偏心球及双球粒子与任意入射高斯波束的相互作用研究
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摘要
粒子与有形波束间的相互作用一直以来都是许多理论工作及实际应用领域中相当活跃的研究内容之一,对生物医学、物理学、化学等许多领域的开发和进一步研究应用具有重要的指导作用和实际意义。粒子对波束的电磁散射、波束对粒子的捕获与操纵成为该研究内容中无可争论的焦点。关于均匀、分层粒子与波束的相互作用的研究已有许多报道,对于自然界中更为普遍存在的偏心粒子和多粒子来说,仍然还有大量的工作值得我们作进一步的研究。
本文围绕偏心球及双球粒子与任意入射单高斯波束、双高斯波束的相互作用开展研究,其中包括粒子对波束的散射和波束对粒子的光捕获与光结合。主要工作成果如下：
1.根据离轴入射波束的球矢量波函数展开式,考虑波束极化方向的影响,利用矢量场的叠加原理获得了极化波束离轴入射时的波束因子；基于斜入射波束的球矢量波函数展开式,结合直角坐标系中的坐标旋转矩阵,导出了极化波束离轴斜入射时在实验室坐标系中的任意入射波束因子表达式,对入射场给出了较为普遍的描述；计算了归一化球矢量波函数对应的任意入射波束因子；重新推导了正、负时间因子对应的离轴入射波束因子之间的关系,并对所得关系式进行了数值验证,修正了已有关系式。
2.基于广义米理论,分别利用球矢量波函数在r≥|d|和r≤|d|时的平移加法定理,结合偏心球粒子、双球粒子系统在各个边界处的边界条件,推导了两种粒子系统在波束任意入射时的散射方程；数值模拟并讨论了粒子大小、球心间距离、入射方向、极化方向等参数对介质偏心球粒子、双介质球粒子的散射特性的影响；对导体内核偏心球、双导体球以及一个导体球一个介质球时的散射方程及散射特性进行了比较分析。
3.研究了高斯波束任意入射偏心球粒子时的辐射力及辐射力矩。基于偏心球粒子对任意入射高斯波束的散射理论研究,利用麦克斯韦张量与广义米理论相结合,推导了波束任意入射时的辐射力、辐射力矩的级数表达式；在与已有文献结果对比的基础上数值计算了不同束腰中心位置、入射方向、极化方向、粒子的大小、内核的相对大小及位置时的辐射力及辐射力矩,讨论了这些参数的变化对辐射力以及辐射力矩的影响。
4.基于单高斯波束任意入射时的矢量波函数展开式,利用矢量场的叠加原理,导出了双高斯波束任意入射时的波束因子表达式；结合偏心球粒子在单波束入射时的散射方程,数值计算并分析了偏心球粒子对任意入射双高斯波束的散射场随入射方向、极化方向、相位差等物理量的变化关系；研究了双高斯光束对偏心球粒子的辐射力及辐射力矩,讨论了粒子参数、双波束的入射方向、相位差等对粒子的辐射力及力矩的影响。
5.基于广义米理论,将双波束任意入射时的矢量波函数展开应用于双介质球粒子的散射研究中,结合双球粒子系统在单波束任意入射时的散射方程,数值分析了双球粒子系统在双高斯波束任意入射时的散射场以及粒子之间的相干散射场；从理论上对粒子系统中单个粒子受到的结合力进行了分析,数值计算了分别处于单波束和双波束势阱中的双球粒子系统的结合力,分析了粒子大小、折射率、球心间距离、入射方向、极化方向、相位差等参数对结合力的影响。
The interaction between the particles and the shaped beams is one of the rather active research topics in many theoretical investigations and engineering applications. It provides a very important guidance and has practical meanings for the development of so many fields such as biomedicine, physics, chemistry, etc. The electric-magnetic scattering of the beam, the optical trapping and manipulating of the particles by the beam are the unquestionable focus of the research. The studies on the interaction between the homogeneous, layered particles and the shaped beams have been reported for many times. However, still there is a number of work should be done about the eccentric particles and multi-particles which more commonly exist in nature.
This article refers to the study on the interaction of arbitrarily incident Gaussian beam with eccentric sphere and bi-sphere. It includes the discussion on the beam scattering of the particles and the optical trapping and optical binding of the particles by the beam. The main achievements are summarized as follows:
Firstly, according to the expansion of the off-axis incidence beam in terms of the spherical vector wave functions (SVWFs) and considering the influence of the polarization direction of the beam, the expansion of the off-axis incidence polarized beam is given by using the superposition of vector field. Based on the expansion of the oblique incidence beam and combining the coordinates rotation matrix in the Cartesian coordinates, the expansion and the beam-shape coefficients (BSCs) of the beam in the particle coordinate system are given when the beam is polarized in any angle, off-axis and obliquely incoming, so the universal description of the incident beam is provided. Then the arbitrarily incident BSCs with respect to the normalized SVWFs are calculated. The relations between the off-axis BSCs with respect to positive-time factor and that with respect to negative-time factor has been re-derived and numerically verified, meanwhile the existed expressions are amended.
Secondly, according to the generalized Lorenz-Mie theory (GLMT), utilizing the boundary conditions at each boundary of the eccentric sphere and bi-sphere, the scattering equations of the two systems have been deduced by using the additional theorems of the spherical vector wave functions when r≥|d| and when r≤|d| respectively. The effects on the scattering characteristics of eccentric sphere and bi-sphere of the parameters, such as the particle size, the distance between the centers of sphere, the incidence angle, polarization angle, etc., have been calculated and analyzed. Additionally, the scattering equations and the scattering characteristics for the cases of a sphere with an eccentric conductor inclusion, two conductor spheres and a bi-sphere composed by a conductor sphere and a dielectric sphere, have been compared and discussed respectively.
Thirdly, the radiation forces and radiation torques exerted on the eccentric sphere by the arbitrarily incident Gaussian beam are investigated. Based on the study on the scattering theoies of the arbitrarily incident Gaussian beam by eccentric sphere, the series expressions of the radiation forces and torques are deduced by combining Maxwell Stress Tensor (MST) and the generalized Lorenz-Mie theory. After the comparison with the results presented in the literature, the radiation forces and torques are numerically calculated when the locations of the beam waist center, the incident directions, the polarized directions, the particle's sizes, the inner core's relative sizes and positions are different respectively, and the influence of the changes of these parameters to the forces and torques is analyzed.
Fourthly, on the basis of the expansion of the arbitrarily incident Gaussian beam, the expression of BSCs for double beams is given by using the superposition of the vector field. Combining with the scattering theory of the eccentric sphere illuminated by a single Gaussian beam, the scattered field of dual-beam is evaluated and analyzed for different parameters, such as the incidence direction, polarization direction and phase difference, etc.. The radiation forces and radiation torques of the eccentric sphere acted by the dual-beam are investigated, and the influence to the forces and torques of the particle's parameters, incidence angle and the phase difference of the two beams is discussed.
Fifthly, based on the generalized Lorenz-Mie theory, the expressions of the dual-beam is applied to the study of the scattering characteristics of bi-sphere, and combining the scattering equations of bi-sphere for single beam incidence, the scattered field of the bi-sphere system is computed when the dual-beam arbitrarily incidents. Then, the optical binding force of the bi-sphere system is analyzed theoretically, the force in the single beam potential well and that in the dual-beam potential well are numerically calculated respectively. And the influence to the optical binding force of such parameters as the particle size, the refractive index, the distance between the centers of the spheres, the incident direction, the polarized direction, etc., is analyzed.
本文围绕偏心球及双球粒子与任意入射单高斯波束、双高斯波束的相互作用开展研究,其中包括粒子对波束的散射和波束对粒子的光捕获与光结合。主要工作成果如下：
1.根据离轴入射波束的球矢量波函数展开式,考虑波束极化方向的影响,利用矢量场的叠加原理获得了极化波束离轴入射时的波束因子；基于斜入射波束的球矢量波函数展开式,结合直角坐标系中的坐标旋转矩阵,导出了极化波束离轴斜入射时在实验室坐标系中的任意入射波束因子表达式,对入射场给出了较为普遍的描述；计算了归一化球矢量波函数对应的任意入射波束因子；重新推导了正、负时间因子对应的离轴入射波束因子之间的关系,并对所得关系式进行了数值验证,修正了已有关系式。
2.基于广义米理论,分别利用球矢量波函数在r≥|d|和r≤|d|时的平移加法定理,结合偏心球粒子、双球粒子系统在各个边界处的边界条件,推导了两种粒子系统在波束任意入射时的散射方程；数值模拟并讨论了粒子大小、球心间距离、入射方向、极化方向等参数对介质偏心球粒子、双介质球粒子的散射特性的影响；对导体内核偏心球、双导体球以及一个导体球一个介质球时的散射方程及散射特性进行了比较分析。
3.研究了高斯波束任意入射偏心球粒子时的辐射力及辐射力矩。基于偏心球粒子对任意入射高斯波束的散射理论研究,利用麦克斯韦张量与广义米理论相结合,推导了波束任意入射时的辐射力、辐射力矩的级数表达式；在与已有文献结果对比的基础上数值计算了不同束腰中心位置、入射方向、极化方向、粒子的大小、内核的相对大小及位置时的辐射力及辐射力矩,讨论了这些参数的变化对辐射力以及辐射力矩的影响。
4.基于单高斯波束任意入射时的矢量波函数展开式,利用矢量场的叠加原理,导出了双高斯波束任意入射时的波束因子表达式；结合偏心球粒子在单波束入射时的散射方程,数值计算并分析了偏心球粒子对任意入射双高斯波束的散射场随入射方向、极化方向、相位差等物理量的变化关系；研究了双高斯光束对偏心球粒子的辐射力及辐射力矩,讨论了粒子参数、双波束的入射方向、相位差等对粒子的辐射力及力矩的影响。
5.基于广义米理论,将双波束任意入射时的矢量波函数展开应用于双介质球粒子的散射研究中,结合双球粒子系统在单波束任意入射时的散射方程,数值分析了双球粒子系统在双高斯波束任意入射时的散射场以及粒子之间的相干散射场；从理论上对粒子系统中单个粒子受到的结合力进行了分析,数值计算了分别处于单波束和双波束势阱中的双球粒子系统的结合力,分析了粒子大小、折射率、球心间距离、入射方向、极化方向、相位差等参数对结合力的影响。
The interaction between the particles and the shaped beams is one of the rather active research topics in many theoretical investigations and engineering applications. It provides a very important guidance and has practical meanings for the development of so many fields such as biomedicine, physics, chemistry, etc. The electric-magnetic scattering of the beam, the optical trapping and manipulating of the particles by the beam are the unquestionable focus of the research. The studies on the interaction between the homogeneous, layered particles and the shaped beams have been reported for many times. However, still there is a number of work should be done about the eccentric particles and multi-particles which more commonly exist in nature.
This article refers to the study on the interaction of arbitrarily incident Gaussian beam with eccentric sphere and bi-sphere. It includes the discussion on the beam scattering of the particles and the optical trapping and optical binding of the particles by the beam. The main achievements are summarized as follows:
Firstly, according to the expansion of the off-axis incidence beam in terms of the spherical vector wave functions (SVWFs) and considering the influence of the polarization direction of the beam, the expansion of the off-axis incidence polarized beam is given by using the superposition of vector field. Based on the expansion of the oblique incidence beam and combining the coordinates rotation matrix in the Cartesian coordinates, the expansion and the beam-shape coefficients (BSCs) of the beam in the particle coordinate system are given when the beam is polarized in any angle, off-axis and obliquely incoming, so the universal description of the incident beam is provided. Then the arbitrarily incident BSCs with respect to the normalized SVWFs are calculated. The relations between the off-axis BSCs with respect to positive-time factor and that with respect to negative-time factor has been re-derived and numerically verified, meanwhile the existed expressions are amended.
Secondly, according to the generalized Lorenz-Mie theory (GLMT), utilizing the boundary conditions at each boundary of the eccentric sphere and bi-sphere, the scattering equations of the two systems have been deduced by using the additional theorems of the spherical vector wave functions when r≥|d| and when r≤|d| respectively. The effects on the scattering characteristics of eccentric sphere and bi-sphere of the parameters, such as the particle size, the distance between the centers of sphere, the incidence angle, polarization angle, etc., have been calculated and analyzed. Additionally, the scattering equations and the scattering characteristics for the cases of a sphere with an eccentric conductor inclusion, two conductor spheres and a bi-sphere composed by a conductor sphere and a dielectric sphere, have been compared and discussed respectively.
Thirdly, the radiation forces and radiation torques exerted on the eccentric sphere by the arbitrarily incident Gaussian beam are investigated. Based on the study on the scattering theoies of the arbitrarily incident Gaussian beam by eccentric sphere, the series expressions of the radiation forces and torques are deduced by combining Maxwell Stress Tensor (MST) and the generalized Lorenz-Mie theory. After the comparison with the results presented in the literature, the radiation forces and torques are numerically calculated when the locations of the beam waist center, the incident directions, the polarized directions, the particle's sizes, the inner core's relative sizes and positions are different respectively, and the influence of the changes of these parameters to the forces and torques is analyzed.
Fourthly, on the basis of the expansion of the arbitrarily incident Gaussian beam, the expression of BSCs for double beams is given by using the superposition of the vector field. Combining with the scattering theory of the eccentric sphere illuminated by a single Gaussian beam, the scattered field of dual-beam is evaluated and analyzed for different parameters, such as the incidence direction, polarization direction and phase difference, etc.. The radiation forces and radiation torques of the eccentric sphere acted by the dual-beam are investigated, and the influence to the forces and torques of the particle's parameters, incidence angle and the phase difference of the two beams is discussed.
Fifthly, based on the generalized Lorenz-Mie theory, the expressions of the dual-beam is applied to the study of the scattering characteristics of bi-sphere, and combining the scattering equations of bi-sphere for single beam incidence, the scattered field of the bi-sphere system is computed when the dual-beam arbitrarily incidents. Then, the optical binding force of the bi-sphere system is analyzed theoretically, the force in the single beam potential well and that in the dual-beam potential well are numerically calculated respectively. And the influence to the optical binding force of such parameters as the particle size, the refractive index, the distance between the centers of the spheres, the incident direction, the polarized direction, etc., is analyzed.
引文
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