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Abstract
In this work, we design an ultrathin 2-bit anisotropic Huygens coding metasurface (AHCM) composed by bilayer metallic square-ring structures for flexible manipulation of the terahertz wave. Based on the polarized-dependent components of electric surface admittance and magnetic surface impedance, we confirm that both the electric and magnetic resonances on coding meta-atoms are excited, so as to provide a full phase coverage and significantly low reflection. By encoding the elements with distinct coding sequences, the x- and y-polarized incident waves are anomalously refracted into opposite directions. More uniquely, we also demonstrate that the designed AHCM can be utilized as a transmission-type quarter-wave plate. The proposed metasurface paves a new way toward multifunctional terahertz wavefront manipulation.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurface has been paid significant attentions during the last decade for its unique electromagnetic (EM) properties that is not available in naturally occurring materials [1–3]. Traditional metasurface merely relying on the manipulation of induced electric currents is insufficient to control the transmitted waves with high efficiency due to the low transparency and limited phase shift coverage it can reach. As a contrast, Huygens metasurface is able to achieve near-unity transmission magnitude and also 2π phase coverage because it can simultaneously support two orthogonally electric and magnetic dipole currents in response to the incident EM waves [4]. The well-designed Huygens metasurface not only efficiently tailors the transmission with zero reflection but also manipulate the amplitude, phase and polarization of EM waves [5–8]. Thus, numerous fascinating phenomena such as anomalous refraction [9,10], beams focusing [11,12], airy beams [13,14] and holography [15,16] are realized by Huygens metasurface, which covers the frequency band from microwave to visible light. To realize wavefront manipulation at microwave or THz range based on Huygens metasurface, cascaded metasurface composed of at least three-layer metallic structures is proposed [17,18]. However, the multilayer cascaded metasurface with the increased thickness inevitably introduces extra losses, which decreases the transmission efficiency and increase difficulty in real device fabrications. Recently, some efforts have been made to achieve high transmission and 2π phase control with bilayer metallic structures operating in microwave and THz band [19–22]. Nevertheless, Huygens metasurface consisted of double-layer elements on one-layer substrate is still either a polarization-selective or polarization-insensitive device [23,24], which limits the application in multifunctional device and multi-channel information processing [25–27].
Recently, Cui et al. have put forward the concept of coding metasurface and managed to manipulate the EM wave with different functionalities by controlling the sequence of digital coding states ‘0’ and ‘1’, which matches phase 0 and π (for 1-bit coding scenario) [28]. Naturally, the coding metasurface idea can be evolved from 1-bit to the general situation of multi-bit. For example, 3-bit coding metasurface is made up of eight coding particles ‘000’, ‘001’, ‘010’, ‘011’, ‘100’, ‘101’, ‘110’ and ‘111’, each of which has 0°, 45°, 90°, 135°, 180°, 225°, 270° and 315° phase responses [29]. And the application scope can be expanded from microwave to terahertz band [30,31]. Coding metasurface could simplify design and optimization procedures due to the digitalization of unit structure. Meanwhile, coding metasurface can achieve the linear-polarized and circular-polarized wave manipulation [32–35]. Benefit from the advantages of coding metasurface, it has been used to manipulate the EM wave in a simpler and more efficient way, bringing about many interesting phenomena such as anomalous reflections and random diffusions [30,34]. Furthermore, coding metasurface as a bridge connecting the physical metamaterial particles with digital codes makes it possible to review metamaterials from the perspective of informational science and realize multi-channel information processing [36–38], e.g., coding metasurface integrating the digital convolution operation could rotate the radiation beam into desired directions [36]. It is worth noting that coding metasurface can not only support reflection mode but also can manipulate the transmitted wave. A transmission-type coding metasurface has been proposed to realize anomalous refraction and nondiffractive Bessel-beam generation in the THz band [39]. However, it is not favorable for application in practice since three-layer metallic C-structures inevitably introduce extra losses and have single polarization response. Taking advantages of coding metasurface and Huygens metasurface into account, an ultra-thin Huygens coding metasurface can not only overcome the limitation of cascaded coding metasurface but also independently and flexibly manipulate x- and y-polarized terahertz waves, making it useful for multi-channel antennas and devices.
Here, we design an ultrathin 2-bit anisotropic Huygens coding metasurface (AHCM) at the terahertz frequency to realize anomalous refraction and polarization conversion. Frist, we present anisotropic Huygens meta-atoms, composed of bilayer metallic structures on a polyimide substrate, as the coding elements for coding metasurface. The terahertz wave with 0° (state ‘00’), 90° (state ‘01’), 180° (state ‘10’) and 270° (state ‘11’) transmitted phases can be generated independently with normal incidence under two orthogonal polarizations. It is stressed that the origin of our designed Huygens-atoms is derived from the surface electric admittance (Yes) and magnetic impendence (Zms) of the anisotropic Huygens metasurface. And we quantitatively describe the needed Yes and Zms values. Meanwhile, we note that both the electric and magnetic resonances on coding elements are excited to provide full phase coverage and significantly reduce reflections. Then, the proposed AHCM can realize flexible control of the linearly polarized terahertz wave by arranging anisotropic coding Huygens meta-atoms in specific sequences, as shown in Fig. 1(a). When x- and y-polarized terahertz wave are incident normally on the AHCM (M1), they are deflected into opposite anomalous directions in the x-z plane. Thus, the polarization control is flexible and independent, and different functionalities can be achieved via different polarized wave incidence. Moreover, the designed AHCM (M2) generates an anomalously refracted circularly polarized beam under a 45° linearly polarized illumination.
Fig. 1. (a) Schematic of the AHCM for anomalous refraction beams and transmission-type quarter-wave plate. (b) Working mechanism of the proposed AHCM. Electric and magnetic surface current densities are excited under the incident field from the left side of the metasurface.
2. Theoretical analysis and structural design
Here, anisotropic Huygens metasurface is characterized theoretically by electric surface admittance (Yes) and magnetic surface impedance (Zms), which can be numerically obtained by calculating surface currents and the averaged tangential fields on the surface [4]:
In order to obtain 2-bit anisotropic Huygens coding elements under two orthogonal polarization incidences, a double-layer metallic meta-atom structure is presented to match the previously obtained theoretical values and construct the AHCM with simultaneous electric and magnetic dipole resonances, which is inspired by previous works about bilayer Huygens metasurface [19,21,24]. In comparison to previous works on Huygens meta-atom design, such as the vertical wire/loop type and the cascaded three-layer shunt-admittance sheets type [4,14–18,39], the structure designed in our work is also ultra-thin and easy to integrate. The proposed unit structure contains a corner-shaped square metal ring and a strip-type metal ring spaced by a dielectric substrate made of polyimide, see Figs. 2(a-c). The relative permittivity and loss of polyimide utilized in our simulation are ɛr = 3.5 and tan δ = 0.001, respectively, and the thickness of the substrate is td = 30.5 µm. The periodicity of meta-atom is p = 100 µm, and the other parameters shown in Figs. 2(a-c) are a = 96 µm, w = 4 µm, and g1, g2, l1 and l2 are variable parameters for the 2-bit coding element design. The metallic layers are made of gold with the conductivity σ = 4.56×107 S/m and the thickness tAu = 200 nm. Considering the polarization-controlled characteristics of anisotropic coding elements, 16 coding elements are described in Fig. 2(d). To be more specific, we refer to the anisotropic meta-atom as a ‘0/1’ coding particle, and the binary codes before and after the slash symbol (/) represent the digital states under x and y polarization, respectively. Considering the geometry symmetry, parts of meta-atoms are identical after being rotated by 90°, so the number of designed meta-atoms is reduced from 16 to 10 [represented by #1 to #10 shown in Fig. 2(d)]. Here, we use the commercial software CST Microwave Studio to obtain the transmission coefficient and phase distribution of the designed structure and get the anisotropic Huygens coding meta-atoms. Moreover, the boundary conditions are set as periodic in x- and y-directions and open for z-direction in free space.
Fig. 2. (a) Schematic of the proposed AHCM meta-atom. The top view (b) and the bottom view (c) of the unit cell. (d) 16 AHCM meta-atoms along x and y polarization. The serial number with addition rotation symbol indicates that those meta-atoms can be obtained by imposing 90 ° rotation operation on the corresponding meta-atoms without rotation symbols.
In order to explain the designing process clearly, we first consider the isotropic case when the parameters of the structure satisfy g1 = g2 and l1 = l2. The transmission coefficient and phase distributions of the unit structure are displayed in Figs. 3(a) and (b) at 1.37 THz, respectively. Meanwhile, it is convenient to achieve highly efficient transmission and 2π phase coverage at 1.37 THz when the parameters g and l of the meta-atoms satisfy the condition of g + l = 88 µm, as shown by the black dotted line marked in Figs. 3(a) and (b). For intuitively understanding, the transmission coefficient and phase of the transmitted wave is plotted as the function of g at 1.37 THz in Fig. 3(c). The transmission coefficient of the structure remains above 0.8, while the phase change covers the entire 2π range, which imply the designed isotropic structures can be applied to construct a 3-bit coding metasurface. Note that the key to designing the Huygens metasurface is to induce electric current and magnetic current simultaneously. Therefore, as shown in Fig. 3(d), the surface currents Jtop and Jbot are induced in the two layers when illuminated by a y-polarized THz wave. Due to the opposite flowing directions of Jtop and Jbot, the surface currents on the both layers constitute a current loop and generate an orthogonal magnetic field. As illustrated in Figs. 3 (e)-(g), the orthogonal induced magnetic field has concentrated around the top and bottom metallic structures with strong resonant currents. Meanwhile, the induced electric field is yield by the net surface current Jnet which is the difference between Jbot and Jtop. Thus, Huygens coding meta-atoms can efficiently control transmitted waves by generating orthogonal equivalent electric and magnetic currents.
Fig. 3. (a) Transmission coefficient and (b) phase distribution of isotropic meta-atom by changing parameters g1 and l1at 1.37 THz. (c) The transmission coefficient and phase change of the meta-atoms as the parameters satisfy g + l = 88 µm. (d) the surface current distribution, (e) the top view, (f) the bottom view and (g) the side view of induced magnetic field distribution of the meta-atom at 1.37 THz.
Based on above analysis, we can reduce the design parameters from g1, g2, l1 and l2 to g1 and g2 to design anisotropic coding meta-atoms. In addition, it can be seen from Fig. 3(c) that the transmission phase is almost unchanged if g >58 µm. Fig. 4 shows the transmission coefficient and phase distributions of the anisotropic meta-atom under x- and y-polarized incidence at 1.37 THz, respectively, where the g1 and g2 change from 8 µm to 58 µm and the l1 and l2 satisfy the condition of g + l = 88 µm. In order to get the previously designed coding phase in section 2, the final structural parameters and transmitted responses of anisotropic Huygens coding meta-atoms are shown in Fig. 4 and Table 1. Compared with previous bilayer-metallic Huygens meta-atoms, anisotropic coding meta-atoms can generate different transmitted response under x- and y-polarized incidence. As shown in Fig. 2(d), it can be represented by # (0/0), # (0/1), # (0/2), # 5 (1/1), # 6 (1/2), # 7 (1/3), # 8 (2/2), # 9 (2/3), # 10 (3/3), with the transmitted responses under x- and y-polarization marked as white stars and numbers in Fig. 4.
Fig. 4. (a), (c) Transmission coefficient and (b), (d) phase colour map of the anisotropic meta-atom under x, y polarization incidence.
Table 1. Transmission coefficient and phase of the anisotropic Huygens coding meta-atom at 1.37 THz
In order to verify the consistency between the electric (magnetic) surface admittance (impedance) results from designed coding meta-atoms and theoretical calculation based on Eq. (3), the normalized imaginary component of electric (magnetic) surface admittance (impedance) about coding meta-atoms is illustrated in Fig. 5. The normalized surface admittance Yes represented by blued solid line and the surface impedance Zms represented by red solid line about coding meta-atoms #1, #5, #8, #10 are matched with the theoretical results (marked by black stars), which result in highly efficient transmission and coding states (0/0, 1/1, 2/2, 3/3). For the other coding meta-atoms, $\textrm{Y}_{\textrm{es}}^{\textrm{yy}}$(blue solid line), $\textrm{Z}_{\textrm{ms}}^{\textrm{yy}}$ (blue dashed line), $\textrm{Y}_{\textrm{es}}^{\textrm{xx}}$(red solid line) and $\textrm{Z}_{\textrm{ms}}^{\textrm{xx}}$ (red dashed line) have the same change rule indicating that the electric resonance and magnetic resonance exist simultaneously, and the four components of the other meta-atoms almost match the theoretical results $\textrm{Y}_{\textrm{es}}^{\textrm{yy}}$ = $\textrm{Z}_{\textrm{ms}}^{\textrm{yy}}$ (blued star) and $\textrm{Y}_{\textrm{es}}^{\textrm{xx}}\textrm{}$= $\textrm{Z}_{\textrm{ms}}^{\textrm{xx}}$ (red star) apart from the coding meta-atoms #3 and #4. Since there are relatively large differences in value of $\textrm{Y}_{\textrm{es}}^{\textrm{yy}}$ and $\textrm{Z}_{\textrm{ms}}^{\textrm{yy}}$ (see in Figs 5 (b) and 5(c)), the induced orthogonal electric source is weak under y-polarized wave incidence. The transmission coefficient tyy of #3 and #4 is 0.65 and 0.64, respectively. Meanwhile, the parameters g1 of #3 and #4 are substantially bigger than the parameter g2, implying that the top metallic structures have a considerable gap and the length of the bottom metallic strip is shortening in the y directions. When the y-polarized THz wave illuminates normally, the resonant currents on the bilayer metallic structure become weak and the transmission coefficient reduce as g1 increases. Thus, the two parameters g1 and g2 are close to each other in order to improve transmitted response and to ensure the required phase.
Fig. 5. Imaginary parts of Yes and Zms of the anisotropic coding meta-atoms (a) #1 (0/0), (b) #2 (0/1), (c) #3 (0/2), (d) #4 (1/3), (e) #5 (1/1), (f) #6 (1/2), (g) #7 (1/3), (h) #5 (2/2), (i) #9 (2/3), (j) #10 (3/3). These imaginary parts $Y_{es}^{yy}$, $Z_{ms}^{yy}\; $($Y_{es}^{xx}$, $Z_{ms}^{xx}$) are denotated by the blue (red) lines.
Hence, we conclude that the transmission phases of x- and y-polarized waves can be controlled independently by altering surface electric admittance and magnetic impedance. By arranging the coding meta-atoms with the certain coding sequences, arbitrary functionality can be independently realized under x- and y-polarized incidence.
3. Results and discussion
Based on the designed coding meta-atoms, we further construct 2-bit anisotropic coding Huygens metasurface (AHCM), which can provide more flexibility in manipulating the transmitted terahertz waves. It is noted that the design is feasible because the proposed metasurface could be processed by the standard lift-off process and electron beam lithography and the far-field measurement could be tested by rotatory THz-TDS [29,39]. Firstly, we encode a metasurface with the coding sequence ‘0-0-1-1-2-2-3-3’ for x polarization incidence and opposite coding sequence for y polarization incidence shown in Fig. 6(a). In this case, the 2D coding matrix is written as follows:
Fig. 6. Control of anomalous refraction on the proposed AHCM. (a) The coding pattern ${\mathbf{M}}_1^{2 - bit}$ composed of a periodic coding sequence Mx “0 0 1 1 2 2 3 3” and opposite sequence My varying along the x direction. Simulated 3D (b) and 2D (c) scattering patterns of the AHCM under x- and y-polarized incidence at 1.37 THz. Simulated 3D (d) and 2D (e) scattering pattern of the coding pattern ${\mathbf{M}}_1^{2 - bit}\; $ under 45° (with respect to the x axis) polarized THz wave at 1.37 THz.
This matrix generates the 2-bit AHCM composed of 40 × 40 anisotropic coding meta-atoms. To obtain the far-field performance of the proposed AHCM, we set the open boundary condition in the x and y directions and excite plane waves from -z to + z in CST Microwave Studio. Fig. 6(b) displays the three-dimensional (3D) far-field scattering patterns of the AHCM under x- and y-polarized normal incidence at 1.37 THz. Based on the designed coding sequence, the deviation angle θ of the coding metasurface [39] is given by:
where D and λ represent the period of the gradient coding sequence and the incident wavelength, respectively. Substituting λ = 218.98 µm (1.37 THz) and D = 800 µm into Eq. (5), the anomalous refraction angle is calculated as -15.89° and 15.89°, respectively, which is highly consistent with the simulated result as displayed in Fig. 6(c). To clearly illustrate the excellent performance of AHCM, Figs. 6(d) and 6(e) present the 3D and 2D far-field scattering pattern under a normally incident wave that is linearly polarized by 45° with respect to the x axis, from which can be seen that the incident terahertz beam is split into two symmetrically beams at the same angle with respect to the z axis. The amplitudes of decomposed x- and y-polarized waves are lower under 45°-polarized waves incidence since the electric-field amplitudes of plane wave under x-, y- and 45°-polarized waves are set to the same values in the simulation, which has a negative effect on the transmission. When the unwanted coupling effect is taken into account, the main-lobe efficiency in Fig. 6(e) is slightly lower than in Fig. 6(c), but the side-lobe level is slightly higher. The intensities of two deflected beams can be flexibly controlled by adjusting the polarization direction of the incident electric field, and this functionality could be developed in many interesting applications.More uniquely, the 2-bit AHCM can be used to realize a terahertz background-free transmission type quarter-wave plate [40,41] that can generate a circularly polarized beam with anomalous refracted feature. A circularly polarized wave is formed by designing the 90° transmission phase difference of meta-atoms under x and y polarizations when a normally incident wave is linearly polarized by 45° with respect to the x axis. Moreover, it can be deflected to an oblique angle when we arrange these meta-atoms by certain phase gradient along x direction, thus forming a free-background circularly polarized wave. Such functionality is achieved by encoding the metasurface with the following 2D coding matrix:
In this case, the method for the construction of AHCM composed of 40 × 40 anisotropic coding meta-atoms is shown in Fig. 7(a). To illustrate the performance of the proposed metasurface, Figs. 7(b) and 7(c) present the 3D and 2D far-field scattering pattern under 45° linearly polarized (respect to the x axis) illumination, which reveal that the normally incident linearly polarized terahertz beam is anomalously refracted to -15.89° in the x-z plane with the axial ratio being 1.02 at 1.37 THz (Fig. 7(d)). Thus, a nearly ideal circularly polarized wave is generated, indicating that the transmission-type quarter-wave plate with excellent performance can be utilized as a high-efficiency circular polarizer and exploited in a number of interesting applications in terahertz system.
Fig. 7. Background-free transmission-type quarter-wave plate achieved by the designed AHCM. (a) The coding pattern $\mathbf{M}_2^{2 - bit}$ composed of periodic coding sequences Mx “0 0 1 1 2 2 3 3” and My “1 1 2 2 3 3 0 0”. Simulated 3D (b) and 2D (c) scattering patterns of the AHCM under 45° (with respect to the x axis) polarized incidence at 1.37 THz. (d) The axial ratio from -20° to -10° in the x-z plane at 1.37 THz.
4. Conclusion
In conclusion, we proposed an ultrathin 2-bit anisotropic Huygens coding metasurface to manipulate the terahertz wave. The required surface electric admittance (Yes) and magnetic impedance (Zms) of coding Huygens meta-atoms is obtained theoretically, which can be well matched by a compact bilayer anisotropic structure. Highly efficient transmission and full phase modulation of x- and y-polarized transmitted wave can be achieved owing to the generation of both surface current and magnetic surface current. Meanwhile, by arranging anisotropic coding Huygens meta-atoms in specific sequences, we also demonstrate the realization of two types coding metasurfaces for multi-anomalous refraction beams generation and background-free transmission type quarter-wave plate. Compared to the pervious Huygens metasurfaces, the bilayer anisotropic Huygens coding metasurface not only reduces structural complexity and manufacturing difficulty, but also adds a new degree of freedom in THz manipulation, which may open up a new platform to realize miniaturization of multifunctional THz device. And our work can reconstruct the coding metasurface from the perspective of surface admittance and impedance, enriching the construction methods of the coding metasurface. Combining coding metasurface with Huygens metasurface can simplify design and optimization procedures and review Huygens metasurface from the perspective of informational science, which extends the application scope of Huygens metasurface.
Funding
National Natural Science Foundation of China (12104044, 62075048); Natural Science Foundation of Shandong Province (ZR2020MF129).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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