Design of an orbital angular momentum demultiplexing system based on off-axis cascaded metasurfaces

Yi Zhengyu; Li Yang; Liang Houkun; Deng Ang

doi:10.12086/oee.2024.240161

Abstract

When designing metasurface systems, the actual efficiency of the metasurface is much different from the theoretical design efficiency. This can lead to stray light caused by insufficient modulation efficiency of the metasurfaces, which acts as background noise and is magnified in cascaded metasurface systems step by step, affecting system functionality. To reduce the impact of metasurfaces with limited efficiency on system performance, this paper proposes a design method for an orbital angular momentum demultiplexing system based on off-axis cascaded metasurfaces. By incorporating an off-axis phase design, the stray light generated by the reduced efficiency of the metasurface in a cascaded metasurface system is effectively eliminated. Using FDTD (finite difference time domain) simulation software for calculation and validation, the results demonstrate that the off-axis cascaded metasurface system can effectively reduce stray light caused by insufficient modulation efficiency. Compared to the on-axis system, it achieves a maximum reduction in crosstalk of 4.15 dB and an average of 80% stray light elimination, showing a significant performance advantage.

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1. 引　言

光学轨道角动量 (Orbital angular momentum，OAM)由于其空间正交性的特点，在近年来的高速光通信和量子通信领域受到广泛关注^[1-4]。携带OAM的光束在空间相位分布上具有螺旋相位结构exp(il $\theta$ )，其中拓扑荷l可以取任意整数^[5-6]，理论上可以提供无限多个信道，从而极大地提升通信系统的容量。光学超表面，作为一种二维人工微型平面结构阵列，能在亚波长尺度内灵活调控光的振幅、相位和偏振等属性 ^[7-9]。与传统衍射元件相比，超表面能够实现更大的相位梯度，超表面凭借其独特的平面结构和对光波的精确控制能力，在推动空间OAM通信系统小型化、集成化方面展现出巨大的应用潜力^[10]。

基于Berkhout等人提出坐标变换法^[13]，本文设计了一种基于离轴级联超表面的轨道角动量解复用系统。通过在级联超表面中引入离轴量，使得经过调制的目标光束能够按照预设的路径传播，而杂散光则被有效隔离到特定区域，避免了对级联器件性能的影响。通过对比超表面的偏振转化率分别对同轴/离轴级联超表面的轨道角动量解复用系统解复用信噪比后发现，利用离轴设计分离杂散光的方式，在超表面效率较低的情况下，仅需设计合理的相位分布即能达到与高效率同轴级联超表面系统相同的信噪比。这种方法有效降低了系统对设计制作高效率超表面的需求。为了验证所设计系统的有效性，本文通过FDTD (时域有限差分)仿真方法，对比了同轴与离轴条件下轨道角动量解复用系统的效率。仿真结果表明，相较于同轴系统，离轴级联超表面系统能有效减少因调制效率不足而产生的杂散光，实现了最大串扰降低4.15 dB以及平均80%的杂散光消除，显著提高了系统信噪比和解复用效率。

现代的OAM通讯复用系统极快，涡旋光难以被直接加载信号。尽管早期的单层超表面已被应用于产生OAM光束和OAM复用/解复用等领域^[11-12]，但对于复杂系统，单块元件已不足以满足需求。级联超表面系统能够极大扩展光场调控的自由度，成为了未来必然的发展趋势。2010年，Berkhout等人展示了一种简单、高效的OAM分选方式，通过几何坐标变换，仅用两块相位元件就实现不同模式OAM光束的分离和排序^[13]，该方式在推动系统小型化趋势上具有独特优势。最初，这种方法是通过空间光调制器实现，但由于效率原因被折射元件取代^[14]。随着系统小型化、集成化需求的不断增长，衍射元件^[15-19]和级联超表面^[20-21]也开始得到应用。特别是Cheng等人利用全介质级联超表面制作的OAM分选器将系统压缩至毫米尺度，且信道间串扰达到−6.43 dB，表现出了较高的紧凑性和效率^[20]。然而，在传统的同轴级联超表面系统中，由于超表面的调制效率不能达到100%，系统会产生经过第一级超表面调制的光未被第二块超表面调制；未被第一块超表面调制的光经过第二块超表面调制；以及未被第一块超表面调制的光通过第二块超表面也未被调制时产生的背景噪声信号，效率的降低在多层级联超表面系统中的影响会逐级放大。在超表面系统中，系统的信噪比主要受超表面调制效率的影响。但在实际应用中，由于超表面是一种由离散单元结构组成的微纳器件，相邻单元结构间的电磁耦合会显著降低超表面衍射效率并增加噪声^[22]，这导致超表面的实际效率与理论效率往往不匹配。例如，Yang等人所设计的数值孔径(NA=0.32)的硅基超透镜，在1550 nm波长传输下平均聚焦效率为28% (理论聚焦效率为62%)^[23]；Chen等人所设计的数值孔径(NA=0.35)的硅基超透镜，在1550 nm波长传输下平均聚焦效率为51% (理论聚焦效率为85%)^[24]。超表面单元结构间的耦合、加工精度不足常会导致部分光线未得到调制，这也是实验结果均存在较大的背景噪声的主要原因。为了提高超表面调制效率，研究者们常采用遗传算法、拓扑优化、机器学习等方式来设计得到更高效率的超表面结构^[25-28]，或者采用更高精度的加工工艺来制作超表面^[29-30]。然而，这些方法往往伴随着计算过程复杂、制造价格成本高的问题，很大程度限制了超表面在实际光学系统中的广泛应用。离轴超表面的设计概念早在超表面全息投影和OAM复用/解复用的研究中被引入，主要用以分离杂散光和全息像^{[12, 31-32]}。将离轴设计引入级联超表面系统设计中，就可以将杂散光导入到特定区域，从而分离目标光束与杂散光。这种方法在不牺牲系统性能的前提下，避免了复杂的设计和制作高效率超表面过程，同时也能显著提升系统的信噪比。

2. 系统原理与设计

$v = a \arctan \left(\frac{y}{x}\right)\;,$

本文中，为实现紧凑型轨道角动量解复用系统并提高OAM模式的分类能力，对系统特征参数进行计算优化。优化后参数a=100/ $( 2\pi) \;\mu {\rm{m}}$ ，b=954 $\mu {\rm{m}}$ [见式(3)、式(4)]。第一级和第二级超表面的横向尺寸均设置为200 μm×200 μm ，两级超表面间距f=1000 $\mu {\rm{m}}$ ，离轴级联超表面系统添加的离轴角度 ${\theta }_{x}=$ 6°。级联超表面的设计采用了基于Pancharatnam-Berry (PB)相位调制原理^[33-34]的矩形纳米柱单元结构，最终确定的单元结构典型参数：周期T=900 nm，长(l)，宽(w)，高(h)分别为650 nm，250 nm，1300 nm，其中纳米柱材料为Si，衬底为 ${\mathrm{S}\mathrm{i}\mathrm{O}}_{2}$ 。对工作波长1.4~1.7 $\mu {\rm{m}}$ 范围内的单元结构偏振转化率仿真结果如所示，在入射波长为1.55 $\mu {\rm{m}}$ 时，偏振转化率为90%。此外，离轴条件下工作的超表面偏振转化效率也会受到一定影响^[35]，添加离轴角度在0~10°范围内时，单元结构偏振转化率如图2(b)所示，可以观察到添加离轴角度在0~6°范围内时，效率下降较少，当离轴角增加到10°时，偏振转化效率能维持在80%以上。

$\phi _{_{{\mathrm{PC}}}}^{\mathrm{{on}}}(u,v) = - \frac{{{\text{2}}\pi ab}}{{\lambda f}}\left[\exp \left( \frac{- u}{a}\right)\cos \left(\frac{v}{a} + \frac{1}{{ab}}\left(\frac{1}{2}({u^2} + {v^2}\right)\right)\right]\;,$

Berkhout等人提出的解复用系统中，包含两个关键的光学元件：展开器(un-wrapper)和相位校正器(phase corrector)。展开器的作用是将OAM光束沿角向的相位梯度转换为沿横向的相位梯度，从而实现从笛卡尔坐标系到对数-极坐标系的转换，转换关系为

其中： $\lambda$ 为入射光波长；两个自由参数a，b决定了展开后光束的形状和最终光斑的位置，其中a=d/ $(2 \pi)$ ，以确保0~2 $\pi l$ 范围内的角相位转换到宽度为d的空间上，b可单独调节对元件物理尺寸进行优化；f为两块超表面之间的距离。不同OAM分量横向聚焦位置 ${\varDelta }_{x}=l \cdot f \cdot \lambda /d$ ，位置相对坐标与OAM模式的拓扑荷l成正比。同轴级联超表面轨道角动量解复用系统如图1(a)所示。

对于级联超表面相位设计时需要注意的是，当入射光为圆偏振光时，经过第一级超表面的PB相位调制后，出射光会转化为与入射光正交偏振的光束。此时第二级超表面需要对目标光束的相位产生相反的调制效果，因此第二级超表面相位轮廓修正为 ${{\phi }'}_{{\mathrm{PC}}}$ (u,v) = − ${\phi }_{{\mathrm{PC}}}$ (u, v)。

其中：(x，y)是笛卡尔坐标系下的坐标，(u，v)是对数-极坐标系下的坐标。相位校正器的功能是校正在转换过程中产生的倾斜波前，将其转换为沿光轴方向的平面波前。通过聚焦后，可以实现不同OAM模式在横向位置上的分离。根据Berkhout所设计的相位分布，将两块同轴级联超表面元件相位轮廓函数分别设置为

$u = - a {\mathrm{ln}}\left(\frac{\sqrt {{x^2} + {y^2}}}{b}\right)\;,$

$\begin{split} \phi_{{\mathrm{U W}}}^{{\mathrm{on}}}(x, y)=&\frac{2 \pi a}{\lambda f}\left[y \arctan \left(\frac{y}{x}\right)-x \ln \left(\frac{\sqrt{\left(x^2+y^2\right)}}{b}\right.\right. \\ &+\left. x-\frac{1}{a}\left(\frac{1}{2}\left(x^2+y^2\right)\right)\right]\;, \end{split}$

Figure 2. (a) Polarization conversion efficiency of a unitary structure as a function of wavelength; (b) Polarization conversion efficiency of a unitary structure as a function of off-angle

Figure 2. Full-Size Img PowerPoint

(a) Polarization conversion efficiency of a unitary structure as a function of wavelength; (b) Polarization conversion efficiency of a unitary structure as a function of off-angle

$\begin{split} \phi_{{\mathrm{U W}}}^{{\mathrm{o f f}}}(x, y)=&\frac{2 \pi a}{\lambda f}\left[y \arctan \left[\dfrac{y}{x}\right]-x \ln \left(\frac{\sqrt{\left(x^2+y^2\right)}}{b}\right.\right. \\ & +\left.x-\frac{1}{a}\left(\frac{1}{2}\left(x^2+y^2\right)\right)\right]+{ \varphi }\;, \end{split}$

$\begin{split} \phi_{\mathrm{pc}}^{{\mathrm{o f f}}}(u, v)=&-\frac{2 \pi a b}{\lambda f}\Bigg[\exp \left(\frac{-u}{a} \right)\cos \left(\frac{v}{a}\right) \\ & +\frac{1}{a b}\left(\frac{1}{2}\left(u^2+v^2\right)\right)\Bigg]- { \varphi }\;, \end{split}$

Figure 1. Full-Size Img PowerPoint

Schematic of (a) on-axis and (b) off-axis cascade metasurface OAM demultiplexing system

其中：φ = $\dfrac{x \cdot \sin{\theta }_{x}}{2\pi \lambda }$ + $\dfrac{y \cdot \sin{\theta }_{y}}{2\pi \lambda }$ ，φ表示添加的离轴相位， ${\theta }_{x}$ 和 ${\theta }_{y}$ 为初始给定的离轴角度。通过离轴设计，对第一级超表面添加一个离轴角度后，受到调制的光束将沿一个新的路径传播，而未受到调制的光束则继续沿原路径传播，从而将未受到调制的杂散光与目标信号光束分离。再对第二级超表面添加与第一级相反的离轴角度，将光线调整至沿水平方向传播的同时分离未受到第二级超表面调制产生的杂散光。离轴级联超表面轨道角动量解复用系统如图1(b)所示，其中第二级超表面还设置有一个只允许超表面结构区域内的光束通过的特殊孔径，用于阻隔超表面添加离轴角度后分离开的杂散光，避免杂散光产生的二次噪声影响系统的信噪比。

为了消除同轴级联超表面系统中由于调制效率不足而产生的杂散光对输出信号的影响，通过对两级超表面增加相反的离轴相位来实现光线的偏转。优化后的离轴级联超表面元件相位轮廓函数分别为

3. 实验结果

图5(c)展示了在同轴和离轴条件下，不同拓扑荷模式l对应信道的归一化杂散光光强情况，仿真计算得到同轴与离轴条件下系统平均串扰分别为−5.24 dB和−9.39 dB。通过加入离轴设计，系统相较于同轴条件下平均串扰降低4.15 dB，对比图中的数据，我们可以观察到在各个信道中，杂散光光强得到了显著降低，平均减少了大约80%。这些结果表明，采用离轴级联超表面的设计可以有效减少由于同轴级联超表面调制效率不足而产生的杂散光，提高系统解复用信噪比。这种显著的杂散光减少对于提高系统的整体性能至关重要，它有助于减少杂散光对目标信号的串扰，确保了更清晰的信号传输。对于制作高效率超表面要求的降低也意味着离轴级联超表面适用于大规模制备，体现了离轴级联超表面设计在实际应用中具有的潜在优势，特别是在需要高效率和低噪声的光通信系统中。

Figure 4. (a) Schematic of signal/noise in OAM demultiplexing system based on off-axis cascaded metasurface; (b) SNR of demultiplexing system as a function of polarization conversion efficiency and off-angle

Figure 4. Full-Size Img PowerPoint

(a) Schematic of signal/noise in OAM demultiplexing system based on off-axis cascaded metasurface; (b) SNR of demultiplexing system as a function of polarization conversion efficiency and off-angle

$X{T_{{j}}}{ = 10 \times }{{\text{log}}_{{\text{10}}}}\left( {\frac{{{I_{j,{\mathrm{ALL}}\backslash j}}}}{{{I_{j,{\mathrm{ALL}}}}}}} \right),$

基于以上的数值计算和分析结果，使用时域有限差分(FDTD)数值模拟软件对同轴和离轴( ${\theta }_{x}=6^ \circ$ )条件下的级联超表面进行了仿真验证。为了评估系统对杂散光的分离效率，我们计算了各个拓扑荷模式光束在输出信号位置的杂散光占比。由于基于对数极坐标的几何坐标变换法存在一定的分辨率限制，会导致最终输出的相邻拓扑荷模式会有部分重叠，仿真选择了拓扑荷模式l = ±1, ±3的光束来评估杂散光分离情况，采用间隔的拓扑荷模式，可以排除信号光重叠产生的串扰，从而更准确地模拟和评估离轴系统分离杂散光的性能情况。考虑到级联超表面仿真区域的尺寸较大，采取了分步进行计算的方法。首先，利用FDTD计算了入射光穿过第一级超表面后的近场光强分布。接着，应用矢量衍射角谱理论来计算光场在传播至第二级超表面前的分布情况。将这一光场分布作为第二级超表面的入射光场，再次运用FDTD进行模拟，以获得入射光穿过第二级超表面后的近场光强分布。最后，通过矢量衍射角谱理论计算并得到焦平面处的远场光强分布。图5(a)和5(b)分别对应同轴和离轴条件下不同拓扑荷模式的输出光场分布。

展示了离轴级联超表面系统在不同偏振转换率以及引入不同离轴角度条件下的性能变化。从图中可以看出，当离轴角度为0°时，即系统处于同轴状态，100%偏振转换率的系统相较于70%偏振转换率的系统之间的信道串扰差距达到了−2.5 dB。随着离轴角度的增加，信道串扰的差异逐渐减小。特别是当离轴角度增加至 ${\theta }_{x}=$ 6°时，不同偏振转换率的系统在解复用时的信道串扰几乎达到了一致。这一结果表明，通过离轴设计，可以有效地分离由于超表面调制效率不足而产生的杂散光，使较低效率超表面系统达到与高效率超表面系统相同的性能。

在离轴级联超表面系统中，如所示，以拓扑荷l = 3的OAM光束为例，当添加离轴角度 ${\theta }_{x}=6^ \circ$ 时，受到第一级超表面调制的信号光和未受到调制的杂散光在传播过程中会根据各自的相位变化产生分离。此时，通过设置仅允许信号光通过的通光孔径，noise2和noise3可以有效消除。由于第二级超表面引入的离轴相位与第一级相反，未受到第二级超表面调制的杂散光继续沿设定的离轴角度方向传播，受到调制的信号光调整为沿光轴方向传播，从而使信号光(signal)与杂散光(noise1)分离。

其中： ${I}_{j,{\mathrm{ALL}}}$ 表示所有信道的信号强度， ${I}_{{\mathrm{ALL}}\backslash j}$ 表示关闭第j个信道时所有信道的信号强度。通过对拓扑荷模式l = −3~3范围内七个信道串扰的数值计算，结果如图3(b)所示，当超表面的调制效率从100%下降至70%时，系统信道间的串扰会显著提升，从−5.2 dB提升至−2.7 dB，这表明调制效率的降低对系统最终输出的目标信号造成了较大干扰。因此，在设计和优化同轴级联超表面系统时，提高超表面的调制效率至关重要。

在同轴级联超表面系统中，由于超表面的调制效率不能达到100%，因此每次通过超表面时，总会有一部分光束未被完全调制，这部分光束作为杂散光影响系统性能。如图3(a)所示，以拓扑荷l = 3的OAM光束为例，这些杂散光包括受到第一级超表面调制但未被第二级超表面调制的光束(noise1)、未被第一级超表面调制但受到第二级超表面调制的光束(noise2)，以及未被两级超表面调制的光束(noise3)。这些噪声共同构成系统的背景噪声信号。为了评估杂散光对目标信号的影响，采用信道串扰占比来表征系统解复用效率，将第j个信道上的串扰定义为

Figure 3. (a) Schematic of signal/noise in OAM demultiplexing system based on on-axis cascaded metasurface; (b) SNR of demultiplexing system as a function of polarization conversion efficiency

Figure 3. Full-Size Img PowerPoint

(a) Schematic of signal/noise in OAM demultiplexing system based on on-axis cascaded metasurface; (b) SNR of demultiplexing system as a function of polarization conversion efficiency

Figure 5. (a) On-axis and (b) off-axis , intensity profiles corresponding to different OAM states (l = ±1, ±3); (c) Normalized noise intensities in the range of outgoing field for different OAM states (l = ±1, ±3) in on-axis and off-axis system

Figure 5. Full-Size Img PowerPoint

(a) On-axis and (b) off-axis , intensity profiles corresponding to different OAM states (l = ±1, ±3); (c) Normalized noise intensities in the range of outgoing field for different OAM states (l = ±1, ±3) in on-axis and off-axis system

4. 结　论

本文设计了一种基于离轴级联超表面的轨道角动量解复用系统，旨在提高轨道角动量解复用系统集成度和降低级联超表面系统对制作高效率超表面的需求。在设计过程中，我们考虑到超表面由于单元结构设计、单元结构之间相互作用以及加工误差等可能导致超表面整体调制效率下降，所以设计高效的超表面对加工要求极高。为了应对这些问题，引入了离轴级联超表面的设计概念，通过这种设计方法可以有效减少超表面调制效率不足而产生的噪声，将设计高效率超表面对于加工工艺的要求转换到设计合理的相位分布上，极大降低了系统的设计、加工难度。通过使用FDTD仿真软件，我们对同轴与离轴条件下的轨道角动量解复用系统进行了仿真验证。由于极坐标变换法使得解复用相邻拓扑荷模式存在部分重叠，导致目标信号重叠产生串扰，因此通过对拓扑荷模式l = ±1, ±3四个信道仿真计算，最终实现输出光场中，离轴级联超表面系统相较于同轴系统最大串扰降低4.15 dB，能够实现平均80%的噪声消除，这一改进为离轴级联超表面系统提供了坚实的理论基础。对于极坐标变换产生的相邻拓扑荷模式间串扰问题可采用模式复制或螺旋变换法提高分辨率来做到连续的OAM光束解复用分离^[36-37]，但会增加系统横向尺寸和变化复杂度。

通过将多个超表面离轴级联，以一种简单的方式拓展了低效率超表面的应用范围，尽管本研究中仅设计并验证了两级超表面的级联，但该设计方法可以推广应用到多级超表面的级联中，解决级联超表面层数限制问题，对于光学系统的小型化和集成化具有潜在应用价值和意义，将来有望在光通信、光计算、光加密等多个关键领域中应用。

利益冲突

所有作者声明无利益冲突

References (37)

References

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- Corresponding author: Deng Ang, dengang7@scu.edu.cn On this Site On Google Scholar
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DOI: 10.12086/oee.2024.240161

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Yi Zhengyu, Li Yang, Liang Houkun, Deng Ang. Design of an orbital angular momentum demultiplexing system based on off-axis cascaded metasurfaces. Opto-Electronic Engineering 51, 240161 (2024). DOI: 10.12086/oee.2024.240161

Yi Zhengyu, Li Yang, Liang Houkun, Deng Ang. Design of an orbital angular momentum demultiplexing system based on off-axis cascaded metasurfaces. Opto-Electronic Engineering 51, 240161 (2024). DOI: 10.12086/oee.2024.240161

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- Received Date July 11, 2024
- Revised Date August 08, 2024
- Accepted Date August 11, 2024
- Published Date August 24, 2024
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[1]	García-Escartín J C, Chamorro-Posada P. Quantum multiplexing with the orbital angular momentum of light[J]. Phys Rev A, 2008, 78(6): 062320. DOI: 10.1103/PhysRevA.78.062320 CrossRef Google Scholar
[2]	Yan Y, Xie G D, Lavery M P J, et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing[J]. Nat Commun, 2014, 5: 4876. DOI: 10.1038/ncomms5876 CrossRef Google Scholar
[3]	Willner A E, Huang H, Yan Y, et al. Optical communications using orbital angular momentum beams[J]. Adv Opt Photonics, 2015, 7(1): 66−106. DOI: 10.1364/AOP.7.000066 CrossRef Google Scholar
[4]	Yuan X Y, Xu Q, Lang Y H, et al. Tailoring spatiotemporal dynamics of plasmonic vortices[J]. Opto-Electron Adv, 2023, 6(4): 220133. DOI: 10.29026/oea.2023.220133 CrossRef Google Scholar
[5]	Allen L, Beijersbergen M W, Spreeuw R J C, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Phys Rev A, 1992, 45(11): 8185−8189. DOI: 10.1103/PhysRevA.45.8185 CrossRef Google Scholar
[6]	Allen L, Padgett M J, Babiker M. IV the orbital angular momentum of light[J]. Prog Opt, 1999, 39: 291−372. DOI: 10.1016/S0079-6638(08)70391-3 CrossRef Google Scholar
[7]	Pendry J B, Schurig D, Smith D R. Controlling electromagnetic fields[J]. Science, 2006, 312(5781): 1780−1782. DOI: 10.1126/science.1125907 CrossRef Google Scholar
[8]	Yu N F, Capasso F. Flat optics with designer metasurfaces[J]. Nat Mater, 2014, 13(2): 139−150. DOI: 10.1038/nmat3839 CrossRef Google Scholar
[9]	Luo X G, Pu M B, Ma X L, et al. Taming the electromagnetic boundaries via metasurfaces: from theory and fabrication to functional devices[J]. Int J Antennas Propag, 2015, 2015: 204127. DOI: 10.1155/2015/204127 CrossRef Google Scholar
[10]	张飞, 郭迎辉, 蒲明博, 等. 基于非对称光子自旋—轨道相互作用的超构表面[J]. 光电工程, 2020, 47(10): 200366. DOI: 10.12086/oee.2020.200366 Zhang F, Guo Y H, Pu M B, et al. Metasurfaces enabled by asymmetric photonic spin-orbit interactions[J]. Opto-Electron Eng, 2020, 47(10): 200366. DOI: 10.12086/oee.2020.200366 CrossRef Google Scholar
[11]	Yu N F, Genevet P, Kats M A, et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction[J]. Science, 2011, 334(6054): 333−337. DOI: 10.1126/science.1210713 CrossRef Google Scholar
[12]	Li Y, Li X, Chen L W, et al. Orbital angular momentum multiplexing and demultiplexing by a single metasurface[J]. Adv Opt Mater, 2017, 5(2): 1600502. DOI: 10.1002/adom.201600502 CrossRef Google Scholar
[13]	Berkhout G C G, Lavery M P J, Courtial J, et al. Efficient sorting of orbital angular momentum states of light[J]. Phys Rev Lett, 2010, 105(15): 153601. DOI: 10.1103/PhysRevLett.105.153601 CrossRef Google Scholar
[14]	Lavery M P J, Robertson D J, Berkhout G C G, et al. Refractive elements for the measurement of the orbital angular momentum of a single photon[J]. Opt Express, 2012, 20(3): 2110−2115. DOI: 10.1364/OE.20.002110 CrossRef Google Scholar
[15]	Ruffato G, Massari M, Parisi G, et al. Test of mode-division multiplexing and demultiplexing in free-space with diffractive transformation optics[J]. Opt Express, 2017, 25(7): 7859−7868. DOI: 10.1364/OE.25.007859 CrossRef Google Scholar
[16]	Ruffato G, Massari M, Romanato F. Compact sorting of optical vortices by means of diffractive transformation optics[J]. Opt Lett, 2017, 42(3): 551−554. DOI: 10.1364/OL.42.000551 CrossRef Google Scholar
[17]	Ruffato G, Girardi M, Massari M, et al. A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams[J]. Sci Rep, 2018, 8(1): 10248. DOI: 10.1038/s41598-018-28447-1 CrossRef Google Scholar
[18]	Ruffato G, Capaldo P, Massari M, et al. Total angular momentum sorting in the telecom infrared with silicon Pancharatnam-Berry transformation optics[J]. Opt Express, 2019, 27(11): 15750−15764. DOI: 10.1364/OE.27.015750 CrossRef Google Scholar
[19]	Ruffato G, Massari M, Girardi M, et al. Non-paraxial design and fabrication of a compact OAM sorter in the telecom infrared[J]. Opt Express, 2019, 27(17): 24123−24134. DOI: 10.1364/OE.27.024123 CrossRef Google Scholar
[20]	Cheng J P, Sha X B, Zhang H, et al. Ultracompact orbital angular momentum sorter on a CMOS chip[J]. Nano Lett, 2022, 22(10): 3993−3999. DOI: 10.1021/acs.nanolett.2c00572 CrossRef Google Scholar
[21]	Wang B M, Wen Y H, Zhu J B, et al. Sorting full angular momentum states with Pancharatnam-Berry metasurfaces based on spiral transformation[J]. Opt Express, 2020, 28(11): 16342−16351. DOI: 10.1364/OE.393859 CrossRef Google Scholar
[22]	Li Y, Hong M H. Diffractive efficiency optimization in metasurface design via electromagnetic coupling compensation[J]. Materials (Basel), 2019, 12(7): 1005. DOI: 10.3390/ma12071005 CrossRef Google Scholar
[23]	Yang Z Y, Wang Z K, Wang Y X, et al. Generalized Hartmann-Shack array of dielectric metalens sub-arrays for polarimetric beam profiling[J]. Nat Commun, 2018, 9(1): 4607. DOI: 10.1038/s41467-018-07056-6 CrossRef Google Scholar
[24]	Chen R, Zhou Y, Chen W J, et al. Multifunctional metasurface: coplanar embedded design for metalens and nanoprinted display[J]. ACS Photonics, 2020, 7(5): 1171−1177. DOI: 10.1021/acsphotonics.9b01795 CrossRef Google Scholar
[25]	Fan Y L, Xu Y K, Qiu M, et al. Phase-controlled metasurface design via optimized genetic algorithm[J]. Nanophotonics, 2020, 9(12): 3931−3939. DOI: 10.1515/nanoph-2020-0132 CrossRef Google Scholar
[26]	Huang M, Zheng B, Cai T, et al. Machine–learning-enabled metasurface for direction of arrival estimation[J]. Nanophotonics, 2022, 11(9): 2001−2010. DOI: 10.1515/nanoph-2021-0663 CrossRef Google Scholar
[27]	Ji W Y, Chang J, Xu H X, et al. Recent advances in metasurface design and quantum optics applications with machine learning, physics-informed neural networks, and topology optimization methods[J]. Light Sci Appl, 2023, 12(1): 169. DOI: 10.1038/s41377-023-01218-y CrossRef Google Scholar
[28]	Xu M F, Pu M B, Sang D, et al. Topology-optimized catenary-like metasurface for wide-angle and high-efficiency deflection: from a discrete to continuous geometric phase[J]. Opt Express, 2021, 29(7): 10181−10191. DOI: 10.1364/OE.422112 CrossRef Google Scholar
[29]	Nishijima Y, Balčytis A, Naganuma S, et al. Kirchhoff’s metasurfaces towards efficient photo-thermal energy conversion[J]. Sci Rep, 2019, 9(1): 8284. DOI: 10.1038/s41598-019-44781-4 CrossRef Google Scholar
[30]	Xu Z J, Dong Y, Tseng C K, et al. CMOS-compatible all-Si metasurface polarizing bandpass filters on 12-inch wafers[J]. Opt Express, 2019, 27(18): 26060−26069. DOI: 10.1364/OE.27.026060 CrossRef Google Scholar
[31]	Meng W J, Hua Y L, Cheng K, et al. 100 Hertz frame-rate switching three-dimensional orbital angular momentum multiplexing holography via cross convolution[J]. Opto-Electron Sci, 2022, 1(9): 220004. DOI: 10.29026/oes.2022.220004 CrossRef Google Scholar
[32]	Zheng G X, Mühlenbernd H, Kenney M, et al. Metasurface holograms reaching 80% efficiency[J]. Nat Nanotechnol, 2015, 10(4): 308−312. DOI: 10.1038/nnano.2015.2 CrossRef Google Scholar
[33]	Pancharatnam S. Generalized theory of interference, and its applications: part I. Coherent pencils[J]. Proc Indian Acad Sci-Sec A, 1956, 44(5): 247−262. DOI: 10.1007/BF03046050 CrossRef Google Scholar
[34]	Berry M V, Dennis M R. Polarization singularities in isotropic random vector waves[J]. Proc R Soc Lond A Math Phys Sci, 2001, 457(2005): 141−155. DOI: 10.1098/rspa.2000.0660 CrossRef Google Scholar
[35]	Li S Q, Li X Y, Zhang L, et al. Efficient optical angular momentum manipulation for compact multiplexing and demultiplexing using a dielectric metasurface[J]. Adv Opt Mater, 2020, 8(8): 1901666. DOI: 10.1002/adom.201901666 CrossRef Google Scholar
[36]	Mirhosseini M, Malik M, Shi Z M, et al. Efficient separation of the orbital angular momentum eigenstates of light[J]. Nat Commun, 2013, 4: 2781. DOI: 10.1038/ncomms3781 CrossRef Google Scholar
[37]	Wen Y H, Chremmos I, Chen Y J, et al. Spiral transformation for high-resolution and efficient sorting of optical vortex modes[J]. Phys Rev Lett, 2018, 120(19): 193904. DOI: 10.1103/PhysRevLett.120.193904 CrossRef Google Scholar

Robust detection technology of orbital angular momentum of partially coherent vortex light fields in complex environment

Opto-Electronic Engineering, DOI: 10.12086/oee.2025.251003.h03
Deep transfer learning method to identify orbital angular momentum beams

Zheng Chonghui, Wang Tianshu, Liu Zheqi, Yang Qiaochu, Liu Xianzhu

Opto-Electronic Engineering, DOI: 10.12086/oee.2022.210409
Metasurfaces enabled by asymmetric photonic spin-orbit interactions

Zhang Fei, Guo Yinghui, Pu Mingbo, Li Xiong, Ma Xiaoliang, Luo Xiangang

Opto-Electronic Engineering, DOI: 10.12086/oee.2020.200366
Saliency detection hybrid information flows based on sub-network cascading

Dong Bo, Wang Yongxiong, Zhou Yan, Liu Han, Gao Yuanzhi, Yu Jiamin, Zhang Mengyin

Opto-Electronic Engineering, DOI: 10.12086/oee.2020.190627
Analysis of the transmission characteristics of Hank-Bessel beam in anisotropic ocean turbulence

He Fengtao, Fang Wei, Zhang Jianlei, Yang Yi, Du Ying, Zhang Bin

Opto-Electronic Engineering, DOI: 10.12086/oee.2020.190591
Orbital angular momentum Talbot array illuminator based on detour phase encoding

Nie Fangsong, Jiang Meiling, Zhang Mingsi, Cao Yaoyu, Li Xiangping

Opto-Electronic Engineering, DOI: 10.12086/oee.2020.200093
Characteristic analysis of orbital angular momentum of vortex beam propagating in atmospheric turbulent

Zhang Lihong, Shen Feng, Lan Bin

Opto-Electronic Engineering, DOI: 10.12086/oee.2020.190272
Research advances of orbital angular momentum based optical communication technology

Guo Zhongyi, Gong Chaofan, Liu Hongjun, Li Jingjing, Wang Zikun, Yang Yang, Gong Yubin

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Design of an orbital angular momentum demultiplexing system based on off-axis cascaded metasurfaces

Abstract

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1. 引　言

2. 系统原理与设计

3. 实验结果

4. 结　论

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Yi Zhengyu, yzy13026392061@163.com On this Site On Google Scholar

Li Yang On this Site On Google Scholar

Liang Houkun On this Site On Google Scholar

Corresponding author: Deng Ang, dengang7@scu.edu.cn On this Site On Google Scholar

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Design of an orbital angular momentum demultiplexing system based on off-axis cascaded metasurfaces

Abstract

Keywords

1. 引 言

2. 系统原理与设计

3. 实验结果

4. 结 论

利益冲突

References

Author Information

Yi Zhengyu, yzy13026392061@163.com On this SiteOn Google Scholar

Li Yang On this SiteOn Google Scholar

Liang Houkun On this SiteOn Google Scholar

Corresponding author: Deng Ang, dengang7@scu.edu.cn On this SiteOn Google Scholar

Copyright

About this Article

Cite this Article

Article History

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Corresponding author: Deng Ang, dengang7@scu.edu.cn

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1. 引　言

4. 结　论

Yi Zhengyu, yzy13026392061@163.com On this Site On Google Scholar

Li Yang On this Site On Google Scholar

Liang Houkun On this Site On Google Scholar

Corresponding author: Deng Ang, dengang7@scu.edu.cn On this Site On Google Scholar