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Optically transparent metasurface Salisbury screen with wideband microwave absorption

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Abstract

We present an optically transparent broadband microwave absorber based on the concept of metasurface Salisbury screen (MSS). The metasurface with optimized reflection phase profiles is used as the ground plane to excite multi-MSS resonances that are required for achieving continuous wide absorption bandwidth. Meanwhile, by employing indium tin oxide (ITO) film and glass dielectric substrate, high optical transparency and wideband microwave absorption can be obtained simultaneously. Both full-wave electromagnetic simulations and experiments demonstrate that the transparent MSS can perform an efficient absorption over 89% in an ultra-wide frequency band ranging from 4.1 GHz to 17.5 GHz with a sub-wavelength thickness. In addition, good angular performances are observed for all wave polarizations. The proposed MSS may provide a powerful platform for efficiently designing broadband absorption in microwave region with advantages of light weight, thin thickness, and high optical transparency, which could further find potential uses in many real-world applications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Recently, the electromagnetic (EM) absorbers have attracted much attention due to their excellent abilities to dissipate the incident EM power and therefore inhibit the reflection and transmission of EM wave, which have wide uses in many real-world applications, such as electromagnetic shielding, radar stealth technique, etc [1,2]. With the rapid development of science and technology, as well as the increased complexity of EM environments, on-demand applications continuously fuel efforts in designing microwave absorbers with versatile features and enhanced performances, e.g. ultra-thin thickness [3,4], broad bandwidth [5,6], and angular robustness [7,8], to name only a few. However, most microwave absorbers are composed of optically opaque metallic patterns, dielectric substrates and passive circuit elements, inherently making them visually non-transparent [3–8], which in general will limit their potential applications in where the optical field continuity is necessary for observation and communication, such as aircraft or satellite windows, radomes, etc. Besides, such kind of optically transparent devices could promote integration with solar panel applications. Therefore, several approaches are proposed to achieve the high light transmittance, as well as enhance the overall microwave absorption performance, for example, by utilizing optically transparent materials in the absorber design [9–14]. Graphene-based absorbers using Salisbury screen configurations or sandwich structures have been demonstrated successfully with high optical transparency and excellent electromagnetic absorption in designed frequency bands [12–14]. Despite the difficulty of mass production with large area that is typically required for low microwave frequency applications, graphene shows promising prospect in designing optically transparent absorbers. Indium tin oxide (ITO), a typical optical transparent conductive material, has also been implemented to replace the conventional metal (e.g. copper) to form the resonant inclusions in microwave region [9,15,16]. Particularly, a large accessible range of surface resistance can be obtained by simply controlling the thickness of ITO film, offering flexibility in altering lossy components during the design process. Despite these progresses, the absorption bandwidth is still a problem hindering their further applications and efforts on practical solutions should be paid to improve the bandwidth performance of the microwave absorbers with simultaneously high optical transparency.

There are several conventional ways to realize broadband EM absorbers with excellent absorption performances, such as Jaumann screen, circuit analogue (CA) absorbers [17] and high-impedance surface (HIS) based absorbers [18], etc. Recently, the metamaterials, a kind of artificially engineered materials that can emulate exotic EM responses unavailable by natural materials [19,20], have shown great power and flexibility in achieving absorbers with broad operation frequency band, such as by loading chip resistors to increase the lossy components [6,21–23] or judiciously designed multilayered structures [5,24], etc. Very recently, we have proposed a concept of metasurface Salisbury screen (MSS) simultaneously embracing ultra-wide band, high-performance, light-weight, wide-angle, and easy-fabrication in one thin-thickness absorber design [25,26]. The Salisbury screen is one of the classical passive microwave absorbers, which is realized by placing a 377 Ω/□ resistive film a quarter wavelength above a metallic ground plane [27]. Salisbury screen provides a perfect impedance match to free space at the center operation frequency, leading to a strong absorption of the incident signal, but such structure is inherently limited by its relatively narrow absorption bandwidth and discrete spectral absorption peaks. The newly developed metasurfaces are composed of planner sub-wavelength meta-particles, offering new opportunities in controlling the wavefront with desirable manner by introducing phase discontinuity across the interface [28–33]. In the scenario of MSS, metasurface with optimized spatial phase distribution is utilized as the ground plane to excite multi-MSS resonances for efficiently realizing broadband absorption in microwave region.

Here, inspired by our previous works, we show the design, characterization and experimental demonstration of an optically transparent MSS for efficient absorption in microwave region. By using highly conductive ITO film to form the metasurface ground and resistive ITO film to form the resistive layer, with glass serving as the dielectric substrate, the broadband MSS absorber can be high optically transparent suitable for observation applications. Compared with the same-sized conventional Salisbury screen (CSS) (5.2 GHz - 9.8 GHz, 61% relative absorption bandwidth), the low-reflection bandwidth performance of the MSS has been significantly enhanced to 4.1 GHz - 17.5 GHz, about 124% relative bandwidth. It also has relative good polarization-insensitive absorption, as well as stable angular performances until the incident angle up to about 40°. Finally, experiments are carried out to demonstrate the proposed MSS, and relative good agreements are observed between simulations and experiments. The ultra-wideband absorber with optical transparency might be applied in many occasions, for example, in electromagnetic compatibility (EMC) applications with simultaneously providing visual observation.

2. Design and simulation

The basic geometry of Salisbury screen simply consists of a 377 Ω/□ resistive film and a metallic ground plane, with an air spacer of quarter-wavelength thickness between them. When the total reflected phase including the phase accumulated by the wave propagating length and the phase reflected by the ground plane reaches 360°, the Salisbury resonance occurs, leading to an absorption peak [25]. In other words, Salisbury screen has regular absorption when the condition φpath(f)+φpl=2nπ is satisfied, where φpath(f), φpl indicate the phase delay caused by the wave propagating path and the reflection phase by metallic ground plane, respectively, while n=0,1,2 represents the nth order resonance. By introducing the metasurface into Salisbury screen absorber, we can have new degrees of freedom in designing the ground plane with desired reflection phase features, instead of metallic ground plane with unitary reflection phase (φpl=π). Therefore, the absorption peaks and the working bandwidth become controllable. In the MSS, different kinds of metasurface elements should be elaborately designed to excite different metasurface Salisbury resonances, which provide possibilities to continuously suppress the backward reflection within a relative wide bandwidth. To obtain a low backward reflection bandwidth as broad as possible, the constituent elements of the metasurface should be carefully designed and optimized to make sure that their reflection dips are averagely distributed along the frequency axis. Then, optimization algorithm should be considered to acquire the best portion of the constituent elements, as well as their spatial distribution.

Figures 1(a) and 1(b) show the schematic of the MSS and the metasurface element, respectively. The ITO-based resistive film with surface resistance of 377 Ω/□ is coated on an optically transparent thin glass, serving as the top layer to replace the optically opaque ink resistive sheet as conventionally used in Salisbury screen. The reflective metasurface on the bottom layer is composed of several kinds of elements that are also designed by ITO film but with a very small surface resistance of about 6 Ω/□. The low-loss ITO film used here can be viewed as a high-conductive material, which can ensure high reflection with desired phase function of the metasurface element when it is illuminated by the normal incidence. We use glass as the dielectric substrate to ensure a high optical transparency.

 figure: Fig. 1

Fig. 1 (a) Schematic of the optically transparent MSS for ultra-wideband backward reflection suppression. (b) The MSS element configuration. (c) The equivalent circuit model of the MSS element.

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The equivalent circuit model of the MSS based on transmission lines theory is illustrated in Fig. 1(c). Since the little loss of the metasurface can be ignored, the meta-atom is regarded as a lossless load ZL (ZL = 0 in CSS). The air spacer serves as a transmission line with intrinsic impedance Z0 and propagation constant  β0=2πf/c, while the ITO resistive film represents a resistor Rs = 377 Ω in parallel to the transmission line. The thickness of the glass supporting the ITO resistive film is t, with propagation constant of β1. According to the circuit model, the reflection coefficient Γ of a MSS element can be calculated by [25]:

Γ=ZinZ0Zin+Z0=1ei[2(β1t+β0d)φ(f)]1+3ei[2(β1t+β0d)φ(f)].
Clearly, the reflection coefficient will be reduced to zero when the resonance condition is satisfied:
2(β1t+β0d)φ(f)=2nπ,n=0,1,2...
Actually, the above equation reveals that the resonance condition depends on both the φ(f) and the space distance d, which is quite different to that of CSS where the resonance is only determined by the parameter d with fixed value of λ/4 (λ is the wavelength in free space). Therefore, although the spacer distance d between two glass layers of a MSS element decides the path phase and has a great influence on its resonant frequency, we can design the metasurface ground to manipulate the reflection phase φ(f) and so as to adjust the absorption peaks in the frequency spectrum, and eventually to enable an optimized bandwidth performance for a given absorber thickness. Besides, simultaneously exciting several high-order MSS resonances and thus narrowing the intervals between the neighboring resonances could also possibly broaden the bandwidth. Once the metasurface elements with diverse phase responses are designed, we can use algorithms to form the metasurface ground with optimized spatial distributions required for broadband MSS.

To verify the design principle of optically transparent broadband MSS, we have designed five different MSS elements, as shown in Fig. 2. The thickness of the top glass coated with resistive film is 0.4 mm and the bottom glass is 3.1 mm. The distance d between the two glass layers is 3.5 mm, and the total thickness of the MSS element is 7 mm. Therefore, the overall size of each MSS element is uniformly set as 12 × 12 × 7 mm3. The transparent glass substrate has a relative permittivity of 4.1 and loss tangent of about 0.001. The optimized geometric parameters of the five MSS elements are: a round pattern with diameter of 3 mm [(Fig. 2(a)]; a Jerusalem cross with side length of 7 mm [(Fig. 2(b)]; a cross with lateral length of 10 mm and width of 6 mm [(Fig. 2(c)]; a square patch with side length of 11 mm [(Fig. 2(d)]; a bare glass substrate [(Fig. 2(e)]. All the elements are grounded by ITO film at the bottom side. For simplicity, the five MSS elements with different pattern shapes shown in Figs. 2(a) - 2(e) are denoted as element “1”, “2”, “3”, “4” and “5”, respectively. The middle and right columns show the corresponding spectral phase and amplitude responses of each metasurface element. The results are performed by full-wave simulations, with periodic boundary condition along x- and y-direction while free-space boundary along z-direction.

 figure: Fig. 2

Fig. 2 The structure configuration of metasurface element (a) “1”, (b) “2”, (c) “3”, (d) “4”, and (e) “5”. Middle panels show the corresponding reflection phase response, while the right panels show the amplitude response of the MSS elements. The dashed lines represent  2(β1t+β0d)φ(f)=2nπ, n=0,1,2  The intersections of the dashed lines and phase curves show the resonance frequencies, which are in accordance with the zero dips of the reflection amplitude curves shown in right panel.

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Since reflective metasurface is used as the ground plane, the transmission is totally blocked by the metasurface and the absorption performance is only related to the reflection wave. The energy absorption spectrum for a single MSS element can be calculated as  A(f)=1R(f), where R(f) represents the reflected power. As shown in Fig. 2, each type of the elements has two or three resonance modes in the frequency band from 3 to 19 GHz. It can be observed that the intersections of the dashed lines [φ(f)=2β0d+2β1t2nπ,  n=0, 1, 2] and the reflection curves are corresponding to the reflection dips, proving that once the resonance condition is satisfied, the absorption occurs. The reflection dips or the absorption peaks of these elements are adjusted to distribute successively along the frequency axis, potentially ensuring a continuous bandwidth. By combining these elements with certain proportion and distribution to form the MSS, multiple MSS resonances can be simultaneously excited in the frequency band of interest, making the resistive ITO film to efficiently absorb the incident wave in a continuous wide frequency band. In the previous study, we used the genetic algorithm (GA) to optimize the proportion of each MSS element to obtain low backward reflection with maximum continuous working band [25,26]. Similarly, according to the classic phased-array theory, the far-field scattering of the total MSS under normal incidence can be viewed as the collective results of scattering from each MSS element, which is calculated by:

|Es¯(f)|=kE0a24πrg(θ,φ)|x=1Xy=1YΓx,y(f)ejk(sin(θ)cos(φ)xa+sin(θ)sin(φ)ya)|,
where E0 is the electric field amplitude of incidence, r represents the observational radius in far-field, k is the wave number in free-space, a is the periodicity of the element. Гx,y(f) denotes the reflection of MSS element located at the position of (xa, ya), and g(θ,φ) is the element factor given by:
g(θ,φ)=(1+cos(θ))sin(ka2sin(θ)cos(φ))ka2sin(θ)cos(φ)sin(ka2sin(θ)sin(φ))ka2sin(θ)sin(φ),
where θ is the elevation angle and φ is the azimuth angle. The right part of the Eq. (3) indicates that the total scatterings should be as small as possible if we want a high-efficient EM absorber. Since we aim to suppress the total reflection along surface normal direction (θ = 0) to achieve a low backward scattering, the optimization procedure can be further simplified to optimize the proportion of MSS elements. Therefore, the backward RCS reduction (θ = 0°) of the MSS calibrated to a same-sized metallic ground can be calculated as 20lg(|i=15miΓi(f)|), where Гi(f) is the frequency-dependent reflection coefficient of the ith MSS element and mi corresponds to its proportion. Within the pre-designed frequency band, we utilize the genetic algorithm (GA) to obtain the parameters mi to achieve the lowest backward reflection. The defined objective function and its constraint conditions are:
G(m¯)=Max{20lg(|imiΓi(f)|),f(fl,fh)},0mi&imi=1.
When the proportion of the elements {x1, x2, x3, x4, x5} reach {20%, 19%, 20%, 19%, 22%}, the MSS can realize the best bandwidth performance with −10 dB reflection reduction compared with that of a same-sized metallic slab. While the spatial distribution of the element has a great influence on the backward scattering pattern, we then use the simulated annealing algorithm [25] to optimize the spatial profiles of MSS to avoid any anomalous strong scattering beam in the backward half-space, and the final layout of the MSS is shown in Fig. 1(a). As shown in Fig. 3(a), −10 dB backward reflection can be obtained from 4.1 GHz to 18.4 GHz (128% relative bandwidth with respect to the center frequency) when the MSS is normally illuminated by an x-polarized plane wave. Meanwhile, the CSS, with same total thickness, only has a −10 dB bandwidth from 5.2 GHz to 9.8 GHz, about 61% in relative bandwidth. Compared with the CSS, the proposed MSS shows a significant advantage of the bandwidth performance, in addition to the optical transparency. In this scenario, we use the MSS composed of 10 × 10 super-cell array to achieve a continuous absorption band. However, the element number is not limited to this. With more elements, we may envision an enhanced performance, because we could layout the elements with more possibilities to further reduce the side-lobes, but this will bring extra burden on the optimization procedure, as well as the fabrication of MSS sample. Reducing the number of the elements, however, may spoil the continuously broad absorption band, because the absorption peaks should be well averaged along the frequency axis.

 figure: Fig. 3

Fig. 3 (a) Simulated backward RCS reduction of the MSS and the CSS. (b) Simulated absorption, reflection and scattering results of the MSS.

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The wave function of the MSS seems similar to that of diffusion-like metasurface, since both of them can realize an ultra-low backward reflection in response to the incident wave. However, the underlying working mechanisms of these two methods are drastically different. For a diffusion-like metasurface, the phase functions of the constituent elements should be designed to out-of-phase to invoke the random destructive interfere in the far-filed region [34–37]. The incident energy is just redirected into numerous directions, thus resulting in a low backward scattering. There is little energy dissipation during the wave propagation and scattering, and the incident power is just averaged to the whole backward half-space. Hence, compared with the bare metallic slab, the side-lobes of the scattering pattern of a diffusion-like metasurface are much larger. On the contrary, the reduced reflection by the MSS is mainly attributed to the energy loss by the ITO resistive film. We have also verified this by calculating the contributions of absorption and diffusion-like behavior to the backward reduction through full-wave simulations. The absorption can be calculated by A(f)=1R(f), where R(f) represents the sum of the whole backward half-space reflection, and A(f) is the corresponding absorption as a function of the frequency. The simulated results in Fig. 3(b) show that the MSS has a good absorption performance with high efficiency at least exceeding 89% across the entire working band for normal incident case. At the same time, the backward scattering reduction attributed to the diffusion-like scattering is uniformly suppressed to less than 2%. Therefore, most of the incident energy is dissipated by the ITO resistive film on the top layer.

Figures 4(a) - 4(c) illustrate the simulated three-dimensional (3D) scattering patterns of the MSS under the illumination of plane wave at 4.75 GHz, 10 GHz and 16.75 GHz, respectively. Compared with a same-sized bare metallic slab, which has directive pencil-like beam along the surface normal [shown in Figs. 4(d) - 4(f)], the backward scattering patterns of MSS are significantly suppressed to a low level due to the efficient absorption. Figures 4(g) - 4(i) illustrate the corresponding two-dimensional (2D) results in E-plane. Clearly, both the 2D and 3D scattering patterns of the MSS have a dominating beam along the surface normal direction while weak side-lobes in other directions. This unique feature also reveals that negligible energy is scattered to other directions when incident wave impinges on the MSS, which further demonstrates that the working mechanism is different from that of diffusion-like metasurfaces, because diffusion-like metasurfaces always have considerable side-lobes. By introducing the metasurface into Salisbury screen design, the incident energies are efficiently absorbed by the MSS, resulting in a severe attenuation of the reflection energy.

 figure: Fig. 4

Fig. 4 Backward scattering patterns of the MSS under the normal illumination of x-polarized EM wave at (a) 4.75 GHz, (b) 10 GHz, and (c) 16.75 GHz. Backward scattering patterns for a same-sized metallic slab at (d) 4.75 GHz, (e) 10 GHz, and (f) 16.75 GHz. The corresponding 2D results in E-plane are shown in (g) - (i).

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3. Experimental verification

To validate the feasibility and accuracy of the design principle, the optically transparent MSS has been fabricated and experimentally tested. The overall dimension of the fabricated MSS is same as that of Fig. 1, which uses commercially available glass materials and ITO films. The fabricated prototype is shown in Fig. 5(a). Four solid holders (not shown here) are printed by standard 3D printing technique and are used to support the top glass, providing required 3.5 mm air spacer. Obviously, the MSS sample has a high optical transmittance (measured about 75%) to ensure clear optical viewing through it. The experimental measurement is carried out in a microwave anechoic chamber, with a pair of broadband horn antennas serving as the emitter and receiver. The two horn antennas are connected to the two ports of a vector network analyzer (Agilent E8363A) through coaxial lines, respectively. In the experiment, the reflection reference is calibrated to a same-sized copper slab. As aforementioned, the low backward reflection of the MSS is mainly attributed to the efficient absorption by the lossy ITO film, and diffusion-like scattering only contributes little to the scattering reduction. Therefore, we here only measure the mirror reflection for normal incident case, and the absorption rate can be roughly estimated by this reflection results.

 figure: Fig. 5

Fig. 5 (a) Photograph of the fabricated sample. (b) Simulated and measured reflection of the MSS under the normal illumination of x-polarized plane wave (up-panel) and y-polarized plane wave (bottom-panel).

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As shown in Fig. 5(b), for x-polarized incidence, the MSS can provide a stable low reflection below 0.1 from 4.1 GHz to about 17.5 GHz. For y-polarized incidence, both the simulated and measured results have little difference compared with the results for x-polarization. This is mainly due to the anisotropic property of the whole MSS. Although the constituent MSS elements have same EM responses for x- and y-polarization, we will inherently see different spatial distribution along two orthogonal directions when these elements are combined to form a certain asymmetric spatially varying profile. This difference may lead to a different mutual coupling between neighboring elements, further resulting in a slightly different reflection for polarized waves. Considering the fabrication tolerance and the imperfect assembly, the measured results of backward reflection for normal incidence case roughly agree with the full-wave simulations.

The stable angular-independence is also an important criterion to evaluate the quality of EM absorber for practical applications. We also experimentally test the angular performances of the proposed MSS. Figure 6 shows the measured reflection coefficients under the illumination of a plane wave with oblique incident angles from 5° to 45°, with a step of 10°. We investigate both transverse electric (TE) and transverse magnetic (TM) mode for oblique incident case. Here, the TE mode is defined as the incident electric field perpendicular to the incident plane, and similarly, the TM mode is defined as the incident magnetic field perpendicular to the incident plane. As shown in Figs. 6(a) and 6(b), the low reflection band can be well preserved as the incident angles up to about 40° for TE-polarized incidence, indicating a good angular absorption performance for both x- and y-polarization. On the other hand, for TM-polarized wave incidences, the reflection rate rapidly increases when the incident angle exceeds 40°, showing a reduced absorption efficiency compared with the counterpart of TE case, as illustrated in Figs. 6(c) and 6(d). Clearly, the above measured results demonstrate relatively stable angular performances of the proposed MSS, especially for TE incidence cases.

 figure: Fig. 6

Fig. 6 Measured specular reflection for (a) x-polarized and (b) y-polarized TE incidence, and (c) x-polarized and (d) y-polarized TM incidence.

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As aforementioned, the MSS can efficiently absorb the incident energy which is intrinsically different from diffusion-like metasurfaces. Therefore, here we also measure the scattering pattern of the proposed MSS to experimentally verify this working mechanism. In the experimental set-up, the standard transmitting and receiving horn antennas are placed with equal distance away from the MSS sample to measure the far-field scattering patterns. We first fix the transmitting horn antenna perpendicular to the MSS surface, and then move the receiving horn antenna along a circular trajectory to measure the scattering wave at different angles. The measured results are shown in Figs. 7(a) and 7(b), where the scattering energy of side-lobes is much lower than the dominating beam along z-direction. These results indicate that the energy scattered to other directions due to the diffusion-like behavior is very weak, further demonstrating the incident energy being mainly absorbed by the resistive films.

 figure: Fig. 7

Fig. 7 Measured E-plane backward scattering patterns under the normal illumination of (a) x- and (b) y-polarized incidence.

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To evaluate the MSS absorption performance, we also compare it with some representative previous works with optical transparency, as shown in Table 1. The bandwidth considered here is defined by the reflection below 0.1 or backward reflection reduction over 10 dB, and the relative thickness is defined as the ratio of the total thickness of fabricated sample to the lowest working frequency. All of the investigated absorbers have sub-wavelength thickness around 0.1λ, but the proposed MSS in this paper can provide a wider operation bandwidth compared with the others. Meanwhile, the proposed MSS still has a high optical transparency. In addition, we can achieve an easy and fast MSS design through the proposed systematic optimization algorithm. Also, the working frequency can be flexibly tuned or scaled to much higher frequencies, as conventionally achieved by Salisbury screen.

Tables Icon

Table 1. Comparison with other optically transparent microwave absorbers

4. Conclusion

In conclusion, we have demonstrated an optically transparent MSS with wideband microwave absorption from 4.1 GHz to 17.5 GHz. Elaborately designed metasurface consisting of diverse elements is used as ground plane to simultaneously excite multiple MSS resonances, resulting in an improved bandwidth performance compared with conventional Salisbury screen. The experiment results are in agreement with full-wave simulation predictions, which show broad band absorption and stable angular performance till the incident angle up to about 40° for all polarizations. The designed structure can be used in applications where optical field continuity for optical viewing and backward scattering reduction are simultaneously required, for example, viewing window in EMC applications. The MSS design can also be extended to other frequency bands to achieve broad and efficient absorption with relative thin thickness and optical transparency.

Funding

National Key Research and Development Program of China (Grant NO. 2017YFA0700201); National Natural Science Foundation of China (NSFC) (61801207, 61671231, 61731010, 61571218); China Postdoctoral Science Foundation (2017M620202).

Acknowledgments

This work is partially supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), the Fundamental Research Funds for the Central Universities and Jiangsu Provincial Key Laboratory of Advanced Manipulating Technique of Electromagnetic Wave.

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic of the optically transparent MSS for ultra-wideband backward reflection suppression. (b) The MSS element configuration. (c) The equivalent circuit model of the MSS element.
Fig. 2
Fig. 2 The structure configuration of metasurface element (a) “1”, (b) “2”, (c) “3”, (d) “4”, and (e) “5”. Middle panels show the corresponding reflection phase response, while the right panels show the amplitude response of the MSS elements. The dashed lines represent   2 ( β 1 t + β 0 d ) φ ( f ) = 2 n π ,   n = 0 , 1 , 2   The intersections of the dashed lines and phase curves show the resonance frequencies, which are in accordance with the zero dips of the reflection amplitude curves shown in right panel.
Fig. 3
Fig. 3 (a) Simulated backward RCS reduction of the MSS and the CSS. (b) Simulated absorption, reflection and scattering results of the MSS.
Fig. 4
Fig. 4 Backward scattering patterns of the MSS under the normal illumination of x-polarized EM wave at (a) 4.75 GHz, (b) 10 GHz, and (c) 16.75 GHz. Backward scattering patterns for a same-sized metallic slab at (d) 4.75 GHz, (e) 10 GHz, and (f) 16.75 GHz. The corresponding 2D results in E -plane are shown in (g) - (i).
Fig. 5
Fig. 5 (a) Photograph of the fabricated sample. (b) Simulated and measured reflection of the MSS under the normal illumination of x-polarized plane wave (up-panel) and y-polarized plane wave (bottom-panel).
Fig. 6
Fig. 6 Measured specular reflection for (a) x-polarized and (b) y-polarized TE incidence, and (c) x-polarized and (d) y-polarized TM incidence.
Fig. 7
Fig. 7 Measured E -plane backward scattering patterns under the normal illumination of (a) x- and (b) y-polarized incidence.

Tables (1)

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Table 1 Comparison with other optically transparent microwave absorbers

Equations (5)

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Γ = Z i n Z 0 Z i n + Z 0 = 1 e i [ 2 ( β 1 t + β 0 d ) φ ( f ) ] 1 + 3 e i [ 2 ( β 1 t + β 0 d ) φ ( f ) ] .
2 ( β 1 t + β 0 d ) φ ( f ) = 2 n π , n = 0 , 1 , 2...
| E s ¯ ( f ) | = k E 0 a 2 4 π r g ( θ , φ ) | x = 1 X y = 1 Y Γ x , y ( f ) e j k ( sin ( θ ) cos ( φ ) x a + sin ( θ ) sin ( φ ) y a ) | ,
g ( θ , φ ) = ( 1 + cos ( θ ) ) sin ( k a 2 sin ( θ ) cos ( φ ) ) k a 2 sin ( θ ) cos ( φ ) sin ( k a 2 sin ( θ ) sin ( φ ) ) k a 2 sin ( θ ) sin ( φ ) ,
G ( m ¯ ) = M a x { 20 lg ( | i m i Γ i ( f ) | ) , f ( f l , f h ) } , 0 m i & i m i = 1.
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