Metasurface generation of directional circular swallowtail beams carrying power-exponent-phase vortices
doi: 10.37188/CO.EN-2026-0013
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摘要:
与低阶艾里光束、皮尔斯突变光束相比，圆形燕尾光束已被证实具有更为优异的自聚焦能力与调控灵活性。基于全介质超构表面，利用时域有限差分法（FDTD）研究了携带幂指数相位涡旋的定向圆形燕尾（DCS）光束的生成方法，其中定向相位由光束在
x 和y 方向的预设发射角共同调制。在此基础上，详细探讨了定向相位与幂指数相位对光束动态传输及轨道角动量（OAM）的影响。结果表明：通过选取不同的发射角，光束的自聚焦位置可沿预设轨迹进行自由调控；幂指数相位会诱导光束在传输过程中出现旋转行为，且同步演化形成阿基米德螺旋结构。更重要的是，与发射角相关的定向相位可等效为螺旋谱的叠加，它能将OAM模式扩展至更宽的多模态，且该情形下的多模态OAM的功率衰减幅度小于非定向情形。这意味着，多模态 OAM 谱在传输过程中的功率衰减可由各模式共同分摊，而非集中于单一模式，为抑制自由空间传输的轨道角动量衰减提供了可能。本文研究结果对微粒导引或捕获、OAM光通信、光成像具有潜在的应用价值。Abstract:The circular swallowtail beams have recently exhibited better autofocusing ability and more tunability compared with low-order Airy or Pearcey catastrophe beams. However our attention is paid to exploring their metasurface generation and dynamics propagation of directional circular swallowtail (DCS) beams carrying power-exponent-phase vortices based on all-dielectric metasurfaces using finite-difference time-domain (FDTD) method, where the directional phase related to launch angles in
x - andy - directions is considered. The combined influence of directional and power-exponent phases on dynamics propagation and orbital angular momentum (OAM) of the proposed beams is explored. It is found that their autofocusing positions can be freely adjusted along pre-designed trajectories owing to different launch angles. And rotation behavior and Archimede spiral structure originated from power-exponent phase can be also found during propagation. More importantly, the directional phase associated with launch angles can be regarded as the superposition of spiral spectrum, which can further extend OAM modes to wider multimode states compared with the non-directional cases. The OAM reduction in multiple modes with directional cases is smaller than that in non-directional cases during propagation, which indicates that multimode OAM spectra of our proposed beams provide potential for reducing OAM power attenuation in free-space propagation because the power decay is jointly undertaken by multiple modes rather than a single mode. This work may provide inspiration for guiding or trapping microparticles in three-dimension space as requirement, and for OAM-based optical communication and imaging by the modulation of multi-degrees of freedom associated with directional and power-exponent phases. -
Figure 1. (a) Schematic illustration of autofocusing trajectories of the DCS beams carrying PEP vortices based on the designed metasurface; (b) Each unit structure in one period; (c) Transmission phase and amplitude (d) of the unit cell versus rotation angle θ and cylinder radius R; (e) the phase of circular swallowtail factor in Eq. (2); (f)−(g) the power-exponent phase and directional phase; (h) the superimposed phase profile resulted from (e)−(g).
Figure 2. (a) Array structures of circular Si and elliptical Si pillars of the designed metasurface of the proposed beam expressed by Eq. (2); (b)−(c) Metasurface-based amplitude and phase distributions expressed by Eq. (2) at the initial plane; (d)−(g) Metasurface-based amplitude and phase distributions of the other two types of the proposed beam replaced by Sw ( 0, r0 − r/ w0, 0) and Sw ( 0, 0, r0 − r/ w0) in Eq. (2), respectively.
Figure 3. The guided propagations and autofocusing behaviors of the proposed beams expressed by Eq. (2) based on the designed all-dielectric metasurfaces. (a): u = v = 1, n = 1 and the autofocusing plane at z = 122 μm; (b) u = v = −1 and the autofocusing plane at z = 118 μm. Other parameters are the same as those in Fig. (2).
Figure 4. Intensity evolution of the proposed beams for different propagation distances of z = 0, 67, 118, 167 and 220 μm. (a) Numerical integrals using Fresnel diffraction; (b) metasurface-based propagations by the FDTD methods; (c) asymmetrical intensity profile in the y-z longitudinal section using the FDTD methods. Other parameters are the same as those in Fig. 2(b).
Figure 5. (a) The normalized OAM evolution of the proposed beams in the y-z longitudinal section; (b)−(e) OAM in the x-y transverse sections at z = 10, 70, 118, and 180 μm. Other parameters are the same as those in Fig. 2(b).
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