Dual-Band Metasurface With Extreme Angular-Asymmetric Transmission and Frequency Selection Based on Resonant Coupling Effect

Asymmetric transmission plays an important role in many electromagnetic systems. Different to the asymmetric transmissions in full space, angular-asymmetric transmissions in half-space support different characteristics for symmetrical oblique incidences, which has great potentials for antenna designs and wireless systems. By introducing guided wave modes and resonant coupling effect into metasurface design, this communication designs and demonstrates a dual-band multifunctional metasurface with angular-asymmetric transmission and frequency selection under oblique incidences. At 8.7 GHz, the electromagnetic wave under 30° TM oblique incidence is absorbed, and the wave under −30° TM oblique incidence transmits, which presents an angular-asymmetric transmission. At 10.4 GHz, both ±30° TM oblique incident waves can be transmitted, which presents a frequency selection function. The metasurface sample with optimized geometry parameters has been fabricated and measured, and the measurement agrees well with the simulation results.


I. INTRODUCTION
A symmetric transmission of an electromagnetic wave in full space refers to the different transmission properties of an electromagnetic wave in the forward and backward directions when it passes through a transmission medium. These transmission properties include but are not limited to transmission, reflection, absorption, and polarization conversion [1]. As an exciting phenomenon, the asymmetric transmission provides a new method to control electromagnetic waves. It has attracted significant attentions in optics and wireless systems to realize optical isolation [2], [3], optical diodes [4], [5], antenna radomes [6], and noise control or elimination [7], [8].
Distinguished from asymmetric transmissions in full space, angular-asymmetric transmission achieves different wave propagation characteristics under symmetrical oblique incident angles in a halfspace. Since this concept can be utilized to achieve anti-interference devices in free space, it has great potentials in wireless communications, radars antennas, radio astronomy telescopes, and so on.
Metasurfaces are 2-D devices composed of periodic subwavelength artificial structures and have been widely used for electromagnetic wave manipulation [9]. Metasurfaces provide an effective technology to realize asymmetric transmission in full space and half-space. Fedotov et al. [10] proposed, for the first time, that asymmetric transmission of electromagnetic waves in full space can be realized by chiral metasurfaces Subsequently, many chiral metasurfaces that can realize asymmetric transmission have emerged [11], [12], [13], [14], [15], [16]. These chiral metasurfaces have different responses to electromagnetic waves incident in opposite directions. By twisting split resonators on both sides of a dielectric slab, they can achieve the polarization state's asymmetric transmission of linearly polarized electromagnetic waves [12], [13]. Furthermore, stacking multilayers of rotated gold nanorods, the circularly polarized waves can be transmitted and are converted into orthogonal polarization in forward direction, while they can be efficiently reflected in the reverse direction [14]. For asymmetric transmission devices based on chiral metasurfaces, the incident electromagnetic wave usually undergoes cross-polarization conversion, which, however, limits its applications in scenarios requiring an invariant polarization. Asymmetric transmission can also be realized using meta-gratings [17], [18]. By combining a gradient metasurface and a 1-D subwavelength grating, a metasurface can deflect forward incidences and reflect backward incidences [18]. However, these full-space asymmetric transmissions can hardly be applied for devices working in half-space.
Angular-asymmetric reflections have been realized using space-modulated metasurfaces [20], [21], [22]. A loss-assisted non-Hermitian electromagnetic metasurface was proposed to realize unidirectional retroreflection, which exhibits different reflectances under two opposite oblique incident angles [20]. In [22], a coherent asymmetric absorber using space-modulated metasurface was theoretically proposed, which behaves as an absorber or as a retroreflector depending on the angle of incidence by two coherent waves. The 3-D asymmetric meta-gratings were applied for angular-asymmetric transmissions [23], [24]. Based on the anomalous Brewster effect, a transition between perfect transparency and perfect absorption was achieved under 55.6 • and −55.6 • oblique incidences [23]. Similar meta-grating structure was also used to realize a Janus backscattering mirror that retroreflects incident waves for one side while showing transparency in the time-reversed reflection channel [24]. However, space-modulated metasurfaces require several different unit cell designs and a proper area to perform the spatial gradient. The 3-D asymmetric meta-gratings have a relative large thickness and cannot satisfy the requirements of the miniaturized wireless systems. In addition, these designs only have a single function. Thus, space-uniform multifunctional thin metasurface designs supporting angular-asymmetric transmissions are still desirable for engineering applications.
In this communication, by introducing guided wave modes and resonant coupling effect into metasurface design, we propose a dual-band multifunctional metasurface with both angular-asymmetric transmission and frequency selection, as shown in Fig. 1. This design 0018-926X © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. provides a new method to realize angular-asymmetric transmission, which is inspiring for multifunctional metasurface designs. Compared with other designs, the proposed metasurface is space uniform, thin, and dual-functional. At 10.4 GHz, the proposed metasurface shows frequency selection response due to the impedance match. While at 8.7 GHz, based on the resonant coupling effect, the metasurface shows angular-asymmetric transmission for ±30 • TM oblique incidences. Under 30 • illumination, the 8.7-GHz incident wave is bounded in the metasurface and propagates in a parallel plate waveguide mode, which vanished due to the dielectric loss. While under −30 • illumination, the metasurface is transparent for the incoming waves. The proposed metasurface has great potentials for anti-jamming in space domain, secret communications, multifunctional antennas, radio frequency stealth, and so on.
II. PROPOSED DUAL-BAND METASURFACE ELEMENT AND ITS PERFORMANCES To introduce guided wave modes and resonant coupling effect into metasurface design, two patch resonators with grounds were connected by a strip line sandwiched by these ground layers. The resonant coupling at a certain frequency can be tuned by the incident angles, and in turn, the guided wave modes can be converted. The structural diagram of the element is shown in Fig. 2. It is composed of five metal layers (yellow part), which are separated by four dielectric substrate layers (gray part) with the thicknesses of h 1 = 0.762 mm and h 2 = 0.168 mm. The substrate is Rogers 4350B with a relative dielectric constant ε r = 3.48 and loss tangent tan δ = 0.0037. The metallic layers are copper and have a thickness of 0.035 mm.
The top and bottom patches of the unit cell are shown in Fig. 2(a) and (e). The top layer is a square patch, and the bottom layer is a shorted rectangular patch. Similar to microstrip patch antennas, these patches act like a half and a quarter wavelength resonator, respectively. The left-hand side of the bottom patch is shorted using an E-wall realized by inserting a metallic row of vias, as shown in Fig. 2(e). The diameter d e of metallic vias is 0.2 mm, and the length f e between metallic vias is 0.5 mm. Fig. 2(b) and (d) shows the two ground planes, which also contribute the resonances of the top and bottom patches. In addition, the two ground layers form a parallel plate waveguide and form a strip line together with the middle layer shown in Fig. 2(c). This introduces additional guided wave modes into the metasurface unit cell and raises a new design freedom. There are two holes with a diameter d g of 1.3 mm on each ground to avoid direct connection with metallic vias. Fig. 2(f) shows the side-cut view of the unit cell along the central axis. It has two metallic feeding vias, which connect the patches on the top and In order to verify the designed dual-band multifunctional metasurface, we simulated the unit cell in CST Microwave Studio with a unit cell boundary condition and Floquet TM oblique incident excitation. The simulated transmittance and reflectance are shown in Fig. 2(g) and (h). In Fig. 2(g), T(30 • ) and T(−30 • ) represent the transmittance under 30 • and −30 • incidences, respectively. At 10.4 GHz, the metasurface works as an angular-symmetric frequency selective surface and transmits the ±30 • oblique incident waves with a transmittance of 0.81. Such frequency selective transmission is caused by the impedance match between the patches and the stripline [25]. Induced by the resonant coupling effect, an additional transmission peak appears at 8.7 GHz, and the designed metasurface shows angular-asymmetric transmission under ±30 • TM oblique incidences. The −30 • incidence can pass through the metasurface with a transmittance of 0.79. However, the transmission of the 30 • incidence is suppressed below 0.10.
We further simulated the reflection properties of the designed metasurface. Fig. 2(h) shows the reflectances [R(30 • ) and R(−30 • )] of the ±30 • incidence. It can be seen that the reflectances are 0.28 and 0.16 at 8.7 and 10.4 GHz, respectively. Both the transmission and reflection are suppressed under 30 • incidence at 8.7 GHz. This incidence is converted to a guided wave mode in parallel plate waveguide composed by the two metallic ground layers and, in turn, vanishes due to the dielectric loss. According to the simulation data of Fig. 2(g) and (h), the absorption can be calculated as 91%. Thus, a dual-band multifunctional metasurface was realized. At 10.4 GHz, it works like a frequency selective surface. While at 8.7 GHz, it shows an extreme angular-asymmetric transmission under the ±30 • incidences.

III. ANALYSIS OF DUAL-BAND METASURFACE WITH EXTREME ANGULAR-ASYMMETRIC TRANSMISSION AND FREQUENCY SELECTION BASED ON RESONANT COUPLING EFFECT
To further understand the principle of the proposed metasurface, we additionally observed the electric field on the patches and within the unit cell, as shown in Figs. 4 and 5.
The electric fields in the structure at 10.4 GHz are shown in Fig. 4. Fig. 4(a) and (b) shows the electric field on the top and bottom patches under 30 • incidence. Fig. 4(c) and (d) shows the electric field on the top and bottom patches under −30 • incidence. The electric field's magnitude is represented by the color bar from −1 to 1. Under ±30 • incidences, the top and bottom patches resonate in dipole mode and monopole mode, which are their basic modes for half and shorted quarter wavelength resonators, respectively. The resonate modes under ±30 • incidences are the same and are out of phase due to the opposite incident angles, as shown in Fig. 4(a)-(d). Notably, the coupling of these two resonator modes leads to a stripline-guided wave mode in the unit cell, as shown in Fig. 4(e) and (f). Such stripline-guided wave mode matches the impedance between the free space and the unit cell [25], which results in a frequency selective transmission. Fig. 5 shows the electric fields in the structure at 8.7 GHz. Fig. 5(a) and (b) shows the electric field of the top and bottom patches when the incident angle is 30 • . Fig. 5(c) and (d) shows the electric field of the top and bottom patches under −30 • incidence. As shown in Fig. 5(c), (d), and (f), under −30 • incidence, the top and bottom patches still resonate in their main modes like the situation at 10.4 GHz, and the incident wave can be transmitted through a stripline mode. In contrast, under 30 • incidence, the top patch resonates in its main mode; however, the bottom patch resonates in its higher order mode, as shown in Fig. 5(a) and (b). This results to different resonant coupling effects for ±30 • incidences. In turn, the guided wave modes at 8.7 GHz under 30 • incidence is converted to a parallel plate waveguide mode [as shown in Fig. 5(e)] and mismatches to the impedance of the bottom patch.
As shown in Fig. 5(f), the stripline-guided wave mode can excite the bottom patch by the metallic line on the middle layer. However,  as shown in Fig. 5(e), the parallel plate waveguide mode almost ignores the metallic line on the middle layer and, thus, cannot excite the bottom patch to realize a transmission. Thus, at 8.7 GHz under 30 • incidence, the incident wave is transformed to a guided wave propagating along the metasurface and is attenuated by the dielectric loss, which suppresses both the transmission and the reflection. Hence, by implementing this special resonate coupling effect, an extreme angular-asymmetric transmission is induced at 8.7 GHz.

IV. MEASUREMENTS OF THE DESIGNED METASURFACE
To demonstrate the proposed metasurface, a 20 × 20 square latticed metasurface sample is fabricated for measurement. The image of the metasurface is shown in Fig. 6. The metasurface consists of 400 units, with a total size of 300 × 300 mm. Fig. 7 shows the setup to measure both the angular-asymmetric transmission and frequency selective transmission of the proposed metasurface. The hollowed absorbing material box is utilized to support the metasurface while reducing unwanted electromagnetic interferences. When measuring the transmission at TM oblique incidence, we use two X-band standard horn antennas as transmitting (T TM ) and receiving (R TM ) antennas, respectively. As displayed in Fig. 7(a) and (b), a perpendicular line  from the center of the metasurface to the ground plane is marked for incidence angle reference. The transmitting horn is offset by 30 • to the normal line, and the receiving antenna is offset by 30 • to the other side of the normal line. Besides, we also ensured that the centers of the transmitting antenna, the receiving antenna, and the metasurface are aligned. The measurement was calibrated by "through" (without samples) and "isolation" (with a metallic plate in the same size of the sample). When measuring the metsureface sample, the transmitting antenna radiates to 30 • , and the measured |S 21 | can be recorded as the transmission amplitude at the oblique angle of 30 • . The transmitting and receiving antennas were then mirrored with respect to the normal line to measure the transmission amplitude for the incidence of −30 • . Fig. 8(a) shows that the measurement results are consistent with the simulation results. At 8.7 GHz, the designed metasurface shows angular-asymmetric transmission under ±30 • TM oblique incidences. The −30 • incidence can pass through the metasurface with a transmittance of 0.75. However, the transmission of the 30 • incidence is suppressed below 0.21. At 10.4 GHz, both the ±30 • TM oblique incidences can pass through with a transmittance of about 0.76.
When measuring the reflection of oblique incidence, we also use two X-band standard horn antennas as transmitting (T TM ) and receiving (R TM ) antennas, respectively. The test setup, similar to the transmission measuring case, is shown in Fig. 7(c). We place the two antennas symmetrically on both sides of the normal line, with an angle of 30 • . Taking the reflection test with an inclination of 30 • as an example, antenna A is used as the transmitting antenna, and antenna B is used as the receiving antenna. First, we calibrate the copolarized reflection amplitude of a metal plate as 1 and the cross-polarized reflection amplitude as 0. During the test, the metal plate is removed, and the metasurface is placed instead. At this time, the measured S 21 is the amplitude of the reflection obtained by 30 • TM oblique incidence. In addition, the transmitting antenna and receiving antenna are exchanged for −30 • TM oblique incidence measurement. The measurement result of reflection is shown in Fig. 8(b), and it is consistent with the simulation result. The measurement reflectances are 0.41 and 0.30 at 8.7 and 10.4 GHz, respectively. There is no reflected wave at 8.7 GHz at 30 • oblique incidence, indicating that the incident wave is absorbed. According to the measurement data of Fig. 8(a) and (b), the absorption can be calculated as 79%. Due to possible manufacture and measurement errors, the absorption is decreased, but the extreme angular-asymmetric transmission at 8.7 GHz is still obvious.
In summary, the metasurface we designed manifests two distinct functions at dual bands. At 8.7 GHz, the metasurface shows angular-asymmetric transmission for ±30 • TM oblique incidences. The 30 • TM oblique incident wave is absorbed, and the −30 • TM oblique incidence is transmitted. While, at 10.4 GHz, the proposed metasurface shows frequency selection response, both ±30 • TM oblique incidences can pass through.

V. CONCLUSION
In conclusion, a dual-band multifunctional metasurface with both angular-asymmetric transmission and frequency selection is proposed and verified by experiments. The proposed metasurface adopts a patch-stripline-patch structure. Through the resonant coupling mode of the patch, two working frequencies are realized. At the working frequency triggered by the coupling, the asymmetric transmission of oblique incidence in half-space is realized by using the states of the stripline. At 8.7 GHz, the metasurface we proposed shows angular-asymmetric transmission for ±30 • TM oblique incidences. Under 30 • illumination, the 8.7-GHz incident waves are bounded in the metasurface and propagate in a parallel plate waveguide mode, which vanished due to the dielectric loss, while, under −30 • illumination, the metasurface is transparent for the incoming waves. At 10.4 GHz, the proposed metasurface shows frequency selection response. The numerical simulation of the designed metasurface of the transmission wave incident at ±30 • shows that our design is feasible. On this basis, a square metasurface is fabricated and measured. The measurement results are consistent with the simulation results. The proposed metasurface has multifunctions at dual band. It achieves angular-asymmetric transmission, which has great potentials for multifunctional device designs, e.g., antenna superstrates.