High-precision control of nanoparticles using fractional-order vortex laser beams
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摘要: 提出了一种基于分数阶涡旋光束的纳米粒子三维操控方法。通过建立分数阶涡旋光束的矢量衍射模型，揭示了拓扑系数与光场相位奇异性之间的映射关系。数值模拟结果表明，分数阶涡旋光束的焦场可视为整数阶模式的相干叠加，且其权重分布呈现显著的非对称特性。此外，还建立了基于分数阶涡旋光束捕获纳米粒子的光力模型。研究表明，通过调节分数阶涡旋光束的拓扑系数，可以实现对球形纳米粒子的精确操控。粒子在横向平面上的捕获位置与拓扑系数之间呈线性依赖关系。与传统的整数阶光束相比，该方法通过连续调节拓扑系数，实现了横向捕获位置的精确连续调控。理论计算与Langevin动力学模拟的结果进一步验证了该技术在三维空间内能够实现纳米粒子的多自由度协同操控。Abstract:
Background Optical manipulation based on integer-order vortex beams is widely used in nanotechnology, yet their discrete nature restricts continuous and precise transverse control of nanoparticles.Purpose This study aims to overcome this limitation by proposing a novel approach using fractional-order vortex beams (FVBs), with the goal of achieving continuous and precise transverse optical trapping and manipulation of nanoparticles.Methods We developed a vector diffraction model to characterize the focal field of FVBs, revealing it as a coherent superposition of integer-order modes with a highly asymmetric weight distribution. Additionally, an optical force model was established to analyze the trapping behavior of spherical nanoparticles. Theoretical calculations and Langevin dynamics simulations were employed to evaluate the three-dimensional trapping stability and multi-degree-of-freedom manipulation capability.Results The transverse trapping position exhibits a linear dependence on the fractional topological charge. By continuously tuning the topological charge, nanoparticles can be displaced precisely and continuously in the transverse plane with sub-wavelength accuracy—a capability not achievable with conventional integer-order vortex beams. Simulations further confirm the stability of the three-dimensional trap and the feasibility of coordinated multi-degree-of-freedom manipulation.Conclusions This work demonstrates that fractional-order vortex beams offer a superior alternative for high-precision optical manipulation. They provide a powerful and novel technique for applications in microfluidics, nanofabrication, and lab-on-a-chip devices. -
图 1 具有不同拓扑系数的线偏振涡旋光束的入射光强、偏振态以及相位分布情况
Figure 1. The incident intensity, polarization state, and phase distributions of linearly polarized vortex beams with different topological charges
图 2 具有不同拓扑系数的分数阶线偏振涡旋光束与整数阶涡旋光束的关系图
Figure 2. The diagram illustrating the relationship between fractional-order linearly polarized vortex beams and integer-order vortex beams
图 3 紧聚焦的分数阶线偏振涡旋光束在焦场范围内的归一化强度、偏振态的三维投影及相位分布情况
Figure 3. (a)The normalized intensity, three-dimensional polarization projections, and (b) phase distribution of tightly focused fractional-order linearly polarized vortex beams within the focal region
图 4 紧聚焦的分数阶线偏振涡旋光束捕获球形纳米粒子时，粒子在焦场范围内受到的光力分布(a)Fxy、(b)Fxz和(c)Fyz
Figure 4. The optical force distributions experienced by spherical nanoparticles captured by tightly focused fractional-order linearly polarized vortex beams within the focal region: (a)Fxy、(b)Fxz和(c)Fyz
图 5 分数阶线偏振涡旋光束捕获球形纳米粒子时，粒子在三维焦场中的运动轨迹
Figure 5. The trajectory of spherical nanoparticles within the three-dimensional focal field when captured by fractional-order linearly polarized vortex beams
图 6 分数阶线偏振涡旋光束捕获球形纳米粒子时，粒子在y方向上的(a)横向光力和(b)稳定捕获位置与拓扑系数a之间的依赖关系
Figure 6. The dependence of (a) the lateral optical force in the y-direction and (b) the stable trapping position on the topological coefficient a when spherical nanoparticles are captured by fractional-order linearly polarized vortex beams
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