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Abstract
In this paper, the physical model of electrically thin weakly conductive film with intrinsic surface impedance is established, indicating that the imaginary part of high surface impedance is non-negligible at microwave frequencies. In the design of lossy frequency selective surface absorbers, we introduce the imaginary part of intrinsic surface impedance for the first time. With the experimentally established relationship between the complex surface impedance and the DC square resistance, this complex surface impedance allows us to accurately predict the electromagnetic response of high surface impedance film at microwave frequencies and provides an advantage in reducing the thickness of absorber. The proposed ultra-thin absorber can provide −10 dB reduction over the frequency range of 4.5–13.3 GHz. Total thickness of microwave absorber is only 0.06λ at lowest operating frequency, which is close to the theoretical limitation. The measurement is provided to verify the validity of the equivalent relationship and the reliability of the full-wave model. This study provides a new way to reduce the thickness of absorber, exhibiting promising potential for stealth technique.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
With the development of stealth technology, light-weight [1], ultra-thin [2,3] and broadband [4,5] absorbers have been widely investigated. Frequency selective surface [6,7] based absorber is one of promising ways. In particular, lossy FSS composed of low-cost conductive ink [8] is very attractive due to its light weight and broadband property.
Surface impedance (ratio of surface tangential electric field and surface current density) is generally used to describe the intrinsic electrical properties of the conductive film that make up a lossy FSS [9–11]. In the early days, the most classic Salisbury screen [12] is a canvas coated with graphite placed in front of a quarter of a wavelength from the ground plane, which square resistance is 377 Ohm/sq. In order to further increase the bandwidth and reduce the thickness, Circuit Analog (CA) absorber have been extensively studied. CA layers are characteristically made of sheets that not only contain a resistive component but are reactive as well [13]. The reactive part is introduced in two main ways. One is to design the surface impedance of the lossy film from the intrinsic properties of the material; the other is to introduce the equivalent reactance from the perspective of the equivalent circuit by patterning the purely resistive film. Chambers theoretically analyzes a uniform layer exhibiting both resistive and capacitive properties [14]. Besides, he experimentally fabricates large area conducting polymer composites [15], and extracts the equivalent RC parallel circuit values from reflection coefficient [16]. Narayanan et al. utilize unidirectional carbon fiber sheets [17] in place of the resistive sheet utilized in the classic Salisbury screen and the surface impedance is highly dependent on incident polarization relative to fiber orientation [18]. Monti et al. modulate surface impedance of plasmonic nanoparticles by optimizing its size and eccentricity to achieve perfect optical absorption [19]. In the design of patterned lossy FSSs, researchers have conducted an in-depth study of equivalent circuits with different topologies and their equivalent impedance characteristics. Zadeh et al. equate the square patch resistive film to an RC series and propose a fast method for designing wideband absorber [20]. Costa [21] and Chen et al. [22] were studied for patterned resistive film and metal FSS loaded with lumped resistor, respectively. The geometrical patterning controls imaginary part of the equivalent circuits’ impedance and the conductive ink or lumped resistor controls the real part. In the above studies, the surface resistance of intrinsic electrical properties of the lossy FSS is characterized by square resistance measured using four-point probes method [23]. But weakly conductive films at microwave frequencies exhibit complex surface impedance characteristic [24]. From the published literature on surface impedance measurement of thin conductive films [25–27], it usually has significant imaginary part. However, the origin of this imaginary part is unclear. Besides, in most design of lossy FSS microwave absorbers, only the equivalent impedance of the equivalent circuit is analyzed without considering the effect of the imaginary part of the intrinsic surface impedance of the conductive film. This imaginary part will produce a great deviation in predicting the electromagnetic performance of the absorber.
In this paper, the physical mechanism of electrically thin high impedance film with intrinsic complex surface impedance at microwave frequencies is clarified. The relationship between the square resistance under DC conditions and the corresponding surface impedance at microwave frequencies is given experimentally, leading to more accurate prediction of absorber performance. Taking advantage of the imaginary part of intrinsic surface impedance, the thickness is further reduced by introducing a patch pattern, on which a double ring structure is introduced to expand the low-frequency absorption performance. The fully printed single-layer double-side ultra-thin absorber is proposeded. The −10 dB absorption bandwidth is from 4.5 GHz to 13.3 GHz and total thickness is 4.05 mm, which is close to the theoretical limit of lowest operating frequency thickness: $d \ge {{{\lambda _{\max }}} / {17.2}}$ [28].
2. Relationship between surface impedance and square resistance
As shown in Fig. 1(a), the half space of $z < 0$ and $z > d$ is the free-space with the parameter ${\varepsilon _1},{\mu _1}$. $0 < z < d$ is conductive medium 2 with the parameter ${\varepsilon _2},{\mu _2},{\sigma _2}$. The uniform plane wave is incident perpendicularly from the free-space 1 to the boundary of $z = 0$, assuming that the incident wave is a linearly polarized wave along the x direction. This is, the incident electric field and magnetic field in the free-space 1 are:
Fig. 1. (a) A model of uniform plane waves incident vertically into electrically-thin medium (b) The skin depth of medium when the relative permittivity is 1 and 200 respectively. When ${R_s} = 300\textrm{ Ohm/sq}$ and $d = 20\textrm{ }\mu \textrm{m}$ are fixed, ${Z_s}$ varies with ${\varepsilon _r}$ in the range of (c) 0.01–1 GHz and (d) 2–18 GHz. (e) ${Z_s}$ varies with ${R_s}$ when $d = 20\textrm{ }\mu \textrm{m}$ and ${\varepsilon _r} = 200$ are fixed. (f) ${Z_s}$ varies with d when ${R_s} = 300\textrm{ Ohm/sq}$ and ${\varepsilon _r} = 200$ are fixed in the range of 2–18 GHz.
The reflected wave electric field and magnetic field in free-space 1 are respectively:
Similarly, the synthetic electric and magnetic fields in medium 2 are respectively:
Before deriving the intrinsic surface impedance of medium 2, the skin depth of conductive medium is calculated first:
Assuming that ${\mu _2} = 1$ and ${\sigma _2} = 166S/m$, $\delta$ of the weak conductive medium with ${\varepsilon _2} = 1$ and ${\varepsilon _2} = 200$ in the range of 0.1–20 GHz is calculated in Fig. 1(b). The thickness of medium prepared by screen printing is about $20\; \mathrm{\mu}\textrm{m}$, far less than the skin depth. In this manuscript, the weakly conductive film with a certain thickness can be equivalent to a two-dimensional impedance sheet, which can be described by the intrinsic surface impedance:
The relationship between ${Z_s}$ and ${\varepsilon _2},{\sigma _2},d$ is obtained in Fig. 1(c)–1(f). When the DC square resistance ${R_s} = 300\textrm{ Ohm/sq}$ and thickness $d = 20\textrm{ }\mu \textrm{m}$ are fixed (conductivity $\sigma = 166S/m$), the intrinsic surface impedance ${Z_s}$ varies with the relative permittivity ${\varepsilon _r}$ at different frequencies [Figs. 1(c) and (d)]. In the range of 0.01–1 GHz with the change of relative permittivity ${\varepsilon _r}$, the real part of the surface impedance ${\textrm{Re}} ({Z_s})$ changes little around $300\textrm{ Ohm/sq}$ and the imaginary part ${\mathop{\rm Im}\nolimits} ({Z_s})$ is around $0\textrm{ Ohm/sq}$. However, ${Z_s}$ shows interesting and different characteristics at higher frequencies in 1–18 GHz as shown in Fig. 1(d). As ${\varepsilon _r}$ increases, ${\textrm{Re}} ({Z_s})$ becomes smaller and the absolute value of ${\mathop{\rm Im}\nolimits} ({Z_s})$ becomes larger. In the case of high frequency, $|{{\mathop{\rm Im}\nolimits} ({Z_s})} |$ of large ${\varepsilon _r}$ cannot be ignored. Keep ${\varepsilon _r} = 200$ constant and change the conductivity $\sigma = {1 / {({R_s}}} \cdot d)$, results are shown in Figs. 1(e) and 1(f). Assume that $d = 20\textrm{ }\mu \textrm{m}$ is unchanged, when ${R_s} < 100\textrm{ Ohm/sq}$, ${\textrm{Re}} ({Z_s})$ is almost equal to ${R_s}$, and ${\mathop{\rm Im}\nolimits} ({Z_s})$ can be negligible in 1–18 GHz. It is worth noting that when ${R_s} > 100\textrm{ Ohm/sq}$, ${\textrm{Re}} ({Z_s})$ is less than ${R_s}$, and the larger the ${R_s}$, the more ${\textrm{Re}} ({Z_s})$ decreases. The $|{{\mathop{\rm Im}\nolimits} ({Z_s})} |$ increases with increasing ${R_s}$ and tends to saturate at high frequencies. Figure 1(f) keeps ${\varepsilon _r} = 200$ and ${R_s} = 300\textrm{ Ohm/sq}$ constant, changes the thickness d of the conductive film. When d is on the order of micrometers, ${\textrm{Re}} ({Z_s})$ decreases with increasing d and $|{{\mathop{\rm Im}\nolimits} ({Z_s})} |$ is still obvious. When d is on the order of a few tenths of a micrometer (nanoscale), ${\textrm{Re}} ({Z_s})$ and ${R_s}$ are almost equal and $|{{\mathop{\rm Im}\nolimits} ({Z_s})} |$ is tiny and can be ignored.
It is obvious that ${Z_s}$ of electrically-thin weakly conductive film having a large ${\varepsilon _\textrm{r}}$ at high frequency (2–18 GHz) includes a non-negligible negative ${\mathop{\rm Im}\nolimits} ({Z_s})$.
Based on the investigation of intrinsic surface impedance, high surface impedance film with the same thickness but different ${R_s}$ are experimentally prepared by screen printing. Relationship between DC square resistance ${R_s}$ and surface impedance ${Z_s} = {R_{eff}} + j \cdot {X_{eff}}$ at microwave frequencies (2–18 GHz) is obtained by fitting the reflectivity. The real and imaginary parts of the equivalent surface impedance corresponding to its square resistance are shown in Fig. 2, and the relationship is given as follow:
Fig. 2. The relationship between the real part and the imaginary part of the equivalent impedance and square resistance.
The above relationship is of great significance for accurately predicting the performance of high-impedance film absorbers in the microwave band as shown in Fig. 3. The thickness of all absorbers is 7 mm. The square resistance ${R_s}$ obtained by the four-probe test and complex surface impedance ${Z_s}$ are given in Table 1. When the impedance of the simulation model is set to square resistance, it can be seen that as the resistance value changes, the absorption frequency point does not change, and only the absorption depth changes. The performance of the absorber cannot be accurately predicted. When the imaginary part of intrinsic surface impedance is taken into account, it can be seen that the simulation and measurement results are consistent. That is, the surface impedance of conductive film in the microwave frequency band cannot be expressed by the DC square resistance, but by the complex surface impedance.
Fig. 3. Simulation and measurement comparison of the absorber before and after the equivalent relationship is established(a) sample 1 (b) sample 2 (c) sample 3 (d) sample 4
Table 1. ${{R}_{s}}$ and ${{Z}_{s}}$ of four samples
3. Design of the complex equivalent surface impedance ultrathin absorber
High impedance film mentioned above has negative ${\mathop{\rm Im}\nolimits} ({Z_s})$ in microwave frequency band, which is helpful to reduce the thickness of the absorber, as shown in Fig. 4. The traditional Salisbury screen generates an absorption peak at 10 GHz when the thickness of the isolation layer is 7.5 mm. Using the equivalent impedance conditions mentioned above, when the intrinsic surface impedance is ${Z_s} = 168.08 - j187.78({\textrm{ohm}}/{\textrm{sq}})$, similar absorption performance can be achieved only in 3.3 mm. The introduction of patch pattern on the basis of a continuous impedance film can further reduce the thickness of the absorber while maintaining performance, as the blue line shown in Fig. 4.
Fig. 4. The performance of the classic Salisbury screen can be achieved at a thickness of 3 mm when ${Z_{eff}} = 168.08 - j187.78({\textrm{ohm}}/{\textrm{sq}})$. The further introduction of square patterning can further reduce the thickness to 2.8 mm
Based on the conclusion that the patch pattern complex impedance film can effectively reduce the thickness, we further broaden the absorption bandwidth by loading a double ring structure. In next section, a new type of fully-printed single-layer double-sided ultra-thin absorber is designed and manufactured.
3.1 Modeling and mechanism analysis
The structure of absorber is shown in Fig. 5. Figure 5(a) is the top view of the functional layer. The bottom of the layer is patch pattern composed of high surface impedance film, which is ${Z_2} = 168.08 - j182.78({\textrm{ohm}}/{\textrm{sq}})$. The top layer is composed of two square rings, and the metal part is composed of silver paste. Inner and outer rings each have four impedance films which has complex surface impedance characteristics in the microwave frequencies and the complex surface impedance is ${Z_1} = 116.08 - j128.78({\textrm{ohm}}/{\textrm{sq}})$. Structural parameters are marked in detail and given in Table 2. Figure 5(b) shows the overall structure of the absorber. The bottom layer of the absorber is a metal backplane. The honeycomb (${\varepsilon _r} = 1.07$) with thickness ${h_2}$ is placed in the middle, and the functional layer is placed at the top. The functional layer is printed on two sides of Polyimide with thickness ${h_1}$ by screen printing.
Fig. 5. (a) Top view of the functional layer. (b) Schematic diagram of a single-layered double-sided functional layer and the whole absorber.
Table 2. Optimized parameters of absorber
Performance of absorber and impedance analysis are shown in Fig. 6. When there is only an individual patch pattern functional layer, the absorber has a absorption band at 8–12 GHz. When there is only an individual double-ring, the absorber has absorption in lower frequency band. By adding a double-ring structure to the patch pattern, the bandwidth of the absorber is expanded without increasing the thickness, as shown in Fig. 6(a).
Fig. 6. (a) Reflectivity of absorbers under normal incidence (b) Smith chart (c) Conductance and (d) susceptance of freestanding patterned high impedance film.
Impedance matching theory is used to analyze the electromagnetic properties of the absorbers [29]. The reflection coefficient of the absorber is $\Gamma = \frac{{{Y_0} - {Y_{absorber}}}}{{{Y_0} + {Y_{absorber}}}}$, where ${Y_0}$ is the intrinsic admittance of free space, ${Y_{absorber}}$ is the equivalent admittance composed of a metal backplate, a honeycomb layer and functional absorbing layer. Our strategy is to make ${Y_{absorber}}$ equal to ${Y_0}$ in order to achieve low reflection performance. The admittance of the freestanding patterned high impedance film is given in Figs. 6(c), 6(d). As can be seen, the conductance of patch film remains constant at 2–18 GHz. And the susceptance is always positive, showing capacitive characteristics, to cancel the inductive transmission line ${Y_d}$ due to the thickness of the honeycomb layer in the range of about 8–13 GHz. So that the overall admittance of the single-layer patch film absorber satisfies the matching condition [shown by the purple line in Fig. 6(b)], resulting in good absorption performance in 8–13 GHz [shown by the purple line in Fig. 6(a)]. Similarly, susceptance of the freestanding double-ring structure cancels ${Y_d}$ in 4.3–8 GHz, producing impedance matching in this range and thus an absorption peak. When the two layers are connected in parallel, it can be seen that the real part of admittance is in the range of approximately 0.001–0.005, which meets the −10 dB impedance matching requirement. The imaginary part of admittance becomes larger at low frequencies (compared to that of freestanding patch high impedance film), making it possible to cancel ${Y_d}$ in 4.3–13 GHz. The overall absorber impedance is shown by the red line in Fig. 6(b), which is located within the −10 dB reflection circle in 4.3−13GHz, showing good absorption.
To better visualize the loss of electromagnetic energy, the distribution of the surface loss density at the three absorption frequencies is given in Fig. 7. At 4.8 GHz, the loss is mainly concentrated on the impedance film of the outer ring on the top of Polyimide. As the frequency increases to 5.4 GHz, the inner loop and the outer loop are coupled to each other and high impedance films on both rings are lossy to the incident electromagnetic waves. In the meantime, the loss on the patch impedance film on the bottom of Polyimide is small. When the frequency is further increased to 10.6 GHz, the patch impedance film cause the main loss to the electromagnetic waves.
Fig. 7. Surface loss density distribution of absorber at 4.8 GHz, 5.4 GHz and 10.6 GHz under normal incidence.
Oblique incidence performance of absorber at 0−60 degrees under horizontal and vertical polarization is also investigated in Figs. 8(a), 8(b). In the range of 0−30 degrees, the absorption can be maintained at about 90% under both polarizations. The absorption becomes weaker at large incident angles because of worse impedance matching, but it still has absorption because energy loss occurs on the lossy FSS. The abnormal jitter above 15 GHz is due to grating lobes.
3.2 Microwave measurement and discussion
Based on the design above, $500 \times 500 \times 4.05\textrm{ mm}$ electromagnetic absorber is fabricated. Three types of ink are printed on both sides of the flexible Polyimide by screen printing. By controlling the proportion of the ink to adjust its square resistance and equivalent surface impedance, a sample that meets the requirements is obtained. The reflectivity of absorber is measured by the NRL arch test method using a vector network analyzer (8720 ES, Agilent) connected to two broadband double-ridged horn antennas. The functional layer of absorber is shown in Figs. 9(a), 9(b). There are two obvious absorption peaks around 5.5 GHz and 11 GHz, which is consistent with the simulation result as shown in Fig. 9(c). The absorbing bandwidth of measurement is as same as the simulation while the jitter of the reflectivity at 15 GHz is due to the appearance of grating lobes. It can be seen from Fig. 9(d) that the thickness corresponding to the lowest operating frequency in this paper is very close to the theoretical limit given in [28] compared with the published literature. The performance of our design is compared with the published works and the results are presented in Table 3.
Fig. 9. (a)The front and (b) the back of the realized sample. (c) Comparison of measured reflection and simulation. (d) Comparison of absorber parameters in this paper with published literature
Table 3. Performance comparison of the previously reported absorber
4. Conclusion
In summary, the intrinsic surface impedance of weakly conductive thin films has a non-negligible negative imaginary part at microwave frequencies, which has a significant impact on microwave response. The high surface impedance film exhibiting complex surface impedance characteristic is prepared experimentally and the relationship between complex surface impedance at microwave frequencies and square resistance under DC condition is obtained to predict the microwave performance correctly. On this basis, a new type of ultra-thin absorber with −10 dB absorption bandwidth of 4.5–13.3 GHz and a thickness of 4.05 mm is designed and fabricated. The measurement is in good agreement with the simulation, which proves the rationality of fitted relationship. The introduction of the complex surface impedance might have open avenues in lossy FSS absorber design.
Funding
National Natural Science Foundation of China (62071196).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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