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Achromatic metalens based on coordinative modulation of propagation phase and geometric phase
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摘要:
超透镜是超表面在成像领域中具有较大应用潜力的平面光学器件，但限于色差和较窄的工作带宽，通常难以应用于彩色成像及显示技术。本文设计了一种相位调控型透射式超透镜，实现了400 nm~650 nm波段的宽带消色差聚焦功能，带宽范围内焦平面处的平均聚焦效率约为29%。该方法利用具有低损耗、高折射率优势的二氧化钛(TiO2)介质柱结构，在可见光波段内获得了类似截断波导产生的传输相位响应。同时分析了几何相位和传输相位相结合的色散调控机制，并使用粒子群算法对构建的相位响应仿真数据库进行优化，完成了实际波面与理想聚焦波面的相位匹配。设计的宽带消色差器件有望在显微成像、计算机视觉和机器视觉等领域发挥作用。
Abstract:Metalens is considered as one of the most promising planar optical devices composed of the metasurface, but it is usually difficult to realize full-color imaging and display due to the narrow working bandwidth and large chromatic aberration. In this paper, a phase-controlled transmissive metalens is designed to realize the broadband achromatic focusing within 400 nm~650 nm, and the average focusing efficiency is about 29% at the focal plane within the bandwidth range. The titanium dioxide (TiO2) dielectric nanopillar with low loss and high refractive index as a truncated waveguide can control the propagation phase in the visible. At the same time, we analyze the dispersion modulation mechanism which merges the geometric and propagation phases, and the particle swarm optimization (PSO) algorithm is used to optimize the phase response database, and accomplish the phase matching between the ideal and actual wavefronts. The proposed broadband achromatic devices may broaden the applications of metalens in micro-imaging, computer vision, and machine vision.
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Key words:
- metalens /
- visible /
- achromatic /
- broadband
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Overview: As a two-dimension artificial electromagnetic material, metasurface provides the means to accurately control the wavefront by flexibly adjusting the phase, amplitude, and polarization of electromagnetic waves at will. At present, many applications based on metasurface have been proved, such as beam generator, optical holographic imaging, virtual shaping, and so on. As a plane lens, the metasurface can also generate a hyperbolic phase profile to obtain a focused beam with a higher diffraction efficiency. Traditional refractive lenses achieve phase accumulation by changing the thickness of optical materials, which is usually curved. In contrast, the metalens can realize phase modulation of electromagnetic waves in a plane manner. However, it is usually difficult to realize full-color imaging and display due to the narrow working bandwidth and large chromatic aberration which are caused by the intrinsic properties of the material. In this paper, a phase-controlled transmissive metalens is designed, to realize the broadband achromatic focusing within 400 nm~650 nm, and the average focusing efficiency is about 29% at the focal plane within the bandwidth range. The metalens is composed of titanium dioxide (TiO2) dielectric nanopillars arranged periodically on a silicon dioxide (SiO2, n=1.45) substrate. The nanopillar possesses low loss and high refractive index which can be treated as a truncated waveguide to control the propagation phase in the visible. At the same time, we analyze the dispersion modulation mechanism which merges the geometric and propagation phases, and the particle swarm optimization (PSO) algorithm is used to optimize the phase response database, and accomplish the phase matching between the ideal focusing and the actual wavefronts and realize the designed function. The proposed broadband achromatic planar optical device has a simple structure design of unit cell, therefore we can introduce more types of resonance units to realize the achromatic focusing function with a larger bandwidth.
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图 1 宽带消色差超透镜。(a)当波长为400 nm~650 nm的光正入射时，其焦距保持不变，并且可以将入射光束汇聚成一个白色焦点；(b)消色差超透镜在任意波长λ∈(λmin，λmax)的相位轮廓，右侧插图为不同位置处针对不同波长所需的相位
Figure 1. A broadband achromatic metalens. (a) The focal length will always remain unchanged while the incident wavelength varies from 400 nm to 650 nm, and the incident beam will converge into a white focus; (b) The phase profile for a broadband achromatic metalens at arbitrary wavelength of λ∈(λmin, λmax), and the right illustration shows the required phase for different wavelengths at different positions
图 2 单元结构仿真结果。(a)宽带消色差超透镜的单元结构示意图；(b)偏振转换效率(虚线)和相位响应曲线(实线)，其不同结构参数组合(l: 71 nm, w: 125 nm、l: 162 nm, w: 105 nm、l: 176 nm, w: 125 nm)相位响应曲线斜率是变化的；(c)在不同入射波长下，结构参数为l=105 nm，w=80 nm时归一化磁场能量分布，其中黑色线表示TiO2结构的边界
Figure 2. The simulation results of unit-cell. (a) The unit cell of a broadband achromatic metalens in the visible light region; (b) Conversion efficiency (dotted line) and phase profile with varying slope (solid line) for different structure parameter combination (l: 71 nm, w: 125 nm、l: 162 nm, w: 105 nm、l: 176 nm, w: 125 nm); (c) Under different incident wavelengths, the normalized magnetic energy distribution is obtained when the structure parameter is l=105 nm and w=80 nm. The black line indicates the boundary of the TiO2 structure
图 3 (a) 宽带消色差超透镜的粒子群优化流程图；(b) PSO收敛曲线
Figure 3. (a) Flow chart of the PSO for broadband achromatic metalens; (b) The convergence curve of PSO
图 4 超透镜径向单元结构对应的结构参数
Figure 4. Those structure parameters of the radial unit cells for metalens
图 5 超透镜的焦距偏移和强度分布的模拟结果。(a)在正入射的条件下，y-z平面的归一化仿真强度分布及其x-y平面内的聚焦光斑效果图。入射方向是正z轴，白色实线表示理论焦距f=38 μm，黄色虚线代表点扩散函数；(b)不同波长下模拟的焦距和理论预测焦距；(c)聚焦效率(黑色曲线)和半高全宽(full-widths at half maximums，FWHM)(红色曲线)随着入射超透镜的波长变化
Figure 5. Simulated results of the focal length shifts and intensity distributions of metalens. (a) The normalized intensity distribution in the y-z plane and focused spot in the x-y plane at normal incidence. The direction of incidence is towards the positive z-axis. The white dashed line represents theoretical focal length f=38 μm and the yellow dotted lines indicate point spread function; (b) The simulated focal length and the theoretically predicted focal length as a function of the wavelength; (c) Focusing efficiency and FWHM as the changes of incident wavelengths obtained from the broadband achromatic metalens
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