光泳力可以实现空气中吸光性粒子的稳定捕获和操控。对比传统光镊，基于光泳力的光学微操纵技术在对气体环境中吸收性颗粒的捕获和操作上具有明显的优势，可以为空气中微粒特性的在线检测、颗粒分离与精选、体三维显示技术等研究提供更加理想的方案。近几年来随着光场调控技术的发展，结构光场对吸光性粒子光泳捕获研究引起了大量研究者的关注，但由于光泳力特性受到颗粒所处气体环境、颗粒物理化学性质、入射激光参数等因素的多重影响，相关分析涉及电磁场、热场、流场等多场耦合，尚未形成完善的物理模型和完整的理论方法，开发并推动结构光场对气体环境中吸光性粒子的光泳力理论的发展对基于光泳力的光学微操纵技术创新及其在多个领域的应用研究具有重要的科学意义和实用价值。

本文针对结构光场对气体环境中吸光性粒子的力学特性，分别从理论推导、数值仿真的角度进行了研究，详细分析了基模高斯光束和贝塞尔光束照射下，光束的结构特征、粒子的光学参数以及粒子在光束中的位置对光泳力和辐射力的影响，主要内容和结果为：

1. 基于广义洛伦兹米理论，研究了结构激光光场的矢量波函数展开方法，分析了典型结构光场的重建问题。在此基础上，通过求解特定大气条件下均匀介质球的热传导方程和流体力学方程，推导了任意结构光束照射下均匀球粒子的光泳力表达式，并在电磁理论框架下推导了辐射力计算式，为结构光场照射下球形粒子的光泳力和辐射力的分析提供了理论基础。

2. 通过数值仿真方法，详细分析了标准大气压所对应的滑移流态和自由分子流态下，高斯光束的束腰半径、贝塞尔光束的半锥角和阶数、粒子的复折射率虚部和实部以及粒子的横向位移对光泳力和辐射力的影响。结果表明，高斯光束束腰半径变化和贝塞尔光束的阶数变化通常会对光泳力和辐射力产生显著影响。在某些条件下粒子的复折射率虚部变化和实部变化对光泳力和辐射力产生一定影响。对于轴对称的高斯光束和贝塞尔光束，粒子在光束中横向移动时，其所受横向光泳力分布和横向辐射力分布总是关于波束中心呈中心对称，而轴向分量总是关于光轴呈轴对称。

3. 对比分析了标准大气压下微米级粒子和纳米级粒子的光泳力和辐射力，结果表明，在标准大气压下，微米级粒子的光泳力的绝对值总是比辐射力大1-2个数量级，而当粒子小至纳米级粒子时，光泳力绝对值总是比辐射力小1-2个数量级。

Photophoretic forces can be used to achieve stable capture and manipulation of light-absorbing particles in the air. Compared to conventional optical tweezers, optical micromanipulation based on photophoretic force has obvious advantages in the capture and manipulation of absorbing particles in gaseous environments, and can provide a more ideal solution for research on online detection of particle properties in air, particle separation and selection, and volumetric 3D display techniques. With the development of light field modulation technology in recent years, the study of photophoretic capture of absorbing particles by structured light fields has attracted the attention of a large number of researchers, but because the photophoretic force characteristics are affected by multiple factors such as the gas environment in which the particles are located, the physical and chemical properties of the particles, and the incident laser parameters, the relevant analysis involves the coupling of multiple fields such as electromagnetic field, thermal field, and flow field, and has not yet formed a sound physical model and a complete theoretical approach. The development and promotion of the theory of photophoretic force of structured optical fields on light-absorbing particles in the gas environment is of great scientific significance and practical value for the technological innovation of optical micromanipulation based on photophoretic force and its application research in several fields.

In this paper, the mechanical properties of structured light fields on light-absorbing particles in gaseous environments are investigated from the perspective of theoretical derivation and numerical simulation respectively, and the effects of the structural characteristics of the beam, the optical parameters of the particles and the position of the particles in the beam on the photophoretic and radiative forces under the irradiation of the fundamental mode Gaussian and Bessel beams are analyzed in detail, with the main contents and results as follows:

1.Based on the Generalized Lorentz-Mie Theory, the vector wave function expansion method of the structured laser light field is investigated and the reconstruction problem of typical structured light field is analyzed. On this basis, by solving the heat conduction equation and hydrodynamic equation of a uniform media sphere under specific atmospheric conditions, the expressions for the photophoretic force of a uniform spherical particle irradiated by an arbitrary structural light beam are derived, and the equations for the calculation of the radiation force are derived under the framework of electromagnetic theory, providing a theoretical basis for the analysis of the photophoretic force and radiation force of a spherical particle irradiated by a structural light field.

2. The effects of the beam waist radius of the Gaussian beam, the half cone angle and order of the Bessel beam, the imaginary and real parts of the complex refractive index of the particle and the lateral displacement of the particle on the photophoretic and radiative forces are numerically simulated for the slip-flow and free-molecular regimes corresponding to standard atmospheric pressure. The results show that variations in the radius of the Gaussian beam waist and in the order of the Bessel beam usually have a significant effect on the photophoretic and radiative forces. Variations in the imaginary and real parts of the complex refractive index of the particle under certain conditions have some influence on the photophoretic and radiative forces. For axisymmetric Gaussian and Bessel beams, particles moving laterally in the beam are always centrosymmetric with respect to the center of the beam with respect to the transverse photophoretic force distribution and the transverse radiation force distribution, while the axial component is always axisymmetric with respect to the optical axis.

3. the photophoretic and radiative forces of micron-sized particles and nanoscale particles were compared separately at standard atmospheric pressure. The results show that the absolute value of the photophoretic force of micron-sized particles is always 1-2 orders of magnitude larger than the radiative force at standard atmospheric pressure, while the absolute value of the photophoretic force is always 1-2 orders of magnitude smaller than the radiative force when the particles are as small as nanoscale particles.

[1] GONG Z, PAN Y-L, VIDEEN G, et al. Optical trapping and manipulation of single particles in air: Principles, technical details, and applications [J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2018, 214: 94-119.
[2] ASHKIN A. History of optical trapping and manipulation of small-neutral particle, atoms, and molecules [J]. IEEE Journal of Selected Topics in Quantum Electronics, 2000, 6(6): 8418-56.
[3] GRIER D G. A revolution in optical manipulation [J]. Nature, 2003, 424(6950): 810–816.
[4] DHOLAKIA K, REECE P. Optical micromanipulation takes hold [J]. Nano Today, 2006, 1(1): 18-27.
[5] GONG Z, PAN Y-L, WANG C. Optical configurations for photophoretic trap of single particles in air [J]. Review of Scientific Instruments, 2016, 87(10): 103104-103114.
[6] ASHKIN A, DZIEDZIC J M. Optical trapping and manipulation of viruses and bacteria [J]. Science, 1987, 235(4795): 1517-1520.
[7] ASHKIN A, DZIEDZIC J M, YAMANE T. Optical trapping and manipulation of single cells using infrared laser beams [J]. Nature, 1987, 330(6150): 769-771.
[8] ASHKIN A, DZIEDZIC J. Internal cell manipulation using infrared laser traps [J]. Proceedings of the National Academy of Sciences, 1989, 86(20): 7914-7918.
[9] APPLEGATE R W, SQUIER J, VESTAD T, et al. Optical trapping, manipulation, and sorting of cells and colloids in microfluidic systems with diode laser bars [J]. Optics Express, 2004, 12(19): 4390-4398.
[10] XIE C, CHEN D, LI Y-Q. Raman sorting and identification of single living micro-organisms with optical tweezers [J]. Optics Letters, 2005, 30(14): 1800-1812.
[11] APPLEGATE R, SQUIER J, VESTAD T, et al. Microfluidic sorting system based on optical waveguide integration and diode laser bar trapping [J]. Lab on a Chip, 2006, 6(3): 422-426.
[12] SUN Y, YUAN X-C, ONG L, et al. Large-scale optical traps on a chip for optical sorting [J]. Applied Physics Letters, 2007, 90(3): 031107-031110.
[13] ASHKIN A. Optical Trapping and Manipulation of Neutral Particles Using Lasers [J]. Proceedings of the National Academy of Sciences of the United States of America, 1997, 94(10): 4853-4860.
[14] LIU Z, WU J, ZHANG Y, et al. Optical trapping and axial shifting for strongly absorbing particle with single focused TEM 00 Gaussian beam [J]. Applied Physics Letters, 2018, 113(9): 091101.
[15] HE B, CHENG X, ZHAN Y, et al. Investigation on the laser trapping mechanism of light-absorbing particles in air [J]. EPL (Europhysics Letters), 2019, 126(6): 64002-64008.
[16] LIU Z, ZHANG Z, ZHANG Y, et al. Absorbing particle 3D trap based on annular core fiber tweezers [J]. Optics Communications, 2019, 437: 399-402.
[17] PORFIREV A. Spatial-light-modulator-assisted laser manipulation in air [J]. Optical Engineering, 2020, 59(5): 1.
[18] SIL S, BASAK P, PAHI A, et al. A study of photophoretic trapping exploiting motional resonances of trapped particles induced by wideband excitation [J]. Applied Physics Letters, 2020, 117(22): 221106.
[19] MOUSAVI A, HOSSEINIBALAM F, HASSANZADEH S. Laguerre-Gaussian beams as an optical pipeline: Optical forces and intra-fluid micro particle movements [J]. Optik - International Journal for Light and Electron Optics, 2021, 234: 166591.
[20] ZHANG Z, CANNAN D, LIU J, et al. Observation of trapping and transporting air-borne absorbing particles with a single optical beam [J]. Optics Express, 2012, 20(15): 16212.
[21] CHEN G H, HE L, WU M Y, et al. Temporal Dependence of Photophoretic Force Optically Induced on Absorbing Airborne Particles by a Power-Modulated Laser [J]. Physical Review Applied, 2018, 10(5):054027.
[22] PHUOC T X. A numerical study of the radiation forces on an absorbing particle using the ray optics approach [J]. Optics Communications, 2004, 241(4-6): 271-277.
[23] SHVEDOV V G, DESYATNIKOV A S, RODE A V, et al. Optical guiding of absorbing nanoclusters in air [J]. Optics Express, 2009, 17(7): 5743-5757.
[24] LING L, LI Y-Q. Measurement of Raman spectra of single airborne absorbing particles trapped by a single laser beam [J]. Optics Letters, 2013, 38(4): 416-428.
[25] PAN Y L, HILL S C, COLEMAN M. Photophoretic trapping of absorbing particles in air and measurement of their single-particle Raman spectra [J]. Optics Express, 2012, 20(5): 5325.
[26] SMALLEY D E, NYGAARD E, SQUIRE K, et al. A photophoretic-trap volumetric display [J]. Nature, 2018, 553(7689): 486.
[27] BLUNDELL, BARRY G. Trapped particle makes 3D images [J]. Nature, 2018, 553(7689):408-409.
[28] WANG C, PAN Y-L, COLEMAN M. Experimental observation of particle cones formed by optical trapping [J]. Optics Letters, 2014, 39(9): 2767-2770.
[29] HUISKEN J, STELZER E H. Optical levitation of absorbing particles with a nominally Gaussian laser beam [J]. Optics Letters, 2002, 27(14): 1223-1225.
[30] ECKERSKORN N, BOWMAN R, KIRIAN R A, et al. Optically induced forces imposed in an optical funnel on a stream of particles in air or vacuum [J]. Physical Review Applied, 2015, 4(6): 36-45.
[31] HIDY G M, BROCK J R. Photophoresis and the descent of particles into the lower stratosphere [J]. Journal of Geophysical Research, 1967, 72(2): 455-460.
[32] MACKOWSKI D W. Photophoresis of aerosol particles in the free molecular and slip-flow regimes [J]. International Journal of Heat and Mass Transfer, 1989, 32(5): 843-854.
[33] REED L D. Low Knudsen number photophoresis [J]. Journal of Aerosol Science, 1977, 8(2): 123-131.
[34] LI W K, SOONG C Y, TZENG P Y, et al. Analysis of transition and mobility of microparticle photophoresis with slip-flow model [J]. Microfluidics & Nanofluidics, 2011, 10(1): 199-209.
[35] LIU Z H, LI W K, SOONG C Y. Theoretical analysis of micro-particle photophoresis in low-Kn gaseous flows [J]. Zasshi Journal Nihon Kyōbu Geka Gakkai, 2010, 42(2): 105-112.
[36] AMBROSIO L A, WANG J, GOUESBET G. Towards photophoresis with the generalized Lorenz-Mie theory [J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2022: 108266.
[37] EHRENHAFT F. On the physics of millionths of centimeters [J]. Phys Z, 1917, 18: 352-368.
[38] ORR C, KENG E. Photophoretic effects in the stratosphere [J]. Journal of the Atmospheric Sciences, 1964, 21(5): 475-478.
[39] TONG N T. Photophoretic force in the free molecule and transition regimes [J]. Journal of Colloid & Interface Science, 1973, 43(1): 78-84.
[40] YALAMOV Y I, KUTUKOV V B, SHCHUKIN E R. Theory of the photophoretic motion of the large-size volatile aerosol particle [J]. Journal of Colloid and Interface Science, 1976, 57(3): 564–571.
[41] KERKER M, COOKE D D. Photophoretic force on aerosol particles in the free-molecule regime [J]. Journal of the Optical Society of America, 1982, 72(9): 1267-1272.
[42] ARNOLD, S. Size dependence of the photophoretic force [J]. Journal of Applied Physics, 1982, 53(7): 5314-5319.
[43] PLUCHINO, ANTONINO B. Photophoretic force on particles for low Knudsen number [J]. Applied Optics, 1983, 22(1): 103-106.
[44] GREENE W M, SPJUT R E, BAR-ZIV E, et al. Photophoresis of irradiated spheres: Absorption centers [J]. Journal of the Optical Society of America B, 1985, 2(6): 998-1004.
[45] CHERNYAK V, BERESNEV S. Photophoresis of aerosol particles [J]. Journal of Aerosol Science, 1993, 24(7): 857-866.
[46] ZULEHNER W, ROHATSCHEK H. Representation and calculation of photophoretic forces and torques [J]. Journal of Aerosol Science, 1995, 26(2): 201-210.
[47] ROHATSCHEK H. Semi-empirical model of photophoretic forces for the entire range of pressures [J]. Journal of Aerosol Science, 1995, 26(5): 717-734.
[48] TEHRANIAN S, GIOVANE F, BLUM J, et al. Photophoresis of micrometer-sized particles in the free-molecular regime [J]. International Journal of Heat & Mass Transfer, 2001, 44(9): 1649-1657.
[49] KEH H J, TU H J. Thermophoresis and photophoresis of cylindrical particles [J]. Colloids & Surfaces A Physicochemical & Engineering Aspects, 2001, 176(2): 213-223.
[50] OU C L, KEH H J. Low-Knudsen-number photophoresis of aerosol spheroids [J]. Journal of Colloid & Interface Science, 2005, 282(1): 69-79.
[51] AMBROSIO L A. Photophoresis in the slip-flow and free molecular regimes for arbitrary-index particles [J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2020, 255(2): 107276.
[52] AMBROSIO L A. Generalized Lorenz-Mie theory in the analysis of longitudinal photophoresis of arbitrary-index particles: on-axis axisymmetric beams of the first kind [J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2021: 107889.
[53] WANG H, WANG J, DONG W, et al. Theoretical prediction of photophoretic force on a dielectric sphere illuminated by a circularly symmetric high-order Bessel beam: on-axis case [J]. Optics Express, 2021, 29(17): 26894-26908.
[54] MITRI F. Longitudinal and transverse optical scattering asymmetry parameters for a dielectric cylinder in light-sheets of arbitrary wavefronts and polarization [J]. Applied Optics, 2021, 60(6): 1678-1685.
[55] MITRI F. Longitudinal and transverse PAFs for an absorptive magneto-dielectric circular cylinder in light-sheets of arbitrary wavefronts and polarization [J]. Applied Optics, 2021, 60(26): 7937-7944.
[56] MITRI F. Effect of a perfectly conducting corner space on the PAFs for an absorptive dielectric circular cylinder [J]. JOSA B, 2021, 38(12): 3910-3919.
[57] MITRI F. Photophoretic asymmetry factors for an absorptive dielectric cylinder near a reflecting planar boundary [J]. JOSA A, 2021, 38(12): 1901-1910.
[58] MITRI F. Optical Magnus effect in the photophoresis of a spinning absorptive dielectric circular cylinder [J]. Applied Optics, 2022, 61(5): 1203-1211.
[59] SUN Y, WANG J, YU Q, et al. Longitudinal and transverse photophoretic force on a homogeneous sphere exerted by a Bessel beam with selective polarizations [J]. Applied Optics, 2022, 61(26): 7632-7643.
[60] SHVEDOV V G, RODE A V, IZDEBSKAYA Y V, et al. Selective trapping of multiple particles by volume speckle field [J]. Optics Express, 2010, 18(3): 3138-3142.
[61] SHVEDOV V G, RODE A V, IZDEBSKAYA Y V, et al. Giant optical manipulation [J]. Physical Review Letters, 2010, 105(11): 707-712.
[62] SHVEDOV V G, HNATOVSKY C, SHOSTKA N, et al. Optical manipulation of particle ensembles in air [J]. Optics Letters, 2012, 37(11): 1934-1936.
[63] ALPMANN C, ESSELING M, ROSE P, et al. Holographic optical bottle beams [J]. Applied Physics Letters, 2011, 100(11): 111101.
[64] 张垚. 亚波长光纤对策颗粒和细菌的光捕获和迁移研究 [D]. 中山大学, 2011.
[65] 刘丰瑞, 张志刚, 程腾等. 锥环状光阱对微米级气溶胶的动态捕捉[J]. 中国力学大会——2013 论文摘要集, 2013.
[66] LIU F, ZHANG Z, FU S, et al. Manipulation of aerosols revolving in taper-ring optical traps [J]. Optics Letters, 2014, 39(1): 100.
[67] REDDING B, PAN Y L. Optical trap for both transparent and absorbing particles in air using a single shaped laser beam [J]. Optics Letters, 2015, 40(12): 2798-2801.
[68] 吴佳泽. 液体中吸收性颗粒的光捕获特性研究 [D]. 哈尔滨工程大学, 2019.
[69] 贺博. 基于尺寸可调的贝塞尔光束对空气中悬浮微粒的捕获与操控 [D]. 西北大学, 2019.
[70] 张振宇. 基于光纤光镊技术的吸收性粒子捕获及其特性研究 [D]. 哈尔滨工程大学, 2019.
[71] 常树杭. 单颗碳基微粒的光镊操控及燃烧特性研究 [D]. 杭州电子科技大学, 2019.
[72] 杨智焜. 基于局域空心光束的光镊技术研究 [D]. 长春理工大学, 2020.
[73] CHAE M, BANG K, LEE B. P‐8.1: Controlling the Photophoretic Trap Location for Volumetric Display along Multiple Axes in a Compact System; proceedings of the SID Symposium Digest of Technical Papers, F, 2021 [C].
[74] HORVATH H. Photophoresis–a forgotten force?? [J]. KONA Powder and Particle Journal, 2014, 31: 181-199.
[75] JOVANOVIC O. Photophoresis—Light induced motion of particles suspended in gas [J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2009, 110(11): 889-901.
[76] KEITH D W. Photophoretic levitation of engineered aerosols for geoengineering [J]. Proceedings of the National Academy of Sciences, 2010, 107(38): 16428-16431.
[77] DONG S, LIU Y. Investigation on the photophoretic lift force acting upon particles under light irradiation [J]. Journal of Aerosol Science, 2017, 113: 114-118.
[78] SIL S, BANERJEE A. Photophoretic forces: A new enabler for robust single fiber-based optical traps in air [C].Proceedings of The Optical Trapping and Optical Micromanipulation, 2019.
[79] ZHANG Y, TANG X, ZHANG Y, et al. Optical attraction of strongly absorbing particles in liquids [J]. Optics Express, 2019, 27(9): 12414-12423.
[80] ASHKIN A. Acceleration and trapping of particles by radiation pressure [J]. Physical Review Letters, 1970, 24(4): 156.
[81] ASHKIN A, DZIEDZIC J M, BJORKHOLM J E, et al. Observation of a single-beam gradient force optical trap for dielectric particles [J]. Optics Letters, 1986, 11(5): 288-290.
[82] CHU S, BJORKHOLM J, ASHKIN A, et al. Experimental observation of optically trapped atoms [J]. Physical Review Letters, 1986, 57(3): 314.
[83] ASHKIN A, DZIEDZIC J. Optical levitation by radiation pressure [J]. Applied Physics Letters, 1971, 19(8): 283-285.
[84] ASHKIN A, DZIEDZIC J. Stability of optical levitation by radiation pressure [J]. Applied Physics Letters, 1974, 24(12): 586-588.
[85] ASHKIN A, DZIEDZIC J. Optical levitation of liquid drops by radiation pressure [J]. Science, 1975, 187(4181): 1073-1075.
[86] ASHKIN A, DZIEDZIC J. Optical levitation in high vacuum [J]. Applied Physics Letters, 1976, 28(6): 333-335.
[87] ASHKIN A. Applications of laser radiation pressure [J]. Science, 1980, 210(4474): 1081-1088.
[88] ASHKIN A, DZIEDZIC J. Observation of light scattering from nonspherical particles using optical levitation [J]. Applied Optics, 1980, 19(5): 660-668.
[89] TOM C, SCHUT B, HESSELINK G, et al. Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps [J]. Cytometry: The Journal of the International Society for Analytical Cytology, 1991, 12(6): 479-485.
[90] HARADA Y, ASAKURA T. Radiation forces on a dielectric sphere in the Rayleigh scattering regime [J]. Optics Communications, 1996, 124(5-6): 529-541.
[91] GOUESBET G, GREHAN G. Generalized Lorenz-Mie Theories: Second Edition [M]. 2017.
[92] BARTON J P, ALEXANDER D R, SCHAUB S. Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam [J]. Journal of Applied Physics, 1989, 66(10): 4594-4602.
[93] 韩国霞, 韩一平. 激光对含偏心核球形粒子的辐射俘获力 [J]. 物理学报, 2009, 58(9): 6167-6172.
[94] LI Z-J, WU Z-S, SHANG Q-C. Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam [J]. Optics Express, 2011, 19(17): 16044-16057.
[95] 韩一平, 杜云刚, 张华永. 高斯波束对双层粒子的辐射俘获力 [D]. 2006.
[96] GOUESBET G, MAHEU B, GREHAN G. Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation [J]. JOSA A, 1988, 5(9): 1427-1443.
[97] REN K, GREHAN G, GOUESBET G. Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects [J]. Optics Communications, 1994, 108(4-6): 343-54.
[98] REN K F, GREHAN G, GOUESBET G. Prediction of reverse radiation pressure by generalized Lorenz–Mie theory[J]. Applied optics, 1996, 35(15): 2702-2710.
[99] ONOFRI F, GREHAN G, GOUESBET G. Electromagnetic scattering from a multilayered sphere located in an arbitrary beam [J]. Applied optics, 1995, 34(30): 7113-7124.
[100] POLAERT H, GREHAN G, GOUESBET G. Forces and torques exerted on a multilayered spherical particle by a focused Gaussian beam [J]. Optics Communications, 1998, 155(1-3): 169-179.
[101] XU F, REN K, GOUESBET G, et al. Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam [J]. Physical Review E, 2007, 75(2): 026613.
[102] NAHMIAS Y K, ODDE D J. Analysis of radiation forces in laser trapping and laser-guided direct writing applications [J]. IEEE Journal of Quantum Electronics, 2002, 38(2): 131-141.
[103] MAO F-L, XING Q-R, WANG K, et al. Calculation of axial optical forces exerted on medium-sized particles by optical trap [J]. Optics & Laser Technology, 2007, 39(1): 34-39.
[104] 颜兵, 韩香娥. 高斯波束对离心球的辐射俘获力 [J]. 光学学报, 2009, 29(6): 1691.
[105] 张敏, 徐建波, 李杰等 瑞利粒子在贝塞尔光束中的横向受力 [J]. 强激光与粒子束, 2009, 21(1): 135-138.
[106] 王娟, 任洪亮. 拉盖尔-高斯光束捕获双层球的捕获力计算 [J]. 中 国 激 光, 2015, 42(6): 0608001.
[107] 张睿. 涡旋光束的光力特性研究 [D]. 浙江大学, 2014.
[108] GOUESBET G. T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates [J]. Optics Communications, 2010, 283(4): 517-521.
[109] GOUESBET G, LETELLIER C, REN K, et al. Discussion of two quadrature methods of evaluating beam-shape coefficients in generalized Lorenz–Mie theory [J]. Applied Optics, 1996, 35(9): 1537-1542.
[110] GOUESBET G, GRéHAN G, MAHEU B. Expressions to compute the coefficients gmn in the generalized Lorenz-Mie theory using finite series [J]. Journal of Optics, 1988, 19(1): 35.
[111] REN K F, GRéHAN G, GOUESBET G. Localized approximation of generalized Lorenz‐Mie theory: Faster algorithm for computations of beam shape coefficients, g [J]. Particle & particle systems characterization, 1992, 9(1‐4): 144-150.
[112] REN K F, GOUESBET G, GRéHAN G. Integral localized approximation in generalized Lorenz–Mie theory [J]. Applied Optics, 1998, 37(19): 4218-4225.
[113] QIU J, SHEN J. Beam shape coefficient calculation for a Gaussian beam: localized approximation, quadrature and angular spectrum decomposition methods [J]. Applied Optics, 2018, 57(2): 302-313.
[114] DOICU A, WRIEDT T. Plane wave spectrum of electromagnetic beams [J]. Optics Communications, 1997, 136(1-2): 114-124.
[115] GOUESBET G. Second modified localized approximation for use in generalized Lorenz–Mie theory and other theories revisited [J]. JOSA A, 2013, 30(4): 560-564.
[116] GOUESBET G, GREHAN G, MAHEU B. Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory [J]. JOSA A, 1990, 7(6): 998-1007.
[117] WANG J J, WRIEDT T, MäDLER L, et al. Multipole expansion of circularly symmetric Bessel beams of arbitrary order for scattering calculations [J]. Optics Communications, 2017, 387: 102-109.
[118] ASHKIN A. Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime [J]. Biophysical Journal, 1992, 61(2): 569-582.
[119] BOHREN C F, HUFFMAN D R. Absorption and scattering of light by small particles [M]. John Wiley & Sons, 2008.
[120] TALBOT L, CHENG R, SCHEFER R, et al. Thermophoresis of particles in a heated boundary layer [J]. Journal of Fluid Mechanics, 1980, 101(4): 737-758.
[121] HUANG J, ZHAO Y, YANG H, et al. Characteristics of photonic jets generated by a dielectric sphere illuminated by a Gaussian beam [J]. Applied Optics, 2020, 59(21): 6390-6398.
[122] MCGLOIN D, DHOLAKIA K. Bessel beams: diffraction in a new light [J]. Contemporary Physics, 2005, 46(1): 15-28.
[123] WANG J J, WRIEDT T, LOCK J A, et al. General description of circularly symmetric Bessel beams of arbitrary order [J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2016, 184: 218-232.