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超表面是由二维元素微结构周期性或非周期性排列的人工电磁材料, 能够操纵电磁波的振幅和相位, 实现偏振转换[1-4] 、完美吸收[5]振幅和相位调制[6-8] 等特殊功能. 2014年, Cui等[9]提出了微波的数字编码超表面概念. 近年来, 编码超表面在太赫兹频率波段也受到了广泛关注, 研究人员通过使用编码超表面实现了太赫兹波束偏转[10-15]、光谱成像[16-18]、偏振操纵[19-26]、聚焦[27-29]等功能. 2020年, Chen等[30]提出用于涡旋太赫兹波束操纵和聚焦的多功能反射编码超表面. 2021年, Saifullah等[31]提出一种结构为“四叶草形”的编码超表面, 并实现了超宽带漫散射. 2022年, Li等[32]设计了一种左右圆极化太赫兹多功能编码超表面. 上述报道的超表面都是在单一偏振态太赫兹波入射下通过相位、幅度等参数的差异编码构造超表面实现波束分裂、波束偏转和涡旋波束操纵等功能, 由于只利用电磁波单一偏振态, 所以对太赫兹波调控灵活性降低.
本文提出太赫兹多波束调控反射编码超表面, 它将几何相位和幅度变化相结合, 在不同偏振的太赫兹波入射下实现不同的太赫兹波调控功能. 模拟的近场和远场辐射模式, 结果与理论计算预测一致, 设计的超表面提供了一种太赫兹波偏振和相位操控自由度方法, 极大地提高了太赫兹波操纵的效率.
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本文提出的编码超表面结构如图1所示, 其中图1(a)为所设计的幅度编码超表面, 利用入射线偏振 (LP) 波产生反射波的幅度差值进行编码, 图1(b)为相位编码超表面, 通过旋转顶层金属图案利用入射圆偏振 (CP) 波产生PB相位 (几何相位)进行编码. 超表面单元结构如图1(c)所示, 单元周期P = 65 μm, 由3层介质组成, 分别为金属图案(外径r1 = 30 μm, 内径r2 = 25 μm, 厚度为d1 = 0.125 μm), 中间硅介质层(εr = 11.9, 厚度h = 25 μm), 金属板薄膜层(厚度d2 = 2 μm). α是单元结构金属图案沿逆时针方向旋转角度.
图 1 编码超表面结构示意图 (a) 幅度编码超表面; (b) 相位编码超表面; (c) 超表面单元
Figure 1. Schematic diagram of the proposed coding metasurface: (a) Amplitude coding metasurface; (b) phase coding metasurface; (c) unit cell.
利用几何相位原理构造编码超表面, 编码单元所对应的俯视图和相位如表1所示. 对于1-bit数字编码超表面, 数字“0”和“1”代表反射波相对于入射波的相位差为180°的两种编码单元, 对应单元的反射相位为 –137.21°和 43.99°; 对于2-bit数字编码超表面, 它由4个编码单元组成, 分别对应 –137.21°, –49.09°, 43.99°和 131.99°的反射相位响应, 对应的数字 “00”, “01”, “10”和“11”代表反射波相对于入射波的相位差为90°的4个编码超表面单元. 编码单元对应的反射幅度和反射相位如图2(a), (b)所示, 可以看出, 在0.48—0.68 THz之间, 太赫兹波反射幅度均大于0.8, 相邻编码单元反射波相对于入射波的相位差接近90°, 满足2-bit编码超表面设计要求.
1-bit相位编码 0 1 2-bit相位编码 00 01 10 11 旋转角度/(°) 0 45 90 135 相位/(°) –137.21 –49.09 43.99 131.99 俯视图 
表 1 编码超表面单元
Table 1. Unit cell of the proposed coding metasurface.
图 2 圆极化波入射时超表面单元的反射振幅和相位 (a)反射振幅; (b)反射相位
Figure 2. Reflection amplitude and phase of the unit cell under the circularly polarized wave incidence: (a) Reflection amplitude; (b) reflection phase.
编码超表面一般包含有限种单元, 凭借离散化的数字编码序列来调控电磁波, 核心思想是将数字化的二进制编码融入超表面的结构、电磁参数、功能等设计的各个方面. 编码超表面由N × N个相同尺寸为D的方形栅格构成, 每个栅格填充由“0”和“1”单元构成的子阵列, 其散射相位设为φ = (m, n). 在平面波垂直入射的情形下, 超表面的远场函数可表示为
$ \begin{split} f(\theta ,\varphi ) =\;& {f_{\text{e}}}(\theta ,\varphi )\sum\limits_{m = 1}^N \sum\limits_{n = 1}^N \exp \Bigr\{ - {\text{i}} \big\{ \varphi (m,n) \\ & + KD\sin \theta [ (m - 1/2)\cos \varphi \\ & + (n - 1/2)\sin \varphi \big] \big\} \Bigr\}, \end{split} $ 式中θ 和φ 为任意方向上的俯仰角和方位角, fe(θ, φ)为栅格方向函数, 其中θ = arcsin (λ/Γ), λ是自由空间波长, Γ 表示编码序列周期长度. 根据广义斯涅耳定律和超表面散射的远场函数, 反射波束的方位角(φ)和单元“0”或“1”编码粒子的长度(Dx)和宽度(Dy)满足以下关系:
$ \begin{split} & \varphi = \pm \arctan ({D_x}/{D_y}) \text{, } \\ & \varphi = {\text{π }} \pm \arctan ({D_x}/{D_y}). \end{split} $ -
圆极化太赫兹波的垂直入射下, “0”和“1”交错的编码超表面将产生双波束反射, 而用“0”和“1”二维棋盘格编码时, 编码超表面会产生对称的四波束反射. 首先, 设计了如图3(a)所示的编码超表面, 每个“0”和“1”单元格都是由6×6个编码粒子组成, 编码序列“000000-111111···”沿 x 方向呈周期性排列, 沿y方向排布, 编码周期Γ = 780 µm. 当圆极化太赫兹波垂直入射到超表面上时, 在0.5 THz处, 入射太赫兹波沿着x轴被分为两束对称的反射波, 其三维远场如图3(b)所示. 图3(c)描绘了在0.5 THz处反射模式下两分束的归一化幅度曲线, 两个反射波束的峰值分别在–50°和50°出现, 即偏转角为50°. 利用公式计算θ = arcsin (λ/Γ) = 50.2°, 结合归一化反射幅度曲线和三维远场图可以得出模拟与理论计算结果符合.
图 3 产生两分束太赫兹反射波的1-bit编码超表面 (a) 编码排布示意图; (b) 三维远场散射图; (c) 归一化反射振幅图
Figure 3. 1-bit coding metasurface for generating two-reflected beam: (a) Layout diagram of coding metasurface; (b) three-dimensional far field scattering diagram; (c) normalized reflection amplitude diagram.
此外, 本文还排布了一个棋盘编码超表面, 该结构周期性地使用数字序列“000000-111111/111111-000000··· ” 沿 x 方向呈周期性排布, 沿 y 方向排列, 编码周期Γ = 1103 µm, 如图4(a)所示. 当圆极化太赫兹波垂直入射到编码超表面上时, 在0.55 THz处的三维远场和归一化反射振幅图如图4(b), (c)所示. 可以观察到, 入射太赫兹波被分为四束对称的反射波.
图 4 产生四分束的1-bit编码超表面 (a) 编码排布示意图; (b) 三维远场散射图; (c) 归一化反射振幅图
Figure 4. 1-bit coding metasurface for generating quadrant beam: (a) Layout diagram of coding metasurface; (b) three-dimensional far field scattering diagram; (c) normalized reflection amplitude diagram.
为了更加灵活地获得任意散射角调控功能, 本文将编码序列进行基本的卷积运算, 不同编码序列的加法卷积运算可以实现不同的编码周期, 从而获得对入射太赫兹光波不同的散射角度或任意角度. 对于“00”, “01”, “10”, “11”的编码粒子, 每一个编码单元由6×6个编码粒子组成, 四位卷积计算可以执行为 “00 + 00 = 00”, “00 + 11 = 11”, “10 + 10 = 00”, “11+ 10 = 01” 和 “11 + 11 = 10”, 编码超表面的新卷积序列“S3 = S1 + S2”. 结合数字编码原理和卷积定理, 所设计的编码超表面序列S1, S2和S3如图5(a)—(c)所示. 编码超表面序列S1(“00-01-10-11…”)沿x方向呈周期性排列, 沿y方向排布, 当左圆偏振太赫兹波入射到超表面S1时, 在0.48 THz处产生了反射波束的偏转, 相应的三维(3D)和二维(2D)散射图如图5(d), (g)所示, 入射太赫兹波以θ = arcsin (λ/Γ) = 24°的反射波束角度偏转. 编码超表面序列S2 (“00-10”···)是沿y方向呈周期性排列、沿x方向排布的编码超表面, 其3D和2D散射图如图5(e), (h)所示. 可以看出, 太赫兹波被分成两个对称的反射波束, 偏转角为θ = arcsin (λ/Γ) = 53.25°. 编码超表面序列S3 (“00-01-10-11···\10-11-00-01···”) 由S1和S2叠加组成, 根据傅里叶变换的卷积定理, 卷积编码超表面S3的远场散射图由两个编码序列的远场散射图叠加组成, 编码超表面序列S3的3D和2D散射图如图5(f), (i)所示, 可见当左圆极化太赫兹波照射到超表面S3上时, 其反射波束分离成了4个偏转光束, 卷积编码超表面可以实现对反射波束的偏转和分裂.
图 5 编码超表面卷积过程示意图 (a)—(c) S1, S2和S3的超表面单元排布示意图; (d)—(f) 0.48 THz处左圆偏振入射时, S1, S2和S3的3D远场散射图; (g)—(i) 0.48 THz处左圆偏振入射时, S1, S2和S3的2D散射图
Figure 5. Convolution process schematic diagram of the coding metasurface: (a)–(c) Layout diagram of S1, S2 and S3 metasurfaces; (d)–(f) 3D far-field scattering diagram of S1, S2 and S3 under left circularly polarized incidence at 0.48 THz; (g)–(i) 2D scattering diagram of S1, S2 and S3 under left circularly polarized incident at 0.48 THz.
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2-bit编码超表面设计是利用圆极化太赫兹波入射控制反射波束, 实现波束散射角的偏转. 预设的2-bit编码超表面“00-01-10-11···”沿x 方向周期性排布, 沿 y 方向排列, 每个“00” “01” “10” “11”单元格都是由6×6个编码粒子组成, 周期为 Γ = 1560 µm, 超表面单元排布如图6(a), (b)所示. 在0.48 THz处, 当左圆极化太赫兹波垂直入射到编码超表面上时, 太赫兹反射波束发生了偏转, 其三维远场图及对应的归一化幅度曲线分别如图6(c), (d)所示. 从图中可以看出, 相对于z轴的正方向, 反射波束的偏转角接近24°, 偏转角可以利用公式计算出θ = arcsin (λ/Γ) = 23.62°, 仿真结果与计算结果一致. 类似地, 设计的其他 2-bit编码超表面编码序列“0000-0101-1010-1111”沿 x 方向周期性排布, 沿y方向排列, 每个“00” “01” “10” “11”单元格都是由6×6个编码粒子组成, 周期 Γ = 3120 µm, 其超表面单元排布如图7(a), (b)所示. 在0.48 THz处, 当左圆极化太赫兹波垂直入射到编码超表面, 太赫兹反射波束发生了偏转. 编码超表面在反射模式下太赫兹波散射主瓣的三维远场图和对应的归一化反射幅度曲线图如图7(c), (d)所示, 可以看出相对于z轴正方向出现了12°偏转, 理论计算的θ = 11.56°, 这与图7(c), (d)所示的模拟结果非常一致. 结果表明, 可以通过改变编码周期来设计超表面使其反射波束偏转到指定的角度.
图 6 2-bit反射编码超表面(“00-01-10-11···”) (a) 超表面排布示意图; (b) 超表面结构; (c) 三维远场散射图; (d) 归一化反射振幅图
Figure 6. 2-bit reflected coding metasurface (“00-01-10-11···”): (a) Layout diagram of coding metasurface; (b) metasurface structure; (c) three-dimensional far field scattering diagram; (d) normalized reflection amplitude diagram.
图 7 2-bit反射编码超表面(“0000-0101-1010-1111”) (a) 超表面排布示意图; (b) 超表面结构; (c) 三维远场散射图; (d) 归一化反射振幅图
Figure 7. 2-bit reflection encoding metasurface (“0000-0101-1010-1111”): (a) Layout diagram of coding metasurface; (b) metasurface structure; (c) three-dimensional far field scattering diagram; (d) normalized reflection amplitude diagram.
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当线极化太赫兹波入射到超表面单元时, 反射幅度和反射相位的曲线如图8(a), (b)所示. 线极化波入射到超表面单元时, 两个不同超表面单元的反射幅度差异较大, 利用偏振反射幅度差异化特性可以实现近场成像效应. 编码超表面设计为具有两个灰度级(即亮和暗)对应于“1”和“0”的编码单元, 利用振幅编码显示超表面. 幅度高的编码为“1”, 幅度低的编码为“0”, 其编码单元结构如图8(a)所示.
图 8 线极化波入射时超表面单元产生的反射幅度和反射相位 (a) 反射幅度; (b)反射相位
Figure 8. Reflected amplitude and phase of the unit cell under linearly polarized wave incidence: (a) Reflection amplitude; (b) reflection phase.
设计 “CJLU” 图案由两种不同类型的超表面单元结构分别排布在字母方框内外两块区域, 字母部分选择用幅度编码为“1”的单元排布, 字母以外的其余部分用幅度编码为“0”的单元排布, 编码超表面由32×32个单元组成, 如图9(a)—(d)所示, 超表面设置的 “CJLU” 编码图案的轮廓在电场中明显显示出来. 红色部分对应高幅度的编码单元, 蓝色部分对应低幅度的编码单元. 在观测频率为1.22 THz时, 观测平面距离编码超表面60, 80和100 μm的近场图像显示分别如图10—图12所示. 编码图案的近场图像显示随着编码图案单元的增加而增大, “CJLU”编码图案轮廓边缘存在些许的不规则, 是由于两个编码单元幅度差异分布不均匀引起的电场能量分布不均匀, 观测距离为80 μm时可得到最佳的近场图像. 总体而言, 仿真得到的成像效果与预设图像大小、位置、轮廓方面的模拟结果较符合, 验证了利用偏振反射幅度差异化特性可以实现近场成像效应.
图 9 “CJLU”超表面排布示意图
Figure 9. Layout diagram of "CJLU" metasurface.
图 10 观测频率1.22 THz处, 观测平面距离为60 μm的近场图像
Figure 10. Near field image on an observation plane of 60 μm distance at 1.22 THz.
图 11 观测频率1.22 THz处, 观测平面距离为80 μm的近场图像
Figure 11. Near field image on an observation plane of 80 μm distance at 1.22 THz.
图 12 观测频率1.22 THz处, 观测平面距离为100 μm的近场图像
Figure 12. Near field image on an observation plane of 100 μm distance at 1.22 THz.
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本文结合几何相位和幅度两种参量的变化, 提出了一种太赫兹多波束调控反射编码超表面, 在圆偏振入射太赫兹光波作用下, 所设计的超表面结构在0.48—0.68 THz频段内可以实现太赫兹波束分裂和反射模式下波束偏转, 利用卷积运算可以对圆偏振入射太赫兹光波产生反射多波束调控. 在线偏振态太赫兹光波入射下, 所设计的幅度编码超表面可以在1.22 THz处实现成像功能. 研究结果表明, 所设计的超表面对太赫兹波偏振和相位操控自由度提供了一种新思路, 为实现太赫兹波前的动态操作开辟了一条新途径, 在太赫兹系统具有广阔的应用潜力.
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Most of reported coding metasurfaces only use phase encoding or amplitude encoding to regulate electromagnetic waves, which limits the flexibility of terahertz wave regulation. In this work, a metasurface element structure is proposed. The metasurface element is composed of three layers, i.e. metal pattern structure layer, intermediate medium layer, and metal base layer. According to the geometric phase principle, the phase coverage in the 2π range can be achieved by rotating the metal pattern structure layer under the incidence of the circular-polarized terahertz wave. The metasurface element structure is arranged reasonably by using the phase coding, and the 1-bit and 2-bit phase coding metasurface are designed. First of all, the coding metasurface with interlacing “0” and “1” is designed to generate a double beam reflection under the vertical incidence of circular polarized terahertz waves, while the two-dimensional checkerboard coding metasurface with “0” and “1” generates a symmetrical four-beam reflection. In addition, the metasurface is designed to deflect the reflected beam, and the coding period is changed to design the metasurface to deflect the reflected beam to the specified angle, showing good flexibility. Finally, the convolutional operation is introduced to flexibly regulate the circular polarized beam, and the functions of beam splitting and reflection beam deflection are obtained. The amplitude coded metasurface is designed under theincidence of the online polarized terahertz wave, and the near-field imaging effect can be realized by the amplitude differentiation of polarization reflection. The designed amplitude coded metasurface realizes the function of imaging in space, presenting the designed “CJLU” pattern, which has different imaging effects at different observation locations. When the observation plane distance is 80 μm at the observation frequency of 1.22 THz, the near-field imaging effect is best. In conclusion, we propose a terahertz multibeam modulation reflection-coded metasurface, which combines geometric phase and amplitude variation to achieve different terahertz wave modulation functions under different polarization incident terahertz waves. The results from the simulated near-field radiation model and the far-field radiation model are both in agreement with the theoretical calculation predictions. The designed metasurface provides a degree of freedom method for terahertz wave polarization and phase manipulation, which greatly improves the efficiency of terahertz wave manipulation and has potential applications in terahertz systems.
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Keywords:
- terahertz /
- terahertz beam splitting /
- beam deflection /
- terahertz imaging
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图 1 编码超表面结构示意图 (a) 幅度编码超表面; (b) 相位编码超表面; (c) 超表面单元
Fig. 1. Schematic diagram of the proposed coding metasurface: (a) Amplitude coding metasurface; (b) phase coding metasurface; (c) unit cell.
图 2 圆极化波入射时超表面单元的反射振幅和相位 (a)反射振幅; (b)反射相位
Fig. 2. Reflection amplitude and phase of the unit cell under the circularly polarized wave incidence: (a) Reflection amplitude; (b) reflection phase.
图 3 产生两分束太赫兹反射波的1-bit编码超表面 (a) 编码排布示意图; (b) 三维远场散射图; (c) 归一化反射振幅图
Fig. 3. 1-bit coding metasurface for generating two-reflected beam: (a) Layout diagram of coding metasurface; (b) three-dimensional far field scattering diagram; (c) normalized reflection amplitude diagram.
图 4 产生四分束的1-bit编码超表面 (a) 编码排布示意图; (b) 三维远场散射图; (c) 归一化反射振幅图
Fig. 4. 1-bit coding metasurface for generating quadrant beam: (a) Layout diagram of coding metasurface; (b) three-dimensional far field scattering diagram; (c) normalized reflection amplitude diagram.
图 5 编码超表面卷积过程示意图 (a)—(c) S1, S2和S3的超表面单元排布示意图; (d)—(f) 0.48 THz处左圆偏振入射时, S1, S2和S3的3D远场散射图; (g)—(i) 0.48 THz处左圆偏振入射时, S1, S2和S3的2D散射图
Fig. 5. Convolution process schematic diagram of the coding metasurface: (a)–(c) Layout diagram of S1, S2 and S3 metasurfaces; (d)–(f) 3D far-field scattering diagram of S1, S2 and S3 under left circularly polarized incidence at 0.48 THz; (g)–(i) 2D scattering diagram of S1, S2 and S3 under left circularly polarized incident at 0.48 THz.
图 6 2-bit反射编码超表面(“00-01-10-11···”) (a) 超表面排布示意图; (b) 超表面结构; (c) 三维远场散射图; (d) 归一化反射振幅图
Fig. 6. 2-bit reflected coding metasurface (“00-01-10-11···”): (a) Layout diagram of coding metasurface; (b) metasurface structure; (c) three-dimensional far field scattering diagram; (d) normalized reflection amplitude diagram.
图 7 2-bit反射编码超表面(“0000-0101-1010-1111”) (a) 超表面排布示意图; (b) 超表面结构; (c) 三维远场散射图; (d) 归一化反射振幅图
Fig. 7. 2-bit reflection encoding metasurface (“0000-0101-1010-1111”): (a) Layout diagram of coding metasurface; (b) metasurface structure; (c) three-dimensional far field scattering diagram; (d) normalized reflection amplitude diagram.
图 8 线极化波入射时超表面单元产生的反射幅度和反射相位 (a) 反射幅度; (b)反射相位
Fig. 8. Reflected amplitude and phase of the unit cell under linearly polarized wave incidence: (a) Reflection amplitude; (b) reflection phase.
图 10 观测频率1.22 THz处, 观测平面距离为60 μm的近场图像
Fig. 10. Near field image on an observation plane of 60 μm distance at 1.22 THz.
图 11 观测频率1.22 THz处, 观测平面距离为80 μm的近场图像
Fig. 11. Near field image on an observation plane of 80 μm distance at 1.22 THz.
图 12 观测频率1.22 THz处, 观测平面距离为100 μm的近场图像
Fig. 12. Near field image on an observation plane of 100 μm distance at 1.22 THz.
表 1 编码超表面单元
Table 1. Unit cell of the proposed coding metasurface.
1-bit相位编码 0 1 2-bit相位编码 00 01 10 11 旋转角度/(°) 0 45 90 135 相位/(°) –137.21 –49.09 43.99 131.99 俯视图 
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