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随着光学技术的发展, 人们对光场与微粒相互作用的研究越来越深入. 通过研究驻波场中非均匀手性粒子的辐射力特性, 可以深入了解光场对微粒的影响机制, 为微纳米尺度下分层手征粒子的操控和应用提供新思路. 本文对双高斯波束照射下非均匀手征分层粒子的辐射力展开研究. 从广义洛伦兹-米氏理论(generalized Lorentz-Mie theory, GLMT)和球矢量波函数(spherical vector wave functions, SVWFs)出发, 推导了双高斯波束(double Gaussian beams, DGBS)的总入射场展开系数. 基于边界连续条件和电磁动量守恒定理, 得到双高斯波对粒子的辐射力表达式. 通过与现有文献进行比较, 证明了理论和程序的正确性. 详细分析了各种参数对辐射力的影响, 如束腰宽度、偏振形式、粒子半径、内外手征参数、折射率、最外层厚度等. 研究表明, 与单个高斯束相比, 反向传播的高斯驻波在捕获或限制非均匀手性分层粒子方面表现出显著优势, 提供了更强的粒子操控能力. 此外, 通过选择合适的偏振态入射, 可以在这些参数之间实现微妙的平衡, 从而有效地稳定俘获非均匀手性粒子. 这些研究对于分析和理解形状复杂多层生物细胞的光学特性具有重要意义, 并在多层生物结构微操控方面具有重要应用价值.
Objective With the development of optical technology, the investigation of light-field-particle interactions has gained significant momentum. Such studies find widespread applications in optical manipulation, precision laser ranging, laser gas spectroscopy, and related fields. In optical manipulation techniques, employing two or more laser beams proves more effective for capturing and manipulating particles than using a single beam alone. In addition, with the increasing demand for manipulating particles with complex structures, it is necessary to conduct in-depth research on the radiation force characteristics of double Gaussian beams on non-uniform chiral particles. This research aims to deepen our understanding of how optical fields influence particles, thereby offering fresh perspectives in manipulating and utilizing non-uniform chiral layered particles on both a microscale and a nanoscale. Method Based on the generalized Lorentz-Mie theory (GLMT) and spherical vector wave functions (SVWFs), the total incident field of a double Gaussian beam can be expanded by using the coordinate addition theorem. The incident field coefficient and scattering coefficient of each region of the multilayer chiral sphere are obtained by enforcing boundary continuity and employing multilayer sphere scattering theory. The radiation force acting on non-uniform chiral layered particles within a double Gaussian beam is then derived through application of the electromagnetic momentum conservation theorem. Results and Discussions The theory and programs in this paper is compared with those in existing literature. The influence of various parameters on the radiation force is analyzed in detail, such as the incident angle, polarization angle, beam waist width, beam center position, and internal and external chiral parameters. These results indicate that compared with a single Gaussian beam, counter-propagating Gaussian standing waves exhibit significant advantages in capturing or confining inhomogeneous chiral layered particles, offering enhanced particle manipulation capabilities. Additionally, by selecting an appropriate polarization state of the incident light, a delicate balance can be achieved among these parameters, effectively stabilizing the capture of inhomogeneous chiral particles. Conclusions This study employs the generalized Lorenz-Mie theory and the principle of electromagnetic momentum conservation to derive analytical expressions for the transverse and axial radiation forces exerted by dual Gaussian beams on multi-layered chiral particles propagating in arbitrary directions. The research provides an in-depth analysis of how standing wave beams affect the radiation force behavior of non-uniform chiral particles. Numerical analysis reveals significant influences of beam waist, particle size, chiral parameters, polarization angle and mode, as well as particle refractive index on both transverse and axial radiation forces. This research is important in analyzing and understanding the optical properties of complex-shaped multilayer biological cells and realizing the applications in the micromanipulation of multilayer biological structures. -
图 1 两束高斯波束照射多层手性粒子示意图
Fig. 1. structure plan of nonuniform chiral layered particles irradiated by DGBS
图 2 具有相同偏振角的反向传播双高斯波束$zox$平面强度分布图 (a)${w_{01}}\ (\ {w_{02}}\ ) = 1.7\lambda $; (b)${w_{01}}\ (\ {w_{02}}\ ) = 1.8\lambda $; (c) ${w_{01}}({w_{02}}) = $$ 1.9\lambda $
Fig. 2. Intensity distribution of counter propagating DGBs in $zox$plane with different $ {w_1}, {w_2} $: (a) ${w_{01}}({w_{02}}) = 1.7\lambda $; (b) ${w_{01}}({w_{02}}) = 1.8\lambda $; (c) ${w_{01}}({w_{02}}) = 1.9\lambda $.
图 3 与图2相比具有不同偏振角的反向传播双高斯波束$zox$平面强度分布图 (a)${w_{01}}({w_{02}}) = 1.7\lambda $; (b)${w_{01}}({w_{02}}) = 1.8\lambda $; (c) ${w_{01}}({w_{02}}) = 1.9\lambda $
Fig. 3. Intensity distribution of counter propagating DGBs in $zox$plane with different ${\beta _1}$, ${\beta _2}$ compared with Fig. 2: (a) ${w_{01}}({w_{02}}) = 1.7\lambda $; (b) ${w_{01}}({w_{02}}) = 1.8\lambda $; (c) ${w_{01}}({w_{02}}) = 1.9\lambda $.
图 4 与图2相比具有不同入射角度的双高斯波束$zox$平面强度分布图 (a) ${w_{01}}({w_{02}}) = 1.7\lambda $; (b)${w_{01}}({w_{02}}) = 1.8\lambda $; (c)${w_{01}}({w_{02}}) = 1.9\lambda $
Fig. 4. Intensity distribution of counter propagating DGBs in $zox$plane with different ${\alpha _1}, {\alpha _2}$ compared with Fig. 2: (a) ${w_{01}}({w_{02}}) = 1.7\lambda $; (b) ${w_{01}}({w_{02}}) = 1.8\lambda $; (c) ${w_{01}}({w_{02}}) = 1.9\lambda $.
图 5 多层手性粒子对单高斯光束轴向辐射力与文献结果进行对比
Fig. 5. Comparison of radiative force results for multilayer chiral spherical particles with a single Gaussian beam.
图 7 不同束腰半径下, 双高斯波束入射双层手性球的辐射力随轴(横)向位置的变化曲线 (a)沿z轴辐射力${F_z}$;(b)沿x轴辐射力${F_x}$; (c)沿y轴辐射力${F_y}$
Fig. 7. Radiative force of DGBS in different girdle radii on double-layer chiral sphere: (a) z-axis radiative force ${F_z}$; (b) x-axis radiative force ${F_x}$; (c) y-axis radiative force ${F_y}$.
图 8 不同偏振角下, 双高斯波束入射双层手性球的辐射力随轴(横)向位置的变化曲线 (a)沿z轴辐射力${F_z}$;(b)沿x轴辐射力${F_x}$; (c)沿y轴辐射力${F_y}$
Fig. 8. Radiative force of DGBS in different polarization angles on double-layer chiral sphere; (a) Radiative force along the z-axis ${F_z}$; (b) radiative force along the x-axis ${F_x}$; (c) radiative force along the y-axis ${F_y}$.
图 9 不同内层手性下, 双高斯波束入射双层手性球的辐射力随轴(横)向位置的变化曲线 (a)沿z轴辐射力${F_z}$; (b)沿x轴辐射力${F_x}$; (c)沿y轴辐射力${F_y}$; (d)双高斯波束对双层手性球远场散射RCS
Fig. 9. Radiative force of DGBS in different inner layer chiral on double-layer chiral sphere: (a) z-axis radiative force ${F_z}$; (b) x-axis radiative force ${F_x}$; (c) y-axis radiative force ${F_y}$; (d) the RCS of dual Gaussian beams scattering double-layer chiral sphere.
图 10 不同外层手性下, 双高斯波束入射双层手性球的辐射力随轴(横)向位置的变化曲线 (a)沿z轴辐射力${F_z}$; (b)沿x轴辐射力${F_x}$; (c)沿y轴辐射力${F_y}$
Fig. 10. Radiative force of DGBS in different outer layer chiral on double-layer chiral sphere: (a) z-axis radiative force ${F_z}$; (b) x-axis radiative force ${F_x}$; (c) y-axis radiative force ${F_y}$.
图 11 不同球内层半径下, 双高斯波束入射双层手性球的辐射力随轴(横)向位置的变化曲线 (a)沿z轴辐射力${F_z}$; (b)沿x轴辐射力${F_x}$; (c)沿y轴辐射力${F_y}$
Fig. 11. Radiative force of DGBS in different radii of the inner layers on double-layer chiral sphere: (a) z-axis radiative force ${F_z}$; (b) x-axis radiative force ${F_x}$; (c) y-axis radiative force ${F_y}$.
图 12 不同球外层半径下, 双高斯波束入射双层手性球的辐射力随轴(横)向位置的变化曲线 (a)沿z轴辐射力${F_z}$; (b)沿x轴辐射力${F_x}$; (c)沿y轴辐射力${F_y}$
Fig. 12. Radiative force of DGBS in different radii of the outer layers on double-layer chiral sphere: (a) z-axis radiative force ${F_z}$; (b) x-axis radiative force ${F_x}$; (c) y-axis radiative force ${F_y}$.
图 13 不同偏振状态下, 双高斯波束入射双层手性球的辐射力随轴(横)向位置的变化曲线 (a)沿z轴辐射力${F_z}$; (b)沿x轴辐射力${F_x}$; (c)沿y轴辐射力${F_y}$
Fig. 13. Radiative force of DGBS in different polarization states on double-layer chiral sphere: (a) z-axis radiative force ${F_z}$; (b) x-axis radiative force ${F_x}$; (c) y-axis radiative force ${F_y}$.
图 14 折射率由内向外逐层减小时, 辐射力随轴向位置变化曲线
Fig. 14. Curves of radiative force when refractive index decreases layer by layer from inside to outside.
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