1. Introduction

Broadly defined as structures with unique properties that are not found in nature, electromagnetic (EM) metamaterials (MMs) have been widely used to demonstrate interesting and exotic properties, such as negative index of refraction [1–3, 38], zero index of refraction [4] and hyperbolic dispersion [5]. Therefore, MMs with those properties had been studied widely by researchers around the world. In the past decades, MMs have been utilized to design devices with unusual characteristics, such as the invisibility cloaks [6], super-lenses [7,8], hyper-lenses [9,10], time reversal lenses [11], miniaturized microwave components and MM absorbers [12,13].

Asymmetric and nonreciprocal transmission devices have attracted an enormous amount of interest due to its promising prospects in the applications, which operate in the frequency region of microwave, or in the light regime. Nonreciprocal devices had been widely applied in information and communication systems, which include the optical diodes [14], isolators [15] and circulators [16], and so on. Although such a topic of nonreciprocal propagation has attracted much interest, the vast majority of the MMs reported to date are restricted to the reciprocal responses. One of the popular way to realize the nonreciprocal features is breaking time-reversal symmetry such as the isolators and circulators in microwave and communication systems [17]. This can be accomplished via the magneto-optical effect today. However, the magneto-optical approach requires heavy, bulky and costly magnets [18–20] which is incompatible with integrated technology. On the other hand, breaking time-reversal is not the only way to break reciprocity. Spatial-temporal refractive index modulation also can accomplish nonreciprocal isolation [21]. Ref [22] introduces a nonreciprocal non-gyrotropic magnetless metasurface by Surface-Circuit-Surface (SCS) in which time reversal symmetry is broken by the presence of unilateral transistors in the circuit part of the SCS structure. In Ref [23], authors proposed a metamateial slab made of arrays of tilted metal layers to achieve nonreciprocal absorption in optical frequency. They rotate anti-clockwise the coordinate to obtain the nonreciprocal transmission and absorption and proposed that the origin nonreciprocal properties are caused by the non-opposite wave vectors of the two eigen modes in the metamaterial slab. In magneto-optic photonic crystals, the reason for the presence of nonreciprocity is breaking the time-reversal symmetry in the photonic crystals [24]. Obviously, the magneto-optic photonic crystals can be applied as a one-way waveguide. In Ref [25], the authors utilized a nonreciprocal waveguide which is composed of yttrium–iron–garnet (YIG) under a tapered external magnetic field to achieve a trapping effect. Asymmetric transmissions are usually realized by chiral metamaterial structures, where the partial conversion of the incident EM wave into one of the opposite handedness is asymmetric for the opposite directions of propagation. This asymmetric transmission phenomenon originates from the interaction of EM radiation with the structural two-dimensional (2D) chirality in the metamaterials [26]. Although it is easy to confuse this asymmetric transmission with nonreciprocal transmission at first sight, it does not violate Lorentz’s reciprocity theorem for only reciprocal materials are involved [27, 42].

Unfortunately, the chiral structures will alter the polarizations of transmitted waves [28–30]. And there are few researches about the metamaterial structure which shows asymmetric transmission without relying on polarization rotation [36]. In 2016, Pfeiffer and Grbic proposed several metasurfaces which imitate Faraday rotation and optical isolation when illuminated with obliquely incident plane waves and normally incident vortex beams [37].

In this paper, we have designed a metamaterial device and studied the dependence of the absorption and transmission on the incidence direction. Such a three-dimensional (3D) metamaterial device consists of metal resonant structures and common substrates to imitate the anisotropic materials, which can show asymmetric transmission and absorption without any gyromagnetic materials [24], nonlinear materials [25], time-varying electric field [31–33] or static electric (magnetic) field [34,35]. The proposed metamaterial device can provide a high transmission at f₂ = 2.3GHz and the high absorptions at f₁ = 1.72GHz and f₃ = 3.48GHz for TE wave propagating in the + z direction at 30°. However, when TE wave incidents in the -z direction with 30°, the proposed device can achieve the high transmission at f₁ = 1.72GHz and f₃ = 3.48GHz, and a high absorption at f₂ = 2.3GHz. Thus, the proposed metamaterial device can protect devices in the region z < 0 from reflections originating from objects in the region z > 0 at the case of f₂, and shield devices in the region z >0 from reflections originating from objects in the region z<0 at the cases of f₁ and f₃.

The use of lumped resistors and capacitors in a metallic surface leads to complex and expensive structures because of the cost of high frequency resistors and complexity of the manufacturing. Compared with the structure proposed in [37], the device we designed based on the orthogonal 3D structure is simpler and lower cost since no required resistors and capacitors. Besides, the structure in [37] can work only at a single frequency while the presented device proposed in Figs. 2 and 3 can work efficiently at three frequency points although the frequency ranges are narrow. It should be emphasized that the unidirectional transmission and absorption is quite differently from the asymmetric propagation (absorption) which has been reported and discussed in many previous publications [39–41] for the asymmetric transmission in these reports are achieved by rotating the polarization. While the structure designed here can obtain asymmetric propagation and absorption without rotating the polarization of the incident wave. The metamaterial device is light-weight and easily fabricated which can achieve absorption for one direction and transmission for the opposite direction in given specific conditions. The performances of the proposed metamaterial structure are demonstrated with full-wave simulations and measurements.

2. Principle and formula

Considering a metasurface located in the z = 0 plane in the free space, the scattering parameters (S parameters) can be defined as (1), when a plane wave is incident from region m and scattered into region n as shown in Fig. 1.

 

Fig. 1 Relevant scattering parameters when a TE polarized plane wave is obliquely incident from the region z < 0.

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The metamaterial structure proposed here is designed to achieve asymmetric transmission and absorption. An ideal isolator is polarization independent, has S₁₁ = S₂₂ = S₁₂ = 0, and $S_{21}=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$. According to Ref [37], the necessary 3D parameters should be given by

3. Structure design and fabrication

It is necessary to introduce the longitudinal surface current according to Ref [37]. to achieve asymmetric transmission and absorption without cross polarization. And it is easier to achieve this function with three-dimensional asymmetric structure. Figure 2 shows the geometry of the unit cell of the proposed device. The front side of the unit cell consists of two centrosymmetrical back-to-back split-ring resonators as depicted in Fig. 2(a) and the back side of the unit cell is composed of a non-centrosymmetrical metal square with two symmetrical gaps which is shown in Fig. 2(b). Figure 2(c) shows the side view of the unit cell, from which one can easily see that the front view and the back view are asymmetrical. The substrate is FR-4 whose permittivity is$\epsilon ={\epsilon }_r(1-j\tan \delta )$, with${\epsilon }_r=4.4$ and$\tan \delta =0.025$. The specific parameters of the unit cell are listed in Table 1 below.

 

Fig. 2 (a) The front side of one of the metamaterial layers of the device. (b) The back side of one of the metamaterial layers. (c) The thickness of one of the metamaterial layers.

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Table 1. The parameters of the proposed device

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As shown in Figs. 3(a) and 3(b), the unit cell of the device consists of two identical orthogonal metamaterial layers. The metamaterial layer in yz plane is defined as the layer 1 and the metamaterial layer in xy plane is called the layer 2. Each metamaterial layer is shown in Fig. 2. Two metamaterial layers are orthogonal to each other as shown in Figs. 3(a) and 3(b) clearly. To demonstrate the validity of this design, the proposed metamaterial device with 25 × 25 unit cells is fabricated on a low-cost FR4 substrate which is shown in Fig. 3(c). The overall size of the prototype is 300mm × 375mm.

 

Fig. 3 (a) The unit cell of the device. (b) The top view of the device. (c) Fabricated prototype.

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4. Simulation and experimental results

The proposed device is simulated with the full-wave electromagnetic simulation software CST. Figure 4 shows the simulation model, the electromagnetic wave incidents from Port 1 and Port 2 respectively (the part z>0 is defined as Port 1, and z<0 is defined as Port 2.). When it is simulated, the unit cell is extended periodically both in x direction and y direction and the plane wave incident from z direction. It is worthwhile to note that to achieve obvious asymmetry, the structure is illuminated with a plane wave that is obliquely incident in the xz plane and the angle between z axis and the incident wave is$\theta$. Figure 4(b) shows that the metamaterial device provides unidirectional high transmission for obliquely incident plane waves propagating in the + z direction and absorbs radiation propagating in the –z direction at f₂. At f₁ and f₃, the obliquely incident plane waves are transmitted when propagating in the –z direction but absorbed when propagating in the + z direction.

 

Fig. 4 (a) Simulated model with full-wave simulation. (b) unidirectional high transmission for obliquely incident plane waves propagating in the + z direction but absorbs radiation propagating in the –z direction.

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The simulated results of the device are shown in Fig. 5. It is defined that the incident plane wave is TE wave when the electric field along y direction, and TM wave when the electric field along x direction. Modes 1 and 2 indicate that the wave illuminate from Port 1 and Port 2, respectively. It can be seen from Figs. 5(a), 5(b) and 5(c) that both the simulated transmission and absorption have three obvious resonance frequency points at f₁ = 1.72GHz, f₂ = 2.3GHz and f₃ = 3.48GHz. The device has the lowest transmission 0.17 at f₂ while the transmission is 0.81 and 0.82, respectively at f₁ and f₃ in mode 1. Meanwhile when the device work in mode 2, the lower and higher transmissions have been reversed completely with which in mode 1. In mode 2, the highest transmission occurs at f₂ and the transmissions are rather low at f₁ and f₃. The absorption of the device can be derived from the equation $A=1-T-R$(A, T and R represents absorption, transmission and reflection respectively). The absorption is indicated in Fig. 5(c), the highest absorption is 79% at f₂, however, the absorption at f₁ and f₃ is very low in mode 1. But in mode 2, the absorption is quite different. The absorption at f₁ and f₃ is rather high which is 81% and 71%, respectively, and the absorption at f₂ is very small. Thus, it can be concluded that at the frequencies the device shows an excellent transmission performance in mode 1, and behaves as a good absorber in mode 2 and vice versa. That is the device performs obvious asymmetric transmission and absorption at $\theta ={30}^o$for TE incident wave. In Figs. 5(d), 5(e) and 5(f), one can see that the device resonates at the same frequencies as in Figs. 5(a), 5(b) and 5(c). The transmission lines for mode 1 and mode 2 coincide with each other completely and there are only small differences between the absorption (reflection) for mode 1 and mode 2 at$\theta =0^o$in TE mode. Therefore, the asymmetry is not obvious at $\theta =0^o$in TE mode. While in TM mode, the device does not resonant at all which can be seen in Figs. 5(g), 5(h) and 5(i). These results prove that the asymmetric transmission and absorption only occurs at oblique incidence in TE mode.

 

Fig. 5 Simulated transmission, reflection and absorption of the metamaterial device. (a) Transmission (b) Reflection (c) Absorption for TE mode at θ = 30^ο. (d) Transmission (e) Reflection (f) Absorption for TE mode at θ = 0^ο. (g) Transmission (h) Reflection (i) Absorption for TM mode at θ = 30^ο.

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Figure 6 shows the S-parameters of the metamaterial device. The transmission and reflection curves for the obliquely incident case with $\theta ={30}^o$are presented in Figs. 6(a) and 6(b), respectively. As we can see from Figs. 6(a) and 6(b), the cross-polarized scattering is lower than −50dB which can be neglected. Figure 6(c) shows the transmission coefficient of the device as a function of the angle of incidence when illuminated from the front and back. The proposed device has different transmission coefficient for the incident angle from 30° to 60° when TE wave incidents from the front and back sides, respectively. Due to reciprocity, S₂₁(k_x) = S₁₂(-k_x), which is evident in this figure. Additionally, it makes sense that different frequencies show different optimal angles. Based on the effective medium theory, the proposed structure can be regarded as an anisotropic dielectric. Thus, from Eq. (2), we can know that the values of Y_xz, Y_zx, Z_xx, Z_xz, Z_zx depend on k_x. It means that, as shown in Fig. 6(c), S₁₂ and S₂₁ depend on the incident angle. The values of S₁₂ and S₂₁ are the functions of incident angle. In other word, for the Y_xz, Y_zx, Z_xx, Z_xz, Z_zx of proposed structure are dependent on the incident angle. The results of Fig. 6(c) and Eq. (2) are quite consistent.

 

Fig. 6 S-parameters of the metamaterial device. (a) Transmission when illuminated at θ = 30^ο (b) Reflection when illuminated at θ = 30^ο (c) Transmission as a function of incident angle at f₁, f₂ and f₃.

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Figure 7 describes the experimental process of the prototype with 25 × 25 unit cells. An Agilent N5245A vector network analyzer and two standard gain horn antennas working from 2GHz to 18GHz are used when measuring the transmission and absorption of the device. The measurements were completed in the anechoic chamber where wedge-tapered absorbers are used to prevent unwanted reflection. The distance between the sample and the antenna is$d\ge D^2/{\lambda }_0$, D is the diameter of the rectangular horn and d is the distance between the sample and the antenna, which is far enough to avoid the near filed effects of the antenna and the sample being tested.

 

Fig. 7 The experimental setup for measurements and test configurations. (a) is to test transmission. (b) is to test reflection.

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It can be observed from Fig. 8 that the measured results are in reasonable agreement with the simulations both in modes 1 and 2. The experimental results presented above show that the proposed device works as expected. Here, we only measured the transmission, reflection and absorption from 2 to 5GHz because the first resonance frequency 1.72GHz is out of the operating frequency of the antenna. Obviously, the measurement curve is deviated from its simulation curve with a resonance shift. This is mainly because the two orthogonal metamaterial layers are jointed together by welding when measurement and there are some places where the welding is not perfect.

 

Fig. 8 Experimental results compared with simulation results for two modes in TE wave at f₃ = 3.5GHz. (a), (b) and (c) are S₂₁, S₁₁ and absorption for mode 1. (d), (e) and (f) are S₂₁, S₁₁ and absorption for mode 2.

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5. Discussion and conclusion

From Fig. 9, one can find clearly that the metamaterial structures allow high transmission in the –z direction (mode 1) and high absorption in the + z (mode 2) direction at f₁ and f₃. At f₂, high transmission and high absorption can be achieved in the + z direction and –z direction respectively, which is contrary to f₁ and f₃. In Fig. 9, it appears that the incidence angle is not always 30°, in particular, the angle of the far field seems smaller in Fig. 9(a) than in Fig. 9(f). It makes sense that different frequencies show different optimal angles. This change is due to the incident TE wave will be transmitted, reflected and absorbed and the interaction between the reflected wave and the incident wave changes the direction of power flow. The reflection amplitude and phase are different at different frequencies, so the direction of power flow is different at different frequencies. To further explain the performance of the device, the surface electric current distributions are observed in Fig. 10. Modes 1 and 2 indicate that TE wave illuminates from Port 1 and Port 2, respectively. Layers 1 and 2 are defined as Fig. 3(a). We can see from Fig. 10(a) that, for mode 1, the surface currents of the two metamaterial layers are slightly weak at f₁ = 1.72GHz. In other words, TE wave propagating from Port 1 cannot couple to the structure. Therefore, such a device can be looked as a transparent dielectric for mod 1. Obviously, the transmission coefficient is high in such a case. However, there are significantly resonance currents at f₁ = 1.72GHz for mode 2 (see the second line in Fig. 10(a)). Therefore, the presented device strongly interacts with TE wave from Port 2, which makes the device opaque for mode 2, and the absorption is high at f₁ = 1.72GHz. The similar phenomena can be observed at the case of f₃ = 3.48GHz (see the fifth and sixth lines in Fig. 10(a)). However, different phenomena (see the third and fourth lines in Fig. 10(a)) can be seen at the case of f₂ = 2.3GHz, which are that the surface currents for mode 1 are stronger than those for mode 2. In Fig. 10(b), the surface current is high but the current intensity and distributions for the two modes are similar, that is why there is no asymmetry transmission (absorption) for the structure illuminated with TE wave at $\theta =0^o$. For TM incident wave, the metamaterial structure cannot resonant efficiently, so the surface currents are weak as shown in Fig. 10(c). Thus, the asymmetric transmission and absorption cannot be observed in the latter two cases.

 

Fig. 9 Power flow when illuminated with TE polarized plane waves at θ = 30^ο. (a), (b) and (c) when the device operates in mode 1(illuminated from the region z>0). (d), (e) and (f) when the device operates in mode 2 (illuminated from the region z<0).

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Fig. 10 The simulated surface current distributions of the device. (a) TE incident wave at θ = 30^ο, (b) TE incident wave at θ = 0^ο, (c) TM incident wave at θ = 30^ο.

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In summary, an asymmetric metamaterial device is proposed which can achieve absorption for the wave from one direction but transmission for the wave from the opposite direction. The whole structure can be regarded as an anisotropic medium based on the effective medium theory. When TE wave propagates the device from Port 1 at the angle of 30°, the proposed device has a lowest transmission 0.17 and a highest absorption 79% at f₂. At the same time, the higher transmissions are 0.81, 0.82, which can occur at the cases of f₁ and f₃, respectively. However, the absorption at f₁ and f₃ are relative low. Meanwhile, when TE wave incidents from Port 2 to Port 1 with 30°, the lower and higher transmission have been reversed completely with those from Port 1. For different incident directions, the proposed metamaterial device also has different transmission and absorption if the incident angle is changed from 30° to 60°. Furthermore, the device can work without the external magnetic field or nonlinear elements (e.g. amplifier, diode and magneto-optical material). The designed metamaterial device can be used to realize the radar stealth, which can transmit the signals from the antenna inside radar and absorb the unwanted signals.