基于介质超表面的径向偏振贝塞尔透镜

陈俊妍, 张飞, 张明, 等. 基于介质超表面的径向偏振贝塞尔透镜[J]. 光电工程, 2018, 45(11): 180124. doi: 10.12086/oee.2018.180124
引用本文: 陈俊妍, 张飞, 张明, 等. 基于介质超表面的径向偏振贝塞尔透镜[J]. 光电工程, 2018, 45(11): 180124. doi: 10.12086/oee.2018.180124
Chen Junyan, Zhang Fei, Zhang Ming, et al. Radially polarized Bessel lens based on all-dielectric metasurface[J]. Opto-Electronic Engineering, 2018, 45(11): 180124. doi: 10.12086/oee.2018.180124
Citation: Chen Junyan, Zhang Fei, Zhang Ming, et al. Radially polarized Bessel lens based on all-dielectric metasurface[J]. Opto-Electronic Engineering, 2018, 45(11): 180124. doi: 10.12086/oee.2018.180124

基于介质超表面的径向偏振贝塞尔透镜

  • 基金项目:
    国家自然科学基金资助项目(61575032)
详细信息
    作者简介:
    通讯作者: 喻洪麟(1954-),女,博士,教授,博士生导师,主要从事新型微纳红外偏振调控器原理的研究。E-mail:hlyu@cqu.edu.cn
  • 中图分类号: O436.3

Radially polarized Bessel lens based on all-dielectric metasurface

  • Fund Project: Supported by National Natural Science Fundation of China (61575032)
More Information
  • 本文提出了一种基于介质超表面的径向偏振贝塞尔透镜,它可以高效率地将线偏光转换为径向偏振光,并且同时实现贝塞尔聚焦。在线偏振光入射下,利用非对称光子自旋轨道相互作用对线偏振光左右旋分量进行独立调控,最后通过自旋重组同时实现偏振转换和波前调控。在波长为532 nm处,数值孔径NA=0.9,超透镜实现了超越衍射极限聚焦焦斑。该项研究在粒子加速和超分辨率成像方面具有潜在的应用价值。

  • Overview:In the past few decades, cylindrical vector waves have received more and more attention due to their uniqueproperties in focusing and imaging, especially radial polarized light (RPL). RPL is an axisymmetrically polarized beamwith a strong longitudinal component in the focal plane, which allows RPL focusing to produce a tighter focal spot.Nowadays, it has been reported that RPL can be used to realize metalenses. However, most of the common metalensesbased on RPL use spherical phase gradient to design the lens, which results in the influence of diffraction. The full widthat half maximum (FWHM) of the focused spot cannot exceed the diffraction limit. Bessel non-diffracting beam is abeam with the advantages of small center spot, high concentration of light intensity, good directivity, and maximumnon-diffraction distance. Although many studies have been conducted on non-diffracted beams today, no existed metalen can combine the advantages of these two types of beams. In order to design a metalens that exceeds the diffractionlimit, a RPL Bessel lens based on a dielectric metasurface is proposed in this paper. It can efficiently convert linearlypolarized light into radially polarized light and simultaneously achieve non-diffracting Bessel beams. In order to achievesuch design, we need to control the polarization and phase of the incident beam at the same time. In this paper, asymmetric photon spin-orbit interaction is used to achieve arbitrary control of wavefront phase and polarization state simultaneously. Photon SOI describes the coupling relationship between photon spin angular momentum (SAM) andorbital angular momentum (OAM) during light transmission. By separately controlling the size and rotation of the unitcell, the phase and the geometric phase of the waveguide can be introduced at the same time. The combination of thetwo phase gradients can realize the asymmetric photon SOI and further realize independent control of the LCPL and theRCPL. This feature can be used to achieve arbitrary independence. Under linearly polarized light, the left and righthanded components of linearly polarized light are independently regulated by the asymmetric photon SOI. Polarizationconversion and wavefront control are simultaneously achieved by spin recombination. In this paper, the RPL Besselfocusing and RPL spherical focusing simulation results are compared with each other, the FWHM of the two lenses isapproximately 360 nm and 315 nm, respectively. Comparing the simulation results, the RPL Bessel focus has a smallerfocal spot and exceeds the diffraction limit (the diffraction limit is r=0.61λ/NA=360 nm).

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  • 图 1  单元结构设计。(a)径向偏振贝塞尔超透镜示意图;(b)单元结构示意图;(c)~(e)单元结构侧视图和俯视图;(f)针对工作长532 nm单元结构仿真结果,纳米柱材料为二氧化钛(TiO2),基底材料为二氧化硅(SiO2)。固定参数:H=600 nm, P=370 nm, R=30 nm。单元结构(1~4)纳米柱长宽:L=300 nm,290 nm,250 nm,235 nm,W=120 nm, 105 nm, 95 nm, 80 nm。图(f)中单元结构(5~8)需要将单元结构(1~4)的纳米柱旋转90°。相关折射率为2.43(TiO2)和1.46(SiO2)

    Figure 1.  Unit cell design. (a) Schematic diagram of a radially polarized Bessel metalens; (b) Schematic diagram of the unit cell; (c)~(e) Side view and top view of the unit cell; (f) The simulated spin-independent phases and cross-polarized and co-polarized transmissivities of eight unit cells at the wavelength of 532 nm. The materials of nanofins and substrate are titanium dioxide (TiO2) and silicon dioxide (SiO2). Constant parameters: H=600 nm, P=370 nm, R=30 nm. The nanofins sizes (L and W) of unit cells from 1 to 4 are L=300 nm, 290 nm, 250 nm, 235 nm, W=120 nm, 105 nm, 95 nm, 80 nm. The unit cells from 5 to 8 are acquired by rotating the posts from 1 to 4 by an angle of 90° clockwise in (f). Simulations use the finite element method (FEM) in CST microwave studio. The refractive indices are given as 2.43 (TiO2), 1.46 (SiO2), respectively

    图 2  球面聚焦透镜和贝塞尔透镜的设计。(a)为了将平面波聚焦到离平面距离f的单个点上,必须将双曲面相位分布施加到入射波前,在透镜表面上的点PL处的相移与距离PLSL成比例,其中SLPL在等于焦距f的半径的球面上的投影;(b)将点光源成像在沿着光轴的线段上,该段的长度是焦深(DOF),PA平面上的点PA的相位与PASA的距离成正比,其中SAPA在锥面上的投影,顶点位于变焦面与光轴的交点处,底角β=arctan(r/DOF)(r是变面的半径);(c)在球面聚焦透镜上产生的双曲面径向相位分布;(d)在平面轴棱镜上产生的圆锥形径向相位分布

    Figure 2.  Schematic of designing the spherical focusing lens and Bessel lens. (a) To focus a plane wave into a focal spot at a distance f from the plane, a hyperboloid phase distribution must be applied to the incident wavefront. The phase shift at the point PL is propor tional to the distance PLSL, where SL is the projection of PL on a spherical surface equal to the radius of the focal length f; (b) The point light source is imaged on a line segment along the optical axis. The length of the segment is the depth of focus (DOF). The phase of the point PA on the PA plane is proportional to the distance of the PASA, where SA is the projection of the PA on the cone, and the vertex is located at the intersection of the zoom surface and the optical axis. The angle β=arctan(r/DOF) (r is the radius of the facet). (c) The hyperbolic radial phase distribution generated on the spherical focusing lens; (d) The conical radial phase distribution produced on the flat axicon

    图 3  A透镜和B透镜聚焦结果。(a) A透镜理论计算的聚焦结果;(b) B透镜理论计算的聚焦结果; (c) A透镜的仿真焦点结果;(d) B透镜的仿真焦点结果;(e)为图 3(a)3(b)中的横向线y=0 μm;(f)为图 3(c)3(d)中的横向线y=0 μm

    Figure 3.  Focus results for A and B lenses. (a) Focused results of the theoretical calculation of the A lens; (b) Focused results of B-lens theoretical calculations; (c) Simulation focus results of the A lens; (d) Simulation focus results of the B lens; (e) The transverse line in 3(a) and 3(b) at y = 0 μm; (f) The transverse line in 3(c) and 3(d) at y=0 μm

    图 4  B透镜聚焦场分布。(a)整体电场强度分布;(b) FIT数值仿真归一化强度;(c)焦平面径向分量电场强度分布;(d)背景光

    Figure 4.  The electric field intensity distributions of the focal plane of B lens. (a) The total field; (b) The normalized intensity of FIT simulation; (c) The sum of radial component; (d) The sum of longitudinal component

    图 5  A透镜和B透镜焦点的xoz纵向截面结果。(a), (b) A透镜x-z平面强度分布的理论计算和仿真结果;(c) A透镜光轴归一化强度分布曲线的理论结果和仿真结果;(d), (e) B透镜x-z平面强度分布的理论计算和仿真结果;(f) B透镜光轴归一化强度分布曲线的理论结果和仿真结果

    Figure 5.  xoz longitudinal cross-section results for the A and B lens focal points. (a), (b) Theoretical calculations and simulation results for the intensity distribution of the x-z plane of the A-lens; (c) Theoretical results and simulation results of the normalized intensity distribution curve of the A-lens optical axis; (d), (e) Theoretical calculations and simulation results for the intensity distribution of B-lens x-z plane; (f) Theoretical results and simulation results of the normalized intensity distribution curve of the B-lens optical axis

    图 6  (a), (b) x偏振光入射时,C透镜焦平面(z=4.74 μm)和xoz平面强度分布;(c) B透镜焦平面(z=4.76 μm)强度分布;(d)为图 6(a)6(c)中的横轴线y=0

    Figure 6.  (a), (b) Intensity distribution of focal plane (z=4.74 μm) and xoz plane of C-lens when x-polarized light is incident; (c) B lens focal plane (z=4.76 μm) intensity distribution; (d) The horizontal axis at y=0 in 6(a) and 6(c)

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出版历程
收稿日期:  2018-03-14
修回日期:  2018-04-16
刊出日期:  2018-11-01

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