High-efficiency and ultra-broadband asymmetric transmission metasurface based on topologically coding optimization method

Wenye Ji; Tong Cai; Guangming Wang; Haipeng Li; Canyu Wang; Haisheng Hou; Chiben Zhang

doi:10.1364/OE.27.002844

1. Introduction

Controlling the polarization states of electromagnetic (EM) waves as we desire plays an essential role in modern communication systems. As a novel polarization controllable phenomenon, asymmetric transmission (AT) has been firstly discovered by Fedotov in 2006 [1]. Since then, AT effect has aroused scholars' great interest and paved a lot of applications due to its unique EM properties. As schematically shown in Fig. 1, asymmetric transmission can realize a difference in transmission for different polarizations or propagation directions (forward and backward) due to the Lorentz reciprocal phenomenon in metasurfaces. More importantly, the transmission waves exhibit different polarization states.

Fig. 1 Schematic diagram of linearly polarized asymmetric transmission. For the forward direction incidence, (a) x-polarized wave passes through the metasurface and converts to y-polarized wave and (c) y-polarized wave is totally reflected. For the backward direction incidence, (b) y-polarized wave passes through the metasurface and converts to x-polarized wave and (d) x-polarized wave is totally reflected.

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In recent years, metasurfaces (MSs) [2–6], as planar version of metamaterials, have demonstrated strong capabilities to control EM waves, generating many fascinating effects such as ultrathin lenses [7–14], planar holograms [15–19], photonic spin Hall effects [20–26] as well as AT effects [27–34]. AT for both circularly polarized waves and linearly polarized waves have been initially explored in either multilayer structures or single layer profiles [29–32]. For instance, a two-layer L-shaped groove structure has been engineered to realize dual-band linear polarization asymmetric transmission [32]. In a recent paper, we experimentally demonstrated that the high-efficiency AT effect for circularly polarized incidence can be realized by three-layer Pancharatnam-Berry (PB) metasurfaces [31]. Unfortunately, the working bandwidth of the AT metasurfaces are very narrow for the intrinsically dispersion effects and large transmission fluctuations, which limited their further applications. It is highly desired to expand the working bandwidth of AT metasurfaces with very high efficiencies.

In this paper, we propose a new strategy by using topological coding optimization method to solve the mentioned bandwidth and efficiency issues for AT metasurfaces. The introduced genetic algorithms significantly suppress the transmission fluctuations and keep a very high efficiency polarization conversion for the transmission waves. A microwave sample is fabricated and experimentally measured. Numerical results coincide well with the measurements, indicating that our metasurface achieves AT within 5.3 GHz to 16.7 GHz with the efficiencies higher than 80%. Our findings open the door for high efficiency broadband meta-devices, which can lead to many exciting applications in communications.

2. Concept and meta-atom design

Starting from the basic theory, we use the Jones matrix to describe the scattering characteristics of electromagnetic waves when they interact with MSs. As shown in the Fig. 2(e), when EM waves are incident on the MS along the z-direction, the electric fields of reflection and transmission waves are respectively expressed by the Jones matrix as following.

Fig. 2 Schematic diagram of the preliminary unit cell structure. (a) Top layer, (b) middle layer (c) bottom layer, (d) perspective view (e) electromagnetic simulation setup. (f) Transmission coefficient of incident wave propagating in z-direction of the preliminary structure. The preliminary design of the unit cell structure is p = 10 mm, b = 10 mm, a = 4 mm. The substrate (blue part) is made of F4B with relative permittivity of 2.65, a loss tangent of 0.009 and a thickness of d = 2.5 mm. The metal (yellow part) is made of copper with conductivity σ = 5.8 × 10⁷ S/m and the thickness 0.036 mm.

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[\begin{matrix} E_{x}^{r} \\ E_{y}^{r} \end{matrix}] = R [\begin{matrix} E_{x}^{i} \\ E_{y}^{i} \end{matrix}] = [\begin{matrix} r_{x x} & r_{x y} \\ r_{y x} & r_{y y} \end{matrix}] [\begin{matrix} E_{x}^{i} \\ E_{y}^{i} \end{matrix}]

[\begin{matrix} E_{x}^{t} \\ E_{y}^{t} \end{matrix}] = T [\begin{matrix} E_{x}^{i} \\ E_{y}^{i} \end{matrix}] = [\begin{matrix} t_{x x} & t_{x y} \\ t_{y x} & t_{y y} \end{matrix}] [\begin{matrix} E_{x}^{i} \\ E_{y}^{i} \end{matrix}]

Where $E_{m}^{i}$ , $E_{m}^{r}$ and $E_{m}^{t}$ (m = x, y) represents the electric field intensities of m-polarized incidence, reflection and refraction, respectively. R and T are the matrices of reflection and transmission coefficients, respectively. The performance of the linear polarization asymmetric transmission is characterized by the parameter Δ_l_in, defined by Eq. (3).

Δ_{l i n}^{x} = {| t_{y x} |}^{2} - {| t_{x y} |}^{2} = - Δ_{l i n}^{y}

The polarization conversion ratio (PCR) is an important factor to describe the cross-polarization conversion efficiency and the purity of the linearly polarized wave in the transmission field [35], which can be defined as

P C R_{x} = \frac{{|t}_{y x} |^{2}}{{|t}_{y x} |^{2} + {|t}_{x x} |^{2}}

P C R_{y} = \frac{{|t}_{x y} |^{2}}{{|t}_{x y} |^{2} + {|t}_{y y} |^{2}}

According to the definition of asymmetric transmission, we firstly proposed a three-layer metal (yellow part) patch structure, in which the first layer is designed to be a grating placed vertically, the third layer is designed to be a grating placed horizontally, and the middle layer is a linear polarizer with 45 degrees of inclination with the cross-polarization conversion function structure, as shown in the Fig. 2. We characterize the EM property of the element by using the CST Microwave Studio, and the simulation setup is shown in Fig. 2(e). Figure 2(f) depicts the transmission coefficients when the structure is shined normally along z axis. We can see that three transmission peaks (black circle symbols) appear at the particular frequencies due to the multi Lorentz resonators induced by the mutual interactions of three metallic layers [36]. However, the transmission peak at 8 GHz is not totally excited because of the large reflection and the low cross-polarization conversion efficiency. Moreover, large fluctuations are obviously observed which is the main reason limiting the working bandwidth and working efficiency of the asymmetric transmission. As a result, the working bandwidth, ordered by transmission cross-polarized conversion t_yx over 0.8, is from 11.4 GHz to 12.7 GHz, corresponding to 10.8%, which is similar to the performance in the literature reported recently [28,29,32,33]. Our main point is to suppress the large transmission fluctuations to improve the working efficiency and enhance the transmission resonances to extend the operating bandwidth.

In our recent research [7], we significantly suppress the transmission fluctuations of the transmissive system by using the ABBA structure. However, it can only be used to improve the transmission of the co-polarization, and it is meaningless to enhance the performance of the cross-polarization transmission coefficients. Here, we propose a new strategy to tune the mutual coupling by using the topologically coding optimization based on genetic algorithm. Since the gratings at both sides of the structure are used to transmit one polarization perfectly while blocking the orthogonal polarization, which is perfect and should not be optimized. Therefore, we optimize the middle structure to tune the mutual coupling interactions. Figure 3(e) presents the flowchart of the optimization process.

Fig. 3 Schematic diagram of the topologically coding optimization process. (a) Topological coding in the middle layer, (b) the middle layer of the optimization unit cell, (c) perspective view of the optimization unit cell, (d) optimized metasurface convergence curve and (e) flowchart of the optimization process.

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Firstly, the fitness function should be confirmed. In our design, we aim to enhance the bandwidth and improve the working efficiency of the asymmetry transmission metasurface. According to the reversibility of electromagnetic wave propagation, we only consider the cross-polarization conversion ratio of x-polarized wave propagating along the z-direction, namely t_yx. We suppose that the lower and upper limits of the maximum bandwidth for achieving a cross-polarization conversion ratio of over 0.8 are F_min and F_max, respectively. In the genetic algorithm, the fitness function is generally used to distinguish the individual's superiority and inferiority, and then natural selection is performed. The smaller the fitness value is, the better the individual is. Therefore, the individual fitness function can be expressed as

η = \frac{1}{\frac{(F_{\max} - F_{\min})}{\frac{(F_{\max} + F_{\min})}{2}} \times 100 %}

Secondly, we build the optimization matrix to join the calculation software of MATLAB and CST Microwave Studio. As shown in Fig. 3(a), the middle layer structure is divided into M × N particles, with the yellow protruding square covering copper and the blue sunken square without copper. In the optimization matrix, each particle can be represented by the 0-1 code sequence. To improve the cross-polarization conversion t_yx, the system should exhibit axial symmetry along the principal diagonal (red dotted line in Fig. 2(b)) [35]. Therefore, the coding sequence of our design is set to be symmetrical along the principal diagonal, which decreases the length of individual sequence and shortens the calculation time. Here, M and N should be chosen to balance the fabrication accuracy and calculation quantity. We set M = N = 20 in our design with each particle exhibiting a size of 0.2 mm. Then, the structure is divided into 210 particles. As a result, genetic algorithm is applied to a string of 210 bits (0-1 code sequence) for each unit cell to maximize the bandwidth of cross-polarization conversion ratio over 0.8. To accelerate the convergence speed of the genetic algorithm, the initial values of the bits are set according to the preliminary unit cell structure in Fig. 2(d). By joining the MATLAB and CST Microwave Studio, we calculate the bandwidth of cross-polarization conversion transmission coefficient t_yx over 0.8 of each unit cell.

Thirdly, natural selection process is performed to obtain the smallest η. After over 170 iterations, the algorithm converged. Mean fitness value decreases significantly with iteration, as shown in Fig. 3(d). According to the optimization values of the bits, we establish the final structure of the middle layer which is shown in Fig. 3(b). Compared with the theoretical analysis [37], our method has considered the mutual coupling among different particles, which improves the design accuracy and can be used to guide the realistic element design directly. The schematic of the asymmetry transmission element is depicted in Fig. 3(c).

To demonstrate our concept, we fabricate a microwave sample composed of a periodic array of meta-atoms (30 × 30 cells with a total size of 300 × 300 mm²) with its upper and middle pictures shown in Figs. 4(a) and 4(b). Then, we experimentally characterize its transmission and reflection characteristics from frontward and backward directions, respectively, and compare the measured results with the simulated spectra based on finite-difference-time-domain (FDTD) simulations. In the former case, we consider the transmission property of the metasurface under frontward incidence for both polarizations. In the experiments, our sample is placed between two horn antennas (~1 m away from the sample), and both horn antennas are connected to the vector network analyzer (Agilent E8362C PNA) by coaxial cables so that the scattering coefficients (t_xx, t_xy, t_yx and t_yy) can be detected and recorded. Figures 4(c) and 4(d) show the numerical and experimental transmissive spectra against frequency for both polarizations. Good agreements between simulations and measurements are observed, indicating the feasibility of our design. The slight difference is attributed to inevitable fabrication errors and imperfections of the incoming wave fronts generated by our microwave horns. From Fig. 4(c), we note that three transmission peaks for the cross-polarization transmission amplitude (|t_yx|) appear at 6.3 GHz (5.4 GHz), 11.1 GHz (10.8 GHz) and 15.6 GHz (14.5 GHz) for the measurements (simulations), respectively, with the transmission amplitude reaching 0.92 (0.93), 0.95 (0.97) and 0.95 (0.92). More importantly, the transmission fluctuations are largely suppressed due to the introduction of the topologically coding optimization. As a result, the bandwidth of our asymmetry transmission element is about 11.4 GHz, ranging from 5.3 GHz to 16.7 GHz, corresponding to 103.6%, which is several times than those of the reported metasurfaces (see the details in Table 1) [28,29,32,33]. In order to further understand the physical mechanism of broadband asymmetric transmission, we plot the current distributions on the surface of the meta-atom at three peaks of |t_yx|, as shown in Figs. 5(a)-5(c). From Fig. 5, we could find that the current directions of the top layer and the bottom layer are orthogonal to each other in broad bandwidth, which results in broadband and high-efficiency cross-polarization conversion transmission. The other three transmission modes (t_xx, t_yy, t_xy) are totally suppressed among the whole frequency range. In the latter case, the reflection spectra for both polarizations are measured. The characterization procedures are essentially the same as those for the transmission-mode property, only with the receiving antenna now placed at the reflection side of the device. As shown in Figs. 4(e) and 4(f), we can find that better than 90% reflection is obtained for |r_yy| among frequency range 4-15.5 GHz and 4-13.6 GHz for measurements and simulations. The relative bandwidth reaches 117.9% and 109.1%, respectively. Meanwhile, other three modes (r_xy, t_yy, t_xy) are below 0.2 among the whole frequency range. For the backward incidence, our metasurface exhibits a similar performance just by exchanging the polarizations because of the reversibility of electromagnetic waves propagation, and the corresponding simulated spectra are plotted in Figs. 4(g) and 4(h).

Fig. 4 (a) Top layer, bottom layer and (b) middle layer of the fabricated sample. Simulation and experiment results of (c) cross-polarized transmission coefficient and (d) co-polarized transmission coefficient. Simulation and experiment results of (e) cross-polarized reflection coefficient and (f) co-polarized reflection coefficient. Simulation results of (g) transmission and (h) reflection coefficients of electromagnetic waves propagating along -z-direction.

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Table 1. The comparison between references and our work.

View Table

Fig. 5 Schematic diagram of current distributions on surface of the meta-atom at three peaks of |t_yx| at (a) 5.4 GHz, (b) 10.8 GHz and (c) 14.5 GHz.

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Next, we discussed the asymmetric transmission (AT) property ( $Δ_{l i n}^{}$ ) and PCR performance of the structure. $Δ_{l i n}^{}$ can be retrieved based on the simulated and measured transmission spectra, and the results are shown in Fig. 6(a). From the experimental results, $Δ_{l i n}^{x}$ reaches a high level above 0.6 from 5.1 GHz to 16.6 GHz, while y polarization has a high $Δ_{l i n}^{x}$ for the backward incidence, which validates the asymmetric transmission effect of our structure. Figure 6(b) shows experimental and simulated PCR results of incident wave propagating along the frontward direction. From Fig. 6(b), we could find the experimental results are in good agreement with the simulation results. In addition, the experimental results show the maximum PCR of x-polarized incident wave is 0.98 at 9.9 GHz and the PCR is above 0.9 from 5.4 GHz to 16.7 GHz. The relative bandwidth is 102.2%. The results above indicate most of x-polarized wave converts to y-polarized wave when it passes through the metasurface. However, PCR of y-polarized incident wave is lower than 0.2 from 4 GHz to 15.5 GHz. This phenomenon shows the great purity of the linearly polarized wave in the transmission field and proves the robust asymmetric transmission effect of the structure we designed. These results show the high efficiency transmission cross-polarized conversion of the structure, which indicates that our method is effective.

Fig. 6 Simulation and experiment results of (a) asymmetric transmission effect parameter $Δ$ and (b) PCR of incident wave propagating along the z-direction.

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3. Conclusions

In this paper, we propose a novel unit cell by using topologically coding optimization to realize high efficiency and ultra-broadband asymmetric transmission. The unit cell achieved perfect reflection and high-efficiency cross-polarized conversion transmission over 0.8 for y- and x-polarized incidence from 5.3 GHz to 16.7 GHz, respectively. The relative bandwidth reaches 103.6%, which is broadened extremely compared with available technology reported at present. In addition, we fabricated a sample and the experiment results are in great agreement with the simulation results, demonstrating that the proposed new structure could realize asymmetric transmission of the linearly polarized waves as prediction. Thus, the general method we proposed is effective and makes the simple structure we designed has more potential application value in devices such as a polarization rotator and a polarization isolator.

Funding

National Natural Science Foundation of China (NSFC) (61871394, 61701572); Aeronautical Science Foundation of China (ASFC) (20151896014).

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	Structure Characteristics	Structure Layers	Frequency Range of Transmission above 0.8	Relative Band
Literature [28]	F-shaped	Two layers	8.5 GHz-10.7 GHz 12.8 GHz-13.3 GHz 17.8 GHz-19 GHz	22.9% 3.8% 6.5%
Literature [29]	I-shaped	Two layers	10.6 GHz-10.9 GHz 14.3 GHz-14.8 GHz	2.8% 3.4%
Literature [32]	L-shaped	Two layers	3.2 GHz-3.3 GHz 3.6 GHz-3.7 GHz	3.1% 2.7%
Literature [33]	H-shaped	Three layers	7.2 GHz-7.9 GHz 9.4 GHz-9.8 GHz 12.9 GHz-16.2 GHz	9.3% 4.2% 22.7%
Our Work	Reciprocal vertical gratings with topology structure	Three layers	5.3 GHz-16.7 GHz	103.6%

High-efficiency and ultra-broadband asymmetric transmission metasurface based on topologically coding optimization method

Abstract

1. Introduction

2. Concept and meta-atom design

3. Conclusions

Funding

References

Cited By

Figures (6)

Tables (1)

Equations (6)

Optics Express