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Abstract
Half-wave wall is the most common method of achieving electromagnetic (EM) transparency. Transmission windows can be formed when reflected waves are out of phase. Due to the interference mechanism, these windows are dependent on the frequency and incident angle of EM waves, leading to limited bandwidth, especially under extreme angles. In this letter, we propose to extend the bandwidth of the transmission window under extreme angles by utilizing dispersion. To this end, long metallic wires are embedded into the half-wave wall matrix, without increasing the physical thickness. Due to the plasma-like behavior of metallic wires under TE-polarization, the effective permittivity of the half-wave wall, rather than keeping constant, increases with frequency nonlinearly. Such a dispersion will boost wideband transparency in two aspects. On one hand, an additional transmission window will be generated where the effective permittivity equals that of the air; on the other hand, the 1st- and 2nd-order half-wave windows will be made quite closer. By tailoring the dispersion, the three windows can be merged to enable wideband transparency under extreme incident angles. A proof-of-principle prototype was designed, fabricated, and measured to verify this strategy. Both simulated and measured results show that the prototype can operate in the whole Ku-band under incident angle [70°, 85°] for TE-polarized waves. This work provides an effective method of achieving wideband EM transparency under extreme angles and may find applications in radar, communications, and others.
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1. Introduction
The half-wave wall is the most common method of achieving EM transparency. Its basic principle is to enhance the transmission by using destructive interference between reflected waves based on the law of conservation of energy. Generally windowing, transmission windows can be formed when reflected waves are out of phase [1–4]. However, due to the restriction of the interference mechanism, these transparency windows are dependent on frequency and incident angles, leading to limited bandwidth, especially under extreme angles. However, in practical applications, the incident angle of EM waves is often extreme, which limits the practical application performance of half-wave walls. However, at large incident angles, taking ceramic-matrix composite (CMC) materials as an example, as shown in Fig. 1(a), due to the presence of Brewster Angle, the impedance mismatch between dielectric and air under TM polarization is not serious, making the EM transmission still high [5–7]. However, under TE polarization, impedance matching becomes more and more serious with the increase of angle, especially at extreme angles, due to the absence of Brewster Angle. Therefore, it is of great significance to extend the transparency bandwidth of the half-wave wall under extreme incident angles for TE polarization waves.
Fig. 1. (a) TE- and TM- polarized wave impedance of air and dielectric under different incident angles (b) The schematic illustration of reflection/refraction when EM waves impinge upon the dielectric plate. ${\varepsilon _0}$ and $\,{\mu _0}$ represent the permittivity and permeability of air, ${\varepsilon _1}$ and ${\mu _1}$ represent the relative permittivity and permeability of dielectric, ${\theta _i}$ and $\,{\theta _t}$ represent the incident and transmission angle.
Metamaterials are artificial materials composed of sub-wavelength structures that possess properties not found in natural materials and can provide unprecedented degrees of freedom in adjusting EM parameters and controlling EM waves [8–15]. In recent years, the potential of metamaterials in various fields has been further discovered and explored. Ruichao Zhu proposed the concept of remotely mind-controlled metasurface (RMCM) via brainwaves [16]. Lianlin Li explored wave-based computing by using intelligent metasurfaces, focusing on the emerging research direction in intelligent sensing [17]. Jianghao Xiong gave a comprehensive review of the operation principles, device fabrication, and performance of these optical elements [18].
In recent years, with the growing need for EM transparency, metamaterials have attracted considerable attention for their potential uses in EM antireflection field. Fengyuan Yang used a cascaded metasurface to achieve EM transparency in 2.35-2.45 GHz [19]. Yongzhi Li achieved wide-angle transmission enhancement of fiber-reinforced polymers based on the plasma-like effect of long metallic wires [20,21]. And Yuchu He designed a thin double-mesh metamaterial radome that has high transmission at millimeter-wave frequencies [22].
Inspired by the above works, as shown in Fig. 2, in this letter, we propose to extend the transparency window of the half-wave wall under extreme angles by utilizing dispersion. To this end, long metallic wires are embedded in the middle of the dielectric plate, but the physical thickness of the plate isn’t changed due to the small thickness of the wires. Because of the plasma-like effect of long metallic wires under TE-polarization, the effective permittivity of the dielectric, rather than keeping constant, grows from less than 0 to the original value with frequency nonlinearly. Such a peculiar dispersion will boost wideband transparency in two aspects. On one hand, an additional transmission window will be generated at the low-frequency end of the half-wave wall where the effective permittivity of the substrate equals that of air; on the other hand, the 1st- and 2nd-order half-wave windows will be made quite closer. By optimizing the structure of the metasurface, the three windows can be merged to enable wideband transparency under extreme incident angles. In order to make our scheme closer to practical application, we choose the ceramic-matrix composite materials (with a relative permittivity of ${\varepsilon _{1}}$=3.3 and a permeability of ${\mu _1}$=1.0) commonly used to make radome to make the substrate [23–26].
Fig. 2. TE-polarized waves incident to the metallic wire-embedded CMC substrate under extreme angles. The thickness of the substrate $d = 11.6\textrm{mm}$, the width of the metallic wires $w = 1.3\textrm{mm}$, the distance between the upper and lower wires $h = 5.8\textrm{mm}$, $\textrm{px} = 5.5\textrm{mm}$ and $\textrm{py}$ represent the transverse and longitudinal periodicity of the unit cell, the thickness of metallic wires is $0.017\textrm{mm}$.
A series of proof-of-principle prototypes were designed, fabricated, and measured to verify this strategy. Both simulated and measured results show that the prototype can operate in the whole Ku-band under incident angle [70°, 85°] for TE-polarized waves. This work provides an effective method of achieving wideband EM transparency under extreme angles and may find applications in radar, communications, and others.
2. Theory and design
As shown in Fig. 1(b), according to Snell Law [27], when EM waves incident on the empty substrate the optical path difference of reflected waves from interface 1 and interface 2 can be expressed by Eq.(1). $\mathrm{\Delta }$ represents the total optical path difference between the reflected waves and ${\Delta _0}$ represents the optical path difference without half-wave loss, ${n_1}$=$\sqrt {{\varepsilon _1}{\mu _1}} $ and ${n_0}$=1 represent the refractive index of substrate and air, $d$=11.6 mm and ${d_e} = d{n_1}$ represents the physical and electrical thickness of the substrate.
From Eq. (1), when the optical path difference between reflected waves is exactly odd times of half-wavelengths, destructive interference occurs. According to the energy conservation law, transmission waves will be enhanced when the reflected waves are canceled. This phenomenon is called the half-wave wall, and k represents the order of the half-wave wall.
Obviously, when the thickness of the substrate is constant, the half-wave wall is dependent on the frequency and incident angle, leading to limited bandwidth, especially under extreme angles. However, as shown in Eq. (1), On the premise of not changing the physical thickness of the substrate, we can change the relationship between the half-wave wall and the frequency by tailoring the dispersion so as to boost the wideband EM transparency. Therefore, as shown in Fig. 2, metallic wires with the plasma-like effect are embedded into the CMC substrate.
As shown in Fig. 3(a) and (b), we conduct simulations in CST microwave studio, obtain the TE-polarization transmission spectra of the empty and metallic wire-embedded substrates with changed px or w in X and Ku band under the incident angle of 80°. The other structural parameters of the unit cell are consistent with those in Fig. 2. Firstly, we can clearly see there are two transmission windows in the spectra of the empty substrate, which are two half-wave walls of different orders, and their frequencies are defined as ${f_2}$ and ${f_3}$ from low to high.
Fig. 3. (a) and (b) The TE-polarization transmission spectra of empty and metallic wire-embedded substrate with changed px and w under the incident angle of 80°. (c) The overall equivalent permittivity of substrate varies with the frequency of EM waves. (d) The surface currents on metallic wires, ${f_1}$, ${f_2}$ and ${f_3}$ from left to right.
However, after loading the long metallic wires, ${f_3}$ stays basically unchanged while ${f_2}$ moves to the high-frequency end of the spectrum. At the same time, an additional transmission window is generated at the low-frequency end of the two half-wave walls, and its frequency is defined as ${f_1}$.
First, we analyze the transmission spectrum of the empty substrate, when the electromagnetic wave is incident at an angle of 80°:
${\lambda _1} \approx $ 35.3 mm and ${\lambda _2} \approx $ 17.65 mm represent the wavelength of EM wave at 8.5 GHz and 17.0 GHz respectively, as shown in Eq. (2), at this time, the 1st- (k = 1) and 2nd- (k = 2) order half-wave walls are excited and two transmission windows are opened at 8.5 GHz (${f_2}$) and 17.0 GHz (${f_3}$). But the two transmission windows are far apart in the transmission spectrum, as shown in Fig. 3(a), respectively.
However, as shown in Fig. 3(c), as for the metallic wire-embedded substrate, when the TE-polarized waves (the direction of the electric field is always parallel to the y-axis) incident on it, due to the plasma-like effect, the overall relative permittivity of the substrate will grow from less than 0 to the original value (3.3) with the frequency of EM waves nonlinearly [20,21]. And ${\omega _p}$ is expressed by Eq. (3), which represents the point at which the relative permittivity is exactly 0, also known as plasma frequency. Equation (3) is derived from the plasma-like model of long metallic wires in Ref. [21], where a represents the interval between long metal wires, r represents the radius of metal wires, and ${c_0}$ represents the speed of light in vacuum [20,21]. Therefore, the dispersion of the substrate is tailored.
Then we analyze its transmission spectrum, after knowing the dispersion characteristics of the wire-embedded substrate. Where, the transmission window ${f_2}$ in Fig. 3(a) corresponds to ${\omega _2}$ in (c) was originally the 1st-order half-wave wall of the empty substrate. As shown in Eq. (1), at this time, due to the plasma-like effect the overall relative permittivity of the substrate ${\varepsilon _1}$ was reduced and the dispersion of the substrate is tailored, although the physical thickness of the substrate remains the same its electrical thickness ${d_e}$ is reduced and $\mathrm{\Delta }$ was shortened. Take the curve px =5.5 in Fig. 3(a) as an example, under the plasma-like effect ${\varepsilon _1}$ decreases from 3.3 to about 2.1, and ${\Delta _0}$ is reduced to about 24.6 mm which is equal to the wavelength at 12.2 GHz. So the frequency of the 1st-order half-wave wall changes from 8.5 GHz to 12.2 GHz, which is closer to the 2nd-order half-wave wall than before.
And the transmission window ${f_3}$ in Fig. 3(a) corresponding to ${\omega _3}$ in Fig. 3(c), the window was originally the 2nd-order half-wave wall of the empty substrate. Because the plasma-like effect becomes weaker with increasing frequency, even embedded with long metallic wires the overall permittivity of the substrate is basically the same as that of the empty substrate, and the dispersion of the substrate is almost not tailored at ${f_3}$. This makes the optical path difference $\mathrm{\Delta }$ almost unchanged so the frequency of 2nd-order half-wave wall almost not have changed.
${f_1}$ in Fig. 3(a) corresponds to ${\omega _1}$ in Fig. 3(c), due to the low frequency the plasma-like effect is strong, the overall relative permittivity of the substrate is reduced to exactly 1 and the dispersion of the substrate is tailored greatly. As shown in Eq. (4) and Fig. 1(b), ${\Gamma _1}$ and ${\Gamma _2}$ represent reflectivity at interface 1 and 2 respectively, a good impedance matching is formed between the substrate and the air, and the transmission is enhanced [21].
In order to prove the above analysis, we individually change one of $px$ and w respectively and keep the other structural parameters unchanged to observe the change of the transmission spectra of the metallic-wire embedded substrate in CST. From Fig. 3(a) and (b), we can see that when we change $px$ or w, ${f_1}$, ${f_2}$ and ${f_3}$ show a changed pattern consistent with the plasma frequency expressed in Eq. (3): when $px$ is increased and $\textrm{w}$ is decreased, ${\omega _p}$ is decreased, so ${f_1}$ and ${f_2}$ move to low frequency while ${f_3}$ is almost not affected by the change of plasma frequency due to its high frequency.
To further substantiate our analysis, surface currents on metallic wires were monitored in CST at ${f_1}$, ${f_2}$ and ${f_3}$. As shown in Fig. 3(d), we can clearly see that the surface currents decrease with the increase of frequency, and there are almost no surface currents at ${f_3}$, which further explains why the 2nd-order half-wave wall of the empty substrate has no obvious movement in the spectrum.
As shown in Fig. 4, then we analyzed the influence of geometric parameter h on the antireflective performance. It is obvious that when h = 5.8 mm, the long metallic wires have the best anti-reflection effect on the substrate. This is because the long metallic wires are uniformly distributed in the substrate (the thickness of the substrate d = 11.6 mm), which is closest to the plasma-like model, and the surface currents in the metallic wires can uniformly change the field distribution in the substrate [21].
Fig. 4. The TE-polarization transmission spectra of empty and metallic wire-embedded substrate with changed h under the incident angle of 80°.
3. Post-optimized simulation results
Based on the law of plasma frequency ${\omega _p}$ changing with $px$ and w, we optimized the parameters of embedded metallic wires to adjust the positions of ${f_1}$, ${f_2}$ and ${f_3}$ so that the three transmission windows in the spectrum could be connected to each other to form TE-polarization wideband EM transparency under extreme incident angles. As shown in Fig. 5, the TE-polarization transmission of CMC substrate is significantly improved after embedding the metallic wires in 12.0-18.0 GHz ($p = 3.1mm$, $w = 0.8mm$) under incident angles of [70.0°, 85.0°].
Fig. 5. (a), (b), (c) and (d) Comparison of TE-polarization transmission between metallic wire-embedded substrate and empty substrate after optimization of structural parameters with the incident angles of 70°, 75°, 80° and 85°.
4. Experiment
In order to further verify the anti-reflective performance of our scheme, we designed and fabricated a prototype and a CMC empty substrate and measured them. As shown in Fig. 6(a), we first fabricated a 5.8 mm CMC substrate and etched metallic wires with the same structural parameters as shown in Fig. 2 on both sides of it using the printed circuit board (PCT) technique, then we fabricated two 2.9 mm ones and hot-pressed the three substrates together in the order shown. In order to ensure the accuracy of measurement under extreme angles, the size of the CMC substrate fabricated is 300*837 mm, and the thickness of the empty substrate for comparison is 11.6 mm, which is consistent with the thickness of the prototype. The measurement was performed in the EM dark room, as shown in Fig. 6(b), and the horn antennas operate in 12.0-18.0 GHz.
Fig. 6. (a) Etched metallic wires on both sides of the CMC substrate (b) Measured the transmission of the prototype in an EM dark room.
The measured results are shown in Fig. 7, we can see that the measured results are almost consistent with the simulation results although there are some small deviations. After analysis, the deviations may come from the following aspects, first of all, there are some losses in the connection line between the horn antenna and the vector network analyzer, and the antenna itself. Secondly, the glue added during the hot-pressing of CMC substrates also slightly affects the measured results. Even so, the experimental results still prove that the transmission of the CMC substrate under extreme angles is significantly improved after embedding the metallic wires.
Fig. 7. (a), (b), (c) and (d) Measured transmission of metallic wire-embedded substrate and empty substrate with the incident angles of 70°, 75°, 80° and 85°.
5. Conclusion
In this letter, we propose to extend the transparency bandwidth of the half-wave wall under extreme angles by utilizing dispersion. Long metallic wires are embedded into the CMC substrate. Due to the plasma-like effect of long metallic wires under TE-polarization, the overall effective permittivity of the substrate, rather than keeping constant, grows from less than 0 to the original value itself with frequency nonlinearly. Such dispersion boosts wideband transparency in two aspects. On one hand, an additional transmission window is generated at the low-frequency end of the half-wave wall where the effective permittivity equals that of the air; on the other hand, the frequency of the 1st-order half-wave wall is tailored much closer to the 2nd-order half-wave wall than before. By tailoring the dispersion, the three windows are connected to each other to enable wideband transparency under extreme incident angles. A series of proof-of-principle prototypes were designed, fabricated, and measured to verify this strategy. Both simulated and measured results show that the prototype can operate in the whole Ku-band under incident angle [70°, 85°] for TE-polarized waves. This work provides an effective method of achieving wideband EM transparency under extreme angles and may find applications in radar, communications, and others.
Funding
Research Fund for Young Star of Science and Technology in Shaanxi Province, (6197435), (62101588); National Natural Science Foundation of China, (20220102).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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