【作者】 刘鑫；

【导师】 王烈；

【作者基本信息】 广西大学 ， 新一代电子信息技术（专业学位）， 2025， 硕士

【摘要】 光学分辨率是光学显微系统中的关键参数。传统物镜受到衍射极限的制约,导致无法突破0.61λ/NA的分辨率限制。因此,突破衍射极限的光学超分辨技术在显微成像、微纳光刻、粒子操纵和高密度数据等领域具有重要应用价值。近年来,基于光学超振荡理论设计的平面透镜从光学自身机理上突破衍射极限,受到广泛关注。该技术在成像过程中无需依赖倏逝波或样本预标记,因此在远场无标记超分辨成像领域具有广阔的应用前景。但现有研究主要集中于可见光波段,紫外波段尤其是真空紫外波段的超分辨平面透镜设计仍存在挑战。同时,传统启发式优化算法在复杂结构设计时易陷入局部最优,制约了器件性能提升。针对以上问题,本文主要研究了紫外波段平面衍射透镜的设计,以及基于梯度下降算法优化超构透镜结构的策略,主要研究内容包括:(1)针对工作在真空紫外波段(λ=177nm),尺寸小于毫米级(r=20μm)的平面衍射透镜,本文提出了一种能实现高传输效率和亚衍射极限聚焦的设计方案。将入射的高斯光束预先聚焦至与透镜半径相当的尺寸量级,从而确保平面衍射透镜的高传输效率。同时,针对大尺寸和小尺寸高斯光束入射情况,利用二进制粒子群优化算法优化透镜的透射率,保证其均能实现亚衍射极限聚焦。矢量角谱法的仿真结果表明,所设计的真空紫外平面衍射透镜能够在焦距(～56λ)处形成轴向紧聚焦光斑(～3λ),同时保证光能的高传输效率(～86.5%),并形成横向半高全宽为79nm的亚衍射焦斑。(2)针对工作在近紫外边缘波段(λ=405nm),且具有连续相位调制的平面超构透镜(r=20μm),本文提出了一种基于梯度下降算法的逆向设计框架,用于优化超构透镜的相位,进而实现亚衍射极限聚焦。该设计框架将超构透镜沿径向划分为多个圆环,并利用矢量瑞利-索末菲衍射积分计算每个圆环的衍射光场,将其存储为离线数据库。因此,不同相位分布的超构透镜对应的衍射光场,可以通过数据库中圆环光场与其相位系数对应的复振幅的加权和来计算。得益于该衍射求解器的可微分特性,我们能够直接利用梯度信息更新超构透镜的相位,从而显著提升收敛速度和优化效果。在此框架下,本文还设计了三种类型的超分辨超构透镜。单焦点型透镜能够在焦距10μm处,形成半高全宽为185nm的亚衍射焦斑;多焦点型透镜能够在焦距5μm、7.5μm、10μm、12.5μm和15μm处,分别形成半高全宽为183nm、177nm、182nm、192nm和211nm的亚衍射焦斑;光针型透镜则能够生成长度为10μm、横向尺寸约180nm且光强分布均匀的亚衍射光针。更多还原

【Abstract】 Optical resolution is a critical parameter in optical microscopy systems.Traditional objective lenses are constrained by the diffraction limit,which prevents achieving a resolution beyond the 0.61λ/NA limit.Therefore,optical super-resolution technologies that break through the diffraction limit have significant applications in fields such as microscopic imaging,micro-nano lithography,particle manipulation,and high-density data storage.In recent years,planar lenses designed based on optical superoscillation theory have attracted widespread attention as they break through the diffraction limit from an optical mechanism perspective.These lenses enable direct super-resolution imaging without the need for evanescent waves or sample pre-labeling,showing great potential for label-free far-field super-resolution imaging.However,existing research mainly focuses on the visible light band,and the design of super-resolution planar lenses in the ultraviolet band,especially in the vacuum ultraviolet band,still faces challenges.At the same time,traditional heuristic optimization algorithms often fall into local optima when designing complex structures,limiting the performance improvement of devices.To address these issues,this thesis primarily investigates the design of planar diffractive lenses in the ultraviolet band and the strategy of optimizing metalens structure based on a gradient descent algorithm.The main research content includes:(1)For a planar diffractive lens working in the vacuum ultraviolet band(λ=177nm)with a size smaller than one millimeter(r=20μm),this thesis proposes a design scheme that achieves high transmission efficiency and sub-diffraction-limit focusing.The incident Gaussian beam is pre-focused to a dimensional scale comparable to the lens radius,thereby ensuring high transmission efficiency of the planar diffractive lens.Additionally,a binary particle swarm optimization algorithm is used to optimize the lens’s transmittance for both large and small Gaussian beam incidences,ensuring sub-diffraction-limit focusing.Simulation results using the vector angular spectrum method show that the designed vacuum ultraviolet planar diffractive lens can form a tightly focused axial spot(≈3λ)at a focal length of approximately 56λ,while ensuring high transmission efficiency(≈86.5%)and forming a sub-diffraction focus spot with a transverse full-width at half-maximum(FWHM)of79nm.(2)For a planar metalens(r=20μm)working at the near-ultraviolet edge(λ=405nm)with continuous phase modulation,this thesis proposes an inverse design framework based on the gradient descent algorithm to optimize the phase of the metalens,thus achieving sub-diffraction-limit focusing.The design framework divides the metalens radially into multiple rings and uses the vector Rayleigh-Sommerfeld diffraction integral to calculate the diffraction field of each ring,storing this as an offline database.Therefore,the diffraction field corresponding to different phase distributions of the metalens can be calculated by the weighted sum of the ring field in the database and their corresponding complex amplitude transmittances of the phase coefficients.Since this diffraction solver is differentiable,the phase of the metalens can be directly updated using gradient information,significantly improving convergence speed and optimization results.Based on this framework,three types of super-resolution metalenses are designed.The single-focus lens can form a sub-diffraction spot with a FWHM of 185nm at a focal length of 10μm.The multi-focus lens can form sub-diffraction spots with FWHM of 183nm,177nm,182nm,192nm,and 211nm at focal lengths of 5μm,7.5μm,10μm,12.5μm,and 15μm,respectively.The optical needle lens can generate an optical needle with a length of 10μm,maintaining a transverse spot size of around 180nm with a uniform intensity distribution.更多还原