-frequency band. However, in the high-frequency band, salinity has a very small effect on the reflection coefficient, which is not displayed in this figure for the sake of clarity in the range of 1 to 20 GHz. In Fig. 6(a), it is clearly shown that there is a significant difference between the performance of the absorber using pure water and saline water in the range of 1 to 6 GHz. The reason is that in the low-frequency region, the difference between the curves of the dielectric permittivity is obvious (shown in Fig. 1(a)), which leads to a noticeable change in the impedance of the water layer. Therefore, one can say that the ultra-broadband absorption of this absorber can be adjusted by the salinity.
Fig. 6. Reflection spectra of the absorber at different (a) salinities, (b) temperatures and (c) salinities and temperatures, respectively.
Meanwhile, the reflectivity spectra of this absorber under different environmental temperatures with salinity S = 25 PPT were simulated and shown in Fig. 6(b). It can be seen that the change in the reflectivity with the variation in temperature from 0 to 40℃ is quite small over the entire band of interest. As the inserts shown in Fig. 6(b), with increasing temperature, the absorptivity decreases slightly in the higher frequency band but remains lower than -9 dB over the operating band. Moreover, it worthy to study the comprehensive factors of salinity and temperature on the reflection of the absorber to evaluate the tunability. The reflection of the absorber with different combinations was simulated and the corresponding results are sketched in Fig. 6(c). Since the difference between the curves is not obvious in the high-frequency range, we only plot the reflection curves in the range of 1-20 GHz. Compared with Fig. 6(a), we can find that the reflection peak positions for TE polarization exhibit a different movement trend when the frequency is higher than 5 GHz. Although this absorber is very weakly dependent on the working temperature, based on the above analysis, we have a reason to believe that the performance of our water-based absorber can be tunable by salinity and temperature.
4. Interference theoretical explain
To get more insight into the absorption mechanism of this saline water-based absorber, interference theory was employed to analyze the mechanism of the broadband absorption behavior. Multiple reflections between the air-spacer interface and ground plane are illustrated in Fig. 7. At the interface between the air and PTFE substrate, the incident wave is partially reflected in the air and partially transmitted into the substrate, with the reflection and transmission coefficients are ${\tilde{r}_{12}} = {r_{12}}{e^{i{\emptyset _{12}}}}$, and ${\tilde{t}_{12}} = {t_{12}}{e^{i{\theta _{12}}}}$, respectively. The transmitted wave continues to propagate until the metal ground plane and the complex propagation phase is $\tilde{\beta } = {\beta _r} + i{\beta _i} = \sqrt {{{\tilde{\varepsilon }}_{substrate}}} {k_0}d$. Where ${\beta _r}$ is the propagation phase, ${\beta _i}$ and k0 represent the absorption in the substrate and free-space wavenumber in free space, respectively. After many reflections and refractions, the overall reflection coefficient can be obtained by [32]
Where ${\tilde{r}_{21}} = {r_{21}}{e^{i{\emptyset _{21}}}}$ and ${\tilde{t}_{21}} = {t_{21}}{e^{i{\theta _{21}}}}$ represent the reflection coefficient and transmission coefficient at the substrate-air interface. Since the transmission coefficient is zero, the absorptivity can be calculated by $A = 1 - {|{\tilde{r}(\omega )} |^2}$.
Based on the decoupling model of s this absorber, the magnitude and phase coefficients of reflected and transmitted wave at interfaces are simulated and plotted in Fig. 8. As the volume model of the de-coupling model increases with the increase of frequency, the calculation time and the computer memory required also increase sharply. Here, we only calculated the case of 1-10 GHz. The results of the theoretical calculation and simulation at the normal incident direction are presented in Fig. 9. It can be seen that the two are basically aligned with each other, and the smaller difference is due to the data point deviation of the metal ground layer and simulation. Thus, the numerical simulation results are reliable.
Fig. 8. (a) Amplitude and (b) phase of the reflection and transmission coefficients at the air-substrate interface, obtained by numerical simulations using the model shown in Fig. 7.
Fig. 9. Comparison of absorption spectra of theory and simulated results at the normal incident direction.
Therefore, the mechanism of the total electromagnetic wave dissipation can be explained by the above analysis. The main cause of high absorption in this kind of structure is the absorption and interference. The incident energy flow entered the absorber splits into two parts: The saline water absorbs some electromagnetic waves and the others offset by the incident and reflected waves. Although the saline water does not completely absorb all the electromagnetic energy, it is known that it changes the phase of the reflected waves according to the effective medium theory. Meanwhile, saline water reduces the amplitude of the reflected waves.
5. Conclusions
In summary, we propose a design to realize a tunable and ultra-broadband absorber based on the interference theories. The interference mechanism is demonstrated by analytical derivation and numerical calculation. From the simulated and theoretical results, we can find that the absorption bandwidth can reach 60.6 GHz, with the relative absorption bandwidth of 180%. Furthermore, the ultra-broadband absorption can achieve a high value of more than 90% at wide incidence angles for both TE and TM polarizations. Besides, the absorption performance can be tuned by salinity and the combination of different temperatures and salinity. The excellent performance of this absorber is attributed to the dispersion characteristic of saline water. The proposed saline water-based absorber is inexpensive, which may have extensive applications in the field of low-cost chambers and stealth technology. Moreover, this profound understanding of the underlying physical mechanism may provide helpful guidance for designing the more advanced absorber. Of course, there exists a limitation for this proposed absorber. The volume is a little bit large. In practice, however, the size of the cell can be reduced by changing the shape of the absorber.
Funding
Fundamental Research Funds for the Central Universities (2019CDQYTX033); National Natural Science Foundation of China (61501067).
Disclosures
The authors declare no conflicts of interest.
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