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Abstract
In many practical applications, dielectric electromagnetic (EM) windows are usually under large-angle incidence of EM waves rather than normal incidence. To guarantee normal operation of devices inside, high transmission must be maintained under large incident angles, especially for TE-polarized waves. In this work, we propose a method of achieving broadband transmission of TE-polarized waves under large incident angles by embedding meta-atoms within dielectric plates. To this end, long metallic wires and S-shaped structures are embedded in the original dielectric plate, the former of which will dilute the effective permittivity due to plasma oscillation and the latter will increase the effective permeability due to induced strong current loops under large incident angles. In this way, two consecutive transmission peaks can be generated, forming a broad transmission band under large incident angles. A proof-of-principle Ku-band 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 [60°, 85°] for TE-polarized waves, with significantly enhanced transmission. This work provides an effective method of enhancing large-angle transmission of EM waves and may find applications in radar, communications and others.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Dielectric materials such as ceramic matrix composite (CMC) materials are often used as raw materials for electromagnetic (EM) devices such as radomes due to their heat resistance and good mechanical properties [1,2]. In the practical application of electromagnetic devices, electromagnetic waves usually incident at large angles. When the electromagnetic waves impinge onto the dielectric plate at large incident angles, most of the electromagnetic waves are reflected due to the impedance mismatching on air-dielectric interfaces, resulting in a low transmission. This is even more serious for TE-polarized waves because there is no Brewster effect in this polarization mode. Therefore, creating the EM window of TE-polarized waves passing through dielectric materials at large incident angles is crucial for improving the performance of electromagnetic devices.In theory, electromagnetic antireflection can be achieved by using anti-reflection (AR) coating [3–6], but such coating will reduce the mechanical properties of raw materials and make devices bulky. Frequency selective surface (FSS) can achieve the EM window in a broad band [7,8], but their complex structures and inability to operate at large incident angles make them not exactly practical.
Metamaterials, artificial electromagnetic media composed of sub-wavelength structures, have provided an unprecedented degree of freedom (DOF) in adjusting electromagnetic parameters such as effective permittivity and permeability, which can realize unique properties that cannot be realized or are difficult to be obtained in naturally occurring materials [9–13]. Li et al achieved wide-angle transmission enhancement of fiber-reinforced polymers based on the plasma-like effect of long metallic wires [14,15]. Jin et al designed the ultra-wide-angle bandpass frequency selective surface which achieved transmission enhancement for TE and TM waves [16]. Zhang et al realized the Brewster Effect for TE-polarized waves by the metal structure which is suspended above the substrate [17].
As shown in Fig. 1(a) and 1(b), in this work, we propose a method to create a wide-band EM window for TE-polarized waves under large angles by loading the meta-atoms composed of long metallic wires and S-shaped structures. In order to be more practical, the substrate is composed of CMC materials (with a relative permittivity of ${\mathrm{\varepsilon }_{1}} = 3.3$ and a permeability of ${\mu _1} = 1.0$) which has high specific intensity, strong toughness, antioxidation, and high-temperature resistance. In order to make our scheme meet the mechanical properties of electromagnetic devices in practical application, the thickness of our substrate is selected as 10 mm. In the case of the airborne radome, the thickness of the antenna cover is too small (such as 5 mm) to withstand some of the collisions encountered in flight; When the thickness of the antenna cover is too large (such as 15 mm), the overall weight of the antenna system will affect the flight performance of the aircraft. And the meta-atoms we designed are loaded into the substrate in the form of sandwich, which is in line with the modern processing technology of radomes and other enclosures electromagnetic equipment. Both the long metallic wires and S-shaped structures can improve the impedance matching on CMC-air interfaces for TE-polarized waves (the direction of the electric field is always parallel to the y axis) under large angles. But their antireflection frequency bands are different due to the different resonant frequencies. The electromagnetic responses of metal structures affect each other slightly because of the different resonant frequencies. We determined the meta-atoms of the final shape and size by using the variation of resonant frequencies with structural parameters Finally, we get the antireflection meta-atoms with good performance at large angles ($60 - {85^\circ }$) which can work in the whole Ku band. A proof-of-principle prototype was designed, fabricated and measured to verify this strategy. Both simulated, and measured results verify our design.This work provides an effective method of creating EM windows under large angles and may find applications in radomes, IR windows, and others.
Fig. 1. (a) TE-polarized waves impinge onto the metamaterial-embedded CMC plate with a large incident angle. (b) The structure parameters of the unit cell, where h = 2 mm, d = 10 mm (the thickness of the plate), px = 4 mm,py = 3 mm, r = 0.8 mm, ${w_1}$=0.25 mm, ${w_2}$=0.2 mm and the thickness of all the metallic structures t = 0.02 mm.
2. Theory and design
As shown in Fig. 2(a), when TE polarized waves irradiated onto CMC substrate under, the transmittance of electromagnetic waves at interface 1 and interface 2 could be calculated by Eq. (1). ${\mathrm{\varepsilon }_0}$ and ${\mu _0}$ represented the permittivity and permeability of air; ${\mathrm{\varepsilon }_1}$ and ${\mu _1}$ represented the relative permittivity and permeability of CMC, ${\textrm{Z}_0}$ and ${\textrm{Z}_1}$ represented the wave impedance for TE-polarized waves of CMC and air; ${\Gamma _1}$ and ${\Gamma _2}$ represented the reflectivity at the interface 1 and 2. According to Snell's law [18], most of electromagnetic waves are reflected and the transmittance of electromagnetic waves is very small due to the impedance mismatch between CMC and air. And as shown in the Fig. 2(c) the impedance mismatch becomes more severe as the incident angle increases. In order to improve the impedance matching at the interface, we loaded sandwich composed of meta-atoms on CMC substrate, which changed the original material from isotropic material to anisotropic material [19]. At the same time, we obtained a new set of formulas for calculating reflectivity as shown in Eq. (2).
Fig. 2. (a) The schematic illustration of reflection/refraction when TE-polarized waves impinge upon a CMC substrate, (b) The schematic illustration of refraction when TE-polarized EM waves impinge upon CMC plate embed with meta-atoms, (c) The impedance of CMC and air for TE-polarized waves under different incident angles.
In order to maximize the transmittance we need to achieve ${\Gamma _1} = {\Gamma _2} = 0$.Based on the analysis of the Eq. (2), we can achieve our goal by changing one of ${\varepsilon _{1y}}$, ${\mu _{1x}}$ and ${\mu _{1z}}$ and leaving the other two unchanged. It is known that when the CMC substrate is not loaded with metamaterial sandwich ${\mathrm{\varepsilon }_{{1y}}} = 3.3$ and ${\mu _{1x}} = {\mu _{1z}} = 1.0$. In this work, we tried to change ${\varepsilon _{1y}}$ and ${\mu _{1z}}$ without changing ${\mu _{1x}}$, because changing ${\mu _{1x}}$ requires loading resonant rings parallel to the z-axis in the substrate, which is very difficult to process and not in line with modern processing technologies.
It's easy to say that our goal is ${\varepsilon _{1y}} = 1$ when we only change ${\varepsilon _{1y}}$. As shown in Fig. 4(a), our solution is to load long metallic wires parallel to the y-axis in the middle of CMC substrate [14,15], because long metal wires have plasma effect and can reduce the permittivity of the whole plate along the Y-axis. Because the CMC substrate we chose was thick, we loaded two layers of metallic wires.
If we only change ${\mu _{1z}}$ our target is shown as Eq. (3) which is derived from Eq. (2). Let's keep ${\varepsilon _{1y}} = 3.3$ and ${\mu _{1x}} = 1$ the same and assume ${\theta _i} = {70^\circ }$, so we can get the ideal value of ${\mu _{1z}}$ is about 0.277 which means we need to lower ${\mu _{1z}}$.
As shown in Fig. 3(b), our solution is to load S-shaped structures in the middle of CMC substrate because this structure has a unique electromagnetic response under the irradiation of TE-polarized waves [17]. As shown in Fig. 4, when the TE- polarized waves are incident from the z-axis direction, there will be an electric field parallel to the y-axis. When the electromagnetic waves are incident at an angle of $0^\circ $, the electric fields distributed along the x-axis have the same phase. Therefore, the electric fields on the left and right sides of the S-shaped structure always maintain direction. As shown in Fig. 4(a), the surface currents on the S-shaped structure can be regarded as two loops with opposite directions (one clockwise and the other counterclockwise), and the two loops will form two magnetic fields parallel to the z axis in opposite directions. Macro point of view, it can be considered that the two magnetic fields cancel each other, so the distribution of the magnetic field throughout the plate does not change and ${\mu _{1z}}$ does not change. However, when the electromagnetic waves incident at a large angle (such as $70^\circ $), the electromagnetic wave received on both sides of the S-shaped structure has a certain optical path difference, which makes the electric fields on both sides have a phase difference $\Delta \mathrm{\varphi }$. When $\Delta \mathrm{\varphi } = ({2\textrm{k} + 1} )\mathrm{\pi }$, the electric fields on both sides always go in opposite directions. As shown in Fig.(b) the surface currents on the S-shaped structure can be thought of as two loops in the same direction and these two loops will form a magnetic field in the same direction. So the distribution of the magnetic field throughout the plate is changed and you can view this as ${\mu _{1z}}$ is changed.
Fig. 3. (a) and (b) The unit cell of the CMC plate embedded with long metallic wires or S-shaped structures in the middle. (c) The transmission when TE-polarized waves impinge on the metallic wires and S-shaped structures-embedded CMC plate and empty CMC substrate with ${\mathrm{\theta }_\textrm{i}} = {70^\circ }$.
3. Simulation results
In summary, we put forward two methods to increase the transmittance. In order to verify our ideas, we conducted simulation experiments by the frequency domain solver in CST Microwave Studio, and the simulation results are shown in Fig. 3(c). In our simulation experiment, the incident Angle of TE polarized wave is $70^\circ $, and parameters such as metal size, and plate thickness are the same as shown in Fig. 1(b). But instead of loading the wires and the S-shaped structures together into the substrate, we load them separately as shown in Fig. 3(a) and 3(b).
As shown in Fig. 3(c) when we load metal wires or an S-shaped structures onto the substrate we can get a peak (${f_1} = 13.85GHz$ or ${f_2} = 17.56GHz$) in the spectrum of the transmittance of the plate and at ${f_1}$ and ${f_2}$ the transmittance of the plate is as high as −1 dB (90 percent of the energy passes through the plate).
Although both methods can increase transmittance, they do not work in a wide enough band to meet the needs of practical applications. However, in our simulation experiment, ${f_1} \ne {f_2}$ due to the different resonant frequencies of long metal wires and S-shaped structures, which means that if we combine two metamaterial structures together the two consecutive transmission peaks in the spectrum almost unchanged and the two antireflection bands would be perfectly connected and that would give us a wide-band EM window. As shown in Fig. 1(b), we loaded the S-shaped structures into the middle of two layers of long metal wires to obtain a meta-atom.
Although we can't express the relationship between the structural parameters and ${\varepsilon _{1y}}$ and ${\mu _{1z}}$ concretely by the formula, we can get the general law of the change of ${\varepsilon _{1y}}$ and ${\mu _{1z}}$ with the structural parameters by analyzing the resonance models of the metal structures.As shown in Eq. (5) and Fig. 5(a), the plasma effect of long metal lines can be expressed by Drude model [15], whose general variation rule is that the ${w_p}$ decreases with the increase of $\textrm{px}$ and ${w_2}$. In order to confirm this hypothesis, we kept other structural parameters unchanged in the CST microwave studio, adjusted $\textrm{px}$ and ${w_2}$, and observed the TE wave transmittance of the CMC plate at an incident angle of $70^\circ $. As shown in Fig. 5(e) and 5(g), the variation of resonance frequency ${f_1}$ is consistent with our hypothesis. As shown in Eq. (6), the resonance type of the S-shaped structure is Lorentz resonance. The equivalent circuit diagram of the structure is given in Fig. 5(b), in which the electric field carried by the incident electromagnetic wave is equivalent to the electromotive force in the circuit, and the rule of U changing with frequency is shown in Fig. 5(c). Subsequently, we kept other structural parameters unchanged to adjust $\textrm{r}$ and ${w_1}$ (Reducing $\textrm{r}$ is going to increase the length of the wire in the equivalent circuit which will increase ${L_0}$, and reducing ${w_1}$ is going to reduce the radius of the wire in the equivalent circuit which will also increase ${L_0}$) and observed the transmittance of CMC plate. The change rule of ${f_2}$ was consistent with Lorentz model.
Fig. 4. (a) and (b)Surface currents on the S-shaped structure when TE-polarized waves hits it at incident angles of 0 $^\circ $ and $70^\circ $.
Fig. 5. (a) The ${\varepsilon _{1y}}$ resulted from Drude-type resonance of metallic wires, (b) The equivalent circuit diagram of the S-shaped structure. The values of ${\textrm{L}_0}$, ${\textrm{R}_0}$ and ${\textrm{C}_0}$ are determined by the $\textrm{r}$ and ${w_1}$, (c) The ${\mu _{1z}}$ resulted from Lorentz-type resonance of S-shaped structure, (d) TE wave transmission of the substrate meta-atoms with $\textrm{px} = 4,{\;}5{\; }$ and $6$. (e) TE wave transmission of the substrate meta-atoms with ${\textrm{w}_2} = 0.2,{\; }0.4{\; }$ and $0.6$. (f) TE wave transmission of the substrate meta-atoms with $\textrm{r} = 0.9,{\; }0.8{\; }$ and $0.7$. (g) TE wave transmission of the substrate meta-atoms with $\textrm{px} = 0.05,{\; }0.25{\; }$ and $0.45$.
In this process, we can find that the resonant frequencies of the two metal structures hardly change due to the structural parameters of each other, which is also consistent with our previous expectations.
Based on the variation of ${f_1}$ and ${f_2}$ with structural parameters, we determined the final structural parameters of meta-atoms as shown in Fig. 1(b). As shown in Fig. 6(a), the results are almost consistent with our prediction in that the positions of the two transmission peaks in the spectrum do not move significantly (${f_1} = 13.91GHz$ or ${f_2} = 17.12GHz$) and the antireflection bands are connected to each other and eventually cover almost the entire Ku band. It is worth mentioning that when the incident angle is $70^\circ $, the transmittance of the plate is higher than −1 dB from 13.1 GHz to 17.6 GHz. In addition, we extracted the equivalent impedance of the plate in the whole Ku band as shown in the Fig. 1(b) ${Z_1}/{Z_0} = 1$ at ${f_1}$ and ${f_2}$, indicating that the long metal wires and s-shaped structures adjust ${\varepsilon _{1y}}$ and ${\mu _{1z}}$ at these two frequency points to match the impedance of the plate and the air respectively. The fundamental reason for such a good effect is that the resonance frequencies of the two metamaterial structures are different. When the electromagnetic frequency is equal to ${f_1}$, the long metal line resonates and generates strong surface currents, while the S-shaped structures almost have no surface current because there is no resonance. The opposite happens when the frequency is equal to ${f_2}$. So even though we're using meta-atoms, the two structures that make up the meta-atom work independently of each other.
Fig. 6. (a) The reflectivity and transmission when TE-polarized waves impinge on the CMC plate loaded with the meta-atoms under ${\mathrm{\theta }_\textrm{i}} = {70^\circ }$. (b) The equivalent impedance extracted from S parameters under ${\mathrm{\theta }_\textrm{i}} = {70^\circ }$ in CST Microwave Studio.${Z_0}$ is the wave impedance of air and ${Z_1}$ is of the CMC plate loaded with meta-atoms.
To further verify the working principle of meta-atoms we monitored the surface currents and power flows at ${f_1}$ and ${f_2}$.The surface currents on the metamaterials shown in Fig. 7(a) and 7(b) are as expected: there are strong currents on the long metal wire and almost no current on the S-shaped structures at ${f_1}$; There is almost no current on the 2-long metal wire and there are strong currents on the S-shaped structures and they forms two loops in the same direction. And as shown in Fig. 7(c) and 7(d),when the electromagnetic wave passes through the plate at ${f_1}$ and ${f_2}$, there is no violent deflection on interface 1 and 2 but a smooth path through the plate (the angle of refraction is almost equal to the angle of incidence) and the energy on both sides of the plate is almost the same, which also indicates that the impedance match between the plate and the air is good and the electromagnetic wave transmittance is high.
Fig. 7. Simulated surface currents and power flows in the metamaterial-embedded CMC plate. (a) and (b) surface currents on the metamaterials at ${\textrm{f}_1}$ and ${\textrm{f}_2}$, respectively; (c) and (d) power flows in metamaterial-embedded CMC plate at ${\textrm{f}_1}$ and ${\textrm{f}_2}$, respectively.
After obtaining the transmittance at an incident angle of ${70^\circ }$, we obtained the transmittance of the flat plate with an incident angle of $60^\circ $ to $85^\circ $ through simulation experiments.As shown in Fig. 8(a) and 8(b), when the CMC substrate is loaded with meta-atoms, its transmittance is significantly enhanced in the whole Ku band for incident angles ranging from $60^\circ $ to $85^\circ $. Even for ${\theta _i} = 80^\circ $, the performance of transmission enhancement is still obvious and the tansmission at 13.5–14.3 GHz and 17.4–17.9 GHz is larger than −1.0 dB under this extreme incident angle.
4. Experiment
In order to further verify the anti-reflective performance of our meta-atoms we made a prototype and a CMC empty substrate used as a reference sample for experimental testing. As shown in Fig. 9(a), we first machined four 2.5 mm CMC empty substrates and etched long metallic wires or S-shaped structures with the same geometric parameters as shown in Fig. 1(b) on one side of three of them using printed circuit board (PCT) technique, and then hot-pressed them together in the order shown. In order to ensure the accuracy of measurement at a large incidence Angle, the size of CMC substrate processed is 279*880 mm, and the thickness of the empty substrate is 10 mm, which is consistent with the thickness of the prototype.The measurement was performed in a microwave anechoic chamber, as shown in Fig. 9(b), and the horn antennas operate in 12.0–18.0 GHz.
Fig. 9. (a) The structure of the prototype. (b) The measurement setup in the microwave anechoic chamber.
The experimental results are shown in Fig. 10 We can see that the experimental results are almost consistent with the simulation results although there are some small deviations. 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 experimental results. Even so, the experimental results still prove that the transmittance of CMC substrate at large incident angles is significantly improved after loading the meta-atoms designed by us. All in all, the experimental results and simulation results all verify the correctness and feasibility of our scheme.
Fig. 10. (a) The transmission of the prototype under incident angles of [$60^\circ ,85^\circ $]. (b) The transmission of fabricated empty substrate under incident angles of [$60^\circ ,85^\circ $].
5. Conclusion
In this paper, we propose to create an EM window of CMCs at large incident angles by loading meta-atoms composed of S-shaped structures and long metallic wires. Firstly, we adjust ${\varepsilon _{1y}}$ and ${\mu _{1z}}$ of anisotropic dielectric plate at different frequency points by loading long metallic wires and S-shaped structures separately, so as to add two consecutive peaks to the transmission spectrum. Then, we load the two metal structures at the same time so that the two transmission peaks are connected to each other and cover the whole working frequency band. Our scheme significantly enhances the transmittance of CMCs plate at an incident angle ${\in} [{60^\circ ,85^\circ } ]$ and its working frequency band can cover the whole Ku band. In order to verify our design, we designed and fabricated a proof-of-principle prototype and measured it. The experimental results are almost identical to the simulation results and they all verify our strategy. It is worth mentioning that our scheme is of universal significance. For substrates of different thicknesses and materials and different frequency bands, the meta-atoms designed by us can play a role by adjusting their own geometric parameters. This work provides an effective method of creating EM windows under large angles and may find applications in radomes, IR (infra-red) windows, and others.
Funding
National Natural Science Foundation of China.
Disclosures
The authors declare no conflicts of interset.
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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