1.Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China 2.Wuhan Maritime Communication Research Institute Wuhan 430200, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 61675074)
Received Date:30 December 2020
Accepted Date:20 May 2021
Available Online:17 September 2021
Published Online:05 October 2021
Abstract:A kind of off-axis meta-lens with large focal depth based on a single-layer metasurface is designed and fabricated. Our proposed off-axis focus is realized by combining the two functions of deflection and focus through phase superposition method, and the focal depth can be increased by optimizing the input aperture and off-axis deflection angle. Three-dimensional finite difference time domain (FDTD) method is used for numerical simulation to construct the off-axis meta-lens, then the off-axis meta-lens is fabricated and its focus performance is tested in a microwave anechoic chamber.Experimental results indicate that at the designed electromagnetic wave frequency (9 GHz), the measured off-axis deflection angle is 27.5° and the focal length is 335.4 mm, which agree with the designed values of 30° and 350 mm. The measured full-wave half-maximum (FWHM) at the focal point is 48.2 mm, however, the simulated FWHM is 40.2 mm, which means that the imaging quality of the measured focus spot is slightly worse than the simulated one. This is mainly due to the fact that the actual parameters of the fabricated meta-lens are inconsistent with simulated parameters. In addition, during the measurement, the large sampling interval in the x- direction also leads to experimental errors.The focusing efficiency of the off-axis meta-lens at the working frequency of 9 GHz is calculated to be 16.9%. The main reason for the low focusing efficiency is that the plasmonic metasurface works in the transmission mode, which can manipulate only the cross-polarized component of the incident wave, and the maximum efficiency will not exceed 25%. Moreover, the focal depths at 8 GHz, 9 GHz and 10 GHz are 263.2 mm, 278.5 mm and 298.2 mm, respectively, which are 7.02 times, 8.36 times and 9.98 times the corresponding wavelengths, indicating that a larger focal depth off-focus meta-lens is achieved. This kind of off-axis meta-lens has a simple structure, good off-axis focus ability and large focal depth, which has potential applications in a compact and planar off-axis optical system and large focal depth imaging system. Although the working waveband in this article is the microwave band, according to the size scaling effect of the metasurface, it is also possible to design a large focal depth off-axis meta-lens in other bands such as visible light and terahertz bands by using the same method. Keywords:metasurface/ meta-lens/ large focal depth/ phase superposition
3.器件结构及参数离轴超透镜由制作在FR4介质衬底上方的多个L型铜天线组成, 图2(a)给出了离轴超透镜天线单元的结构. 天线单元的长度和宽度均为p = 12 mm, FR4衬底层的厚度为t = 3.79 mm, L型铜天线的厚度为t1 = 0.07 mm, 宽度为w = 2 mm, 两个臂长分别为lx和ly, 且lx = ly, 具体的取值要根据相位分布要求来确定. 图 2 (a)离轴超透镜的天线单元; (b)当频率为9 GHz的x偏振波垂直入射到天线单元时, 正交偏振波的透射率和透射相位随lx的变化关系; (c)满足(3)式的相位分布 Figure2. (a) Antenna unit of the off-axis meta-lens; (b) when an x-polarized wave with frequency of 9 GHz is incident perpendicularly onto the antenna units, transmittance and transmission phase of the orthogonal polarized wave vary with lx; (c) phase distributions satisfying Eq. (3).
为了构建出这种离轴超透镜, 首先, 需要寻找L型天线的臂长lx与透射相位之间的依赖关系. 采用三维时域有限差分(FDTD)方法进行数值仿真. 图2(b)给出了当频率为9 GHz的x偏振波垂直照射到超表面天线单元时, 其正交偏振波的透射率和透射相位随臂长lx的变化关系. 当lx从5.5 mm逐渐增加到10.5 mm时, 正交偏振波的透射率在0.13以上, 透射相位可以覆盖0°—180°. 对于等离子超表面, 将天线单元旋转90°后, 正交偏振分量可以获得额外的180°相位变化[23]. 即, 利用上述原则的操作, 入射正交偏振波的相位可以实现0°—360°范围的变化, 由此就可以设计出合适的天线单元来组成超表面以对透射波的正交偏振分量进行随意操控. 在工作频率f0 = 9 GHz处, 将焦距设置为F0 = 350 mm. 同时, 为了得到较大的焦深, 将透射波束的偏转角度设置为α = 30°、超透镜的入射孔径设置为D = 400 mm. 然后, 基于(3)式计算出相位分布(如图2(c)所示), 并利用图2(b)来选取天线的臂长取值, 依据(3)式的相位分布将这些天线进行排布, 便可构建出所需要的离轴超透镜. 图3(a)为实际制备的超表面样品的照片(矩形红色虚线为局部放大图), 样品总尺寸为400 mm × 400 mm. 图3(b)为实验测试装置. 在微波暗室中, 由发射天线发射出的x极化的电磁波信号垂直照射至测试样品, 然后透射的y极化电磁波信号被接收天线接收. 透射电磁波的电场强度分布通过矢量网络分析仪进行测量并记录. 图 3 (a)制备的超表面样品的正面结构照片, 矩形红色虚线为局部放大图; (b)实验装置 Figure3. (a) Image of the fabricated metasurface sample, and the rectangular red dotted line is a zoom view; (b) experimental set-up.
4.实验结果与分析为了验证所设计超透镜的离轴聚焦功能, 分别选择频率为8, 9和10 GHz的x偏振波垂直照射到该超透镜上, 测试得到的正交偏振波(即y偏振波)的电场强度分布如图4(a)—图4(c)所示. 可以清楚地看到, 由于超表面的色散特性, 其离轴的聚焦点是随频率变化的, 三个频率下的聚焦点的位置可以用(x, z)坐标值来表示, 分别为(–221.3 mm, –278.9 mm), (–231.5 mm, –335.4 mm)和(–220.8 mm, –400.2 mm). 特别地, 在工作频率f0 = 9 GHz处, 测试得到的离轴偏转角为α = 27.5°(预设值为30°), 焦点在z方向上的距离约为F0 = 335.4 mm (预设值为350 mm), 测试值与预设值符合得比较好, 表明所设计的超表面可以同时实现波束偏转和聚焦, 即离轴聚焦的功能. 图 4 测试得到的不同频率处正交偏振波的电场强度分布 (a) 8 GHz; (b) 9 GHz; (c) 10 GHz. 红色点划线代表聚焦平面所在的位置, 倾斜的白色虚线代表u1轴、u2轴和u3轴 Figure4. Measured electric field intensity distributions of the orthogonal polarized waves at different frequencies: (a) 8 GHz; (b) 9 GHz; (c) 10 GHz. The red dotted lines represent the position of the focal planes, and the white dashed lines represent the u1 axis, u2 axis and u3 axis.
透镜焦点处的半峰全宽(full-wave half-maximum, FWHM)可以描述透镜聚焦光斑的成像质量. 一般来说, FWHM越小意味着聚焦能量越集中. 图5(a)和图5(b)分别给出了在预设的工作频率9 GHz处, 透镜焦点平面处归一化电场强度分布的仿真结果和实验结果. 可以看出, 仿真结果中焦点处的半峰全宽FWHM = 40.2 mm, 而实验结果中焦点处的半峰全宽达到了FWHM = 48.2 mm, 因此实际光斑的成像质量要略差一些. 出现这样的误差的原因如下: 样品制作中的工艺误差使得样品实际参数与仿真中的参数不一致. 此外, 在实验测试过程中, x方向上的采样间距过大也导致了实验误差. 除此之外, 还计算了频率为8和10 GHz时透镜焦点处的半峰全宽, 分别为59.2和53.5 mm. 图 5 工作频率9 GHz处, 透镜焦点处归一化电场强度分布 (a)仿真结果; (b)实验结果 Figure5. At the working frequency of 9 GHz, the normalized electric field intensity distribution at the focal point of the metalens: (a) Simulation result; (b) experimental result.