各向异性粒子系对平面波/高斯波束的散射
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摘要
电磁(光)波与各种规则和非规则粒子之间相互作用作为国际上研究的热点课题之一，在粒度分析、生物医学、环境检测等领域中有着广泛的应用。目前对单个各向异性介质球形粒子及多个各向同性介质球形粒子对平面波的散射特性的研究报道较多。但是对于两个或多个各向异性介质球形粒子及其它形状的各向异性介质粒子与电磁波的相互作用仍然是比较新的课题，值得更进一步的研究。
本文围绕单个单轴各向异性介质球、椭球，多个单轴各向异性介质球对（任意方向入射）平面波的散射问题及任意方向高斯波束入射下的聚集各向同性介质球形粒子的散射特性和作用在单轴各向异性介质球上的辐射力和扭矩来展开研究。主要成果如下：
1、导出了具有任意传播方向两种极化模式的平面波用球矢量波函数的展开形式，导出了其展开系数。数值分析了平行主光轴平面波入射时，大尺寸参数单轴各向异性介质球的雷达散射截面的角分布；详细分析了平面波不平行主光轴入射时，介电常数张量元、磁导率张量元、有耗、无耗、尺寸参数、入射角和方位角等对单轴各向异性介质球的雷达散射截面的影响。
2、研究了单轴各向异性介质球对离轴高斯波束的散射特性。应用连带勒让德函数和三角函数的正交递推关系，导出了离轴高斯波束对单轴各向异性介质球的横向和轴向辐射力的解析表达式。数值分析了在轴高斯波束入射时，介电常数张量元对轴向辐射力的影响，详细讨论了单轴各向异性介质的有耗性、球半径、束腰宽度、球心与束腰中心距离对离轴高斯波束作用在单轴各向异性介质上的轴向和横向辐射力的影响。
3、基于球矢量波函数及其坐标旋转理论，导出了任意传播方向高斯波束在固定直角坐标系下的球矢量波函数的展开形式，详细讨论了波束形状因子及其收敛属性。导出了离轴斜入射高斯波束对单轴各向异性介质球的横向和轴向辐射力的解析表达式。数值计算了离轴斜入射高斯波束对单轴各向异性介质球的轴向，横向辐射力以及合力随入射角和方位角的变化。应用连带勒让德函数及三角函数的正交递推关系，导出了离轴斜入射高斯波束对单轴各向异性介质球的辐射扭矩的解析表达式，数值分析了波束中心位置和入射角对作用在单轴各向异性介质球上的辐射扭矩的影响。
4、基于广义多球Mie理论研究了任意结构的均匀各向同性聚集球形粒子对任意方向入射平面波及任意方向入射高斯波束的散射，应用球矢量波函数的平移加法定理导出了相干散射系数及总散射系数。数值计算了几种不同结构的聚集粒子对两种极化模式入射平面波的总散射强度的角分布。数值分析了束腰宽度、球间距、球个数、波束中心位置及入射角对几种分布的聚集球形粒子对两种极化模式高斯波束入射时的散射特性的影响。数值讨论了两种聚集结构的红细胞及烟尘簇团粒子对两种极化模式的入射高斯波束的散射特性。
5、研究了两个主光轴相互平行的均匀单轴各向异性介质球对平行主光轴的平面波的散射，应用切向连续边界条件推导了散射系数的解析表达式。数值分析了尺寸参数、单轴各向异性介质的吸收性及球间距对散射特性的影响。基于双球散射结果，进一步研究了具有相互平行主光轴的任意结构聚集单轴各向异性介质球形粒子对任意方向入射的平面波的散射，导出了相干散射系数及总散射系数的解析表达式。数值分析了入射角和方位角关于几种典型结构的聚集单轴各向异性球形粒子对平面波散射的雷达散射截面的影响。详细讨论了几种聚集单轴各向异性球形粒子对任意方向入射平面波散射的前后向雷达散射截面关于入射波长的变化。
6、首次从理论上导出了单轴各向异性介质椭球对正入射平面波散射的解析解。利用单轴各向异性介质球的内场用球矢量波函数展开的方法，结合完整的球矢量波函数与长旋转椭球矢量波函数之间的关系，导出了单轴各向异性介质长旋转椭球的内场根据长旋转椭球矢量波函数的展开形式，并给出了相应的内场展开系数。利用球矢量波函数与长旋转椭球矢量波函数之间的关系，结合平面波场的球矢量波函数展开的方法，导出了平面波用长旋转椭球矢量波函数的展开形式，给出了展开系数。利用Asano等人提出的一种较为巧妙的处理椭球边界条件的方法，导出了散射系数及内场未知展开系数的方程组，并通过求解方程组给出了散射系数的解析表达式。
Due to wide application in the areas of grain size analysis, biomedical engineering,environmental testing and so on, the interactions of electromagnetic (light) wave withregular and irregular particles have always been an important and hot internationalresearch topic. Recently, the scattering problems of a plane wave by single anisotropicdielectric spherical particle and multiple isotropic dielectric spherical particles havebeen diffusely reported. However, the scattering characteristics of two or multipleuniaxial anisotropic spherical particles and other shaped anisotropic particlesilluminated by an electromagnetic (light) wave are still new and merit problems andneed further research.
In this thesis, we principally investigated scattering properties of single uniaxialanisotropic dielectric sphere, spheroid, multiple uniaxial anisotropic dielectric sphericalparticles illuminated by a plane wave (arbitrary incident direction); and the radiationforce and torque exerted on a uniaxial anisotropic dielectric spherical particle by anarbitrary direction incident Gaussian beam. The main contributions and results of thethesis are as follows:
1. The expansion formats and expansion coefficients of two polarization modelsplane wave with an arbitrary propagating direction are derived. The angulardistributions of radar cross section (RCS) of larger particle size parameter are analyzednumerically when the plane wave incident along the primary optical axis. The effects ofpermittivity and permeability tensor elements, lossy and lossless dielectric, incidentangle and azimuth angle on the RCS of a uniaxial anisotropic sphere illuminated by anarbitrary direction incident plane wave are numerically analyzed in detail.
2. Scattering of an off-axis Gaussian beam by a uniaxial anisotropic sphere isstudied. Applying orthogonal and recursive relationships of associated Legendrefunction and trigonometric function, analytical expressions of the transverse and axialradiation forces exerted on a uniaxial anisotropic dielectric spherical particle by anoff-axis incident Gaussian beam are derived. The effects of permittivity tensor elementson axis radiation forces are numerically analyzed by an on-axis Gaussian beam. Theinfluences of the anisotropic absorbing dielectric, sphere radius, beam waist width,distance between sphere center and beam waist center on the axial and transverseradiation forces exerted on a uniaxial anisotropic dielectric sphere by an off-axisGaussian beam are discussed in detail.
3. Using spherical vector wave functions (SVWFs) and their coordinate rotation theory, the field of a Gaussian beam with an arbitrary propagating direction expanded interms of the SVWFs is derived. The beam shape coefficients and its convergenceproperty are discussed in detail. Analytical expressions of the transverse and axialradiation forces exerted on a uniaxial anisotropic dielectric spherical particle by anoff-axis obliquely incident Gaussian beam are derived. The changes of axial, transverseand resultant radiation forces with the incident angle and azimuth angle are numericallyanalyzed. Applying orthogonal and recursive relationships of associated Legendrefunction and trigonometric function, analytical expressions of the transverse and axialradiation torque exerted on a uniaxial anisotropic dielectric spherical particle by anoff-axis obliquely incident Gaussian beam are derived. The effects of location of beamcenter and incident angle on the radiation torque exerted on a uniaxial anisotropic by anoff-axis obliquely incident Gaussian beam are numerically discussed.
4. Based on generalized multi-spheres Mie theory (GMM), scattering of anarbitrary direction incident plane wave and Gaussian beam by a random aggregate ofhomogeneous isotropic spherical particles is investigated. The interactive scatteringcoefficients and total scattering coefficients are derived by using the addition theorem ofSVWFs. The angular distributions of total scattering intensity of several kinds ofaggregate spherical particles with different configurations are calculated. The effects ofbeam waist width, sphere separation distance, sphere number, beam center positioningand incident angle for a Gaussian beam with two polarization models incident onvarious shaped clusters spherical particles are numerically analyzed. The scatteringcharacteristics of two kinds of shaped red blood cells and soot aggregation particlesilluminated by an arbitrary direction incident Gaussian beam with two polarizationmodels are numerically discussed in detail.
5. The scattering of two interacting homogeneous uniaxial anisotropic spheres withparallel primary optical axes illuminated by a plane wave propagating parallel to theoptical axes is investigated. The analytical expressions of scattering coefficients arederived through the continuous boundary conditions on which the interaction of thebispheres is considered. The effects of the size parameter, the uniaxial anisotropicabsorbing dielectric and the sphere separation distance on the scattering characteristicare numerically analyzed. Based on scattering results of uniaxial anisotropic bispheres,an exact analytical solution is obtained for the scattering of a plane wave with arbitrarypropagation directions by a random aggregate of interacting homogeneous uniaxialanisotropic spherical particles with parallel primary optical axes. The interactivescattering coefficients and total scattering coefficients are derived. The effects of the incident angle and azimuth angle on RCSs of several types of collective uniaxialanisotropic spheres are numerically analyzed in detail. The characteristics of theforward and backward RCSs in relation to the incident wavelength are also numericallystudied.
6. The scattering of a uniaxial anisotropic rotation dielectric spheroid illuminatedby a plane wave propagating parallel to the primary optical axis is firstly investigated intheory. Utilizing the expansion method of internal fields of a uniaxial anisotropic spherein terms of SVWFs and complete relationship of SVWFs and spheroidal vector wavefunctions, the expansion formats of the electromagnetic fields in a uniaxial anisotropicprolate rotation spheroid in terms of prolate spheroidal vector wave functions arederived. The corresponding expansion coefficients of internal fields are given.Expansion formats and coefficients of the incident plane wave field in terms of prolatespheroidal vector wave functions are also derived by using the expansion of a planewave field in terms of SVWFs and the relationship of SVWFs and spheroidal vectorwave functions. Applying a smart method dealing with boundary condition of spheroidwhich is proposed by Asano et al., the equation set on the scattering coefficients andunknown expansion coefficient are obtained. The analytical expressions of thescattering coefficients are derived by solving this equation set.
本文围绕单个单轴各向异性介质球、椭球，多个单轴各向异性介质球对（任意方向入射）平面波的散射问题及任意方向高斯波束入射下的聚集各向同性介质球形粒子的散射特性和作用在单轴各向异性介质球上的辐射力和扭矩来展开研究。主要成果如下：
1、导出了具有任意传播方向两种极化模式的平面波用球矢量波函数的展开形式，导出了其展开系数。数值分析了平行主光轴平面波入射时，大尺寸参数单轴各向异性介质球的雷达散射截面的角分布；详细分析了平面波不平行主光轴入射时，介电常数张量元、磁导率张量元、有耗、无耗、尺寸参数、入射角和方位角等对单轴各向异性介质球的雷达散射截面的影响。
2、研究了单轴各向异性介质球对离轴高斯波束的散射特性。应用连带勒让德函数和三角函数的正交递推关系，导出了离轴高斯波束对单轴各向异性介质球的横向和轴向辐射力的解析表达式。数值分析了在轴高斯波束入射时，介电常数张量元对轴向辐射力的影响，详细讨论了单轴各向异性介质的有耗性、球半径、束腰宽度、球心与束腰中心距离对离轴高斯波束作用在单轴各向异性介质上的轴向和横向辐射力的影响。
3、基于球矢量波函数及其坐标旋转理论，导出了任意传播方向高斯波束在固定直角坐标系下的球矢量波函数的展开形式，详细讨论了波束形状因子及其收敛属性。导出了离轴斜入射高斯波束对单轴各向异性介质球的横向和轴向辐射力的解析表达式。数值计算了离轴斜入射高斯波束对单轴各向异性介质球的轴向，横向辐射力以及合力随入射角和方位角的变化。应用连带勒让德函数及三角函数的正交递推关系，导出了离轴斜入射高斯波束对单轴各向异性介质球的辐射扭矩的解析表达式，数值分析了波束中心位置和入射角对作用在单轴各向异性介质球上的辐射扭矩的影响。
4、基于广义多球Mie理论研究了任意结构的均匀各向同性聚集球形粒子对任意方向入射平面波及任意方向入射高斯波束的散射，应用球矢量波函数的平移加法定理导出了相干散射系数及总散射系数。数值计算了几种不同结构的聚集粒子对两种极化模式入射平面波的总散射强度的角分布。数值分析了束腰宽度、球间距、球个数、波束中心位置及入射角对几种分布的聚集球形粒子对两种极化模式高斯波束入射时的散射特性的影响。数值讨论了两种聚集结构的红细胞及烟尘簇团粒子对两种极化模式的入射高斯波束的散射特性。
5、研究了两个主光轴相互平行的均匀单轴各向异性介质球对平行主光轴的平面波的散射，应用切向连续边界条件推导了散射系数的解析表达式。数值分析了尺寸参数、单轴各向异性介质的吸收性及球间距对散射特性的影响。基于双球散射结果，进一步研究了具有相互平行主光轴的任意结构聚集单轴各向异性介质球形粒子对任意方向入射的平面波的散射，导出了相干散射系数及总散射系数的解析表达式。数值分析了入射角和方位角关于几种典型结构的聚集单轴各向异性球形粒子对平面波散射的雷达散射截面的影响。详细讨论了几种聚集单轴各向异性球形粒子对任意方向入射平面波散射的前后向雷达散射截面关于入射波长的变化。
6、首次从理论上导出了单轴各向异性介质椭球对正入射平面波散射的解析解。利用单轴各向异性介质球的内场用球矢量波函数展开的方法，结合完整的球矢量波函数与长旋转椭球矢量波函数之间的关系，导出了单轴各向异性介质长旋转椭球的内场根据长旋转椭球矢量波函数的展开形式，并给出了相应的内场展开系数。利用球矢量波函数与长旋转椭球矢量波函数之间的关系，结合平面波场的球矢量波函数展开的方法，导出了平面波用长旋转椭球矢量波函数的展开形式，给出了展开系数。利用Asano等人提出的一种较为巧妙的处理椭球边界条件的方法，导出了散射系数及内场未知展开系数的方程组，并通过求解方程组给出了散射系数的解析表达式。
Due to wide application in the areas of grain size analysis, biomedical engineering,environmental testing and so on, the interactions of electromagnetic (light) wave withregular and irregular particles have always been an important and hot internationalresearch topic. Recently, the scattering problems of a plane wave by single anisotropicdielectric spherical particle and multiple isotropic dielectric spherical particles havebeen diffusely reported. However, the scattering characteristics of two or multipleuniaxial anisotropic spherical particles and other shaped anisotropic particlesilluminated by an electromagnetic (light) wave are still new and merit problems andneed further research.
In this thesis, we principally investigated scattering properties of single uniaxialanisotropic dielectric sphere, spheroid, multiple uniaxial anisotropic dielectric sphericalparticles illuminated by a plane wave (arbitrary incident direction); and the radiationforce and torque exerted on a uniaxial anisotropic dielectric spherical particle by anarbitrary direction incident Gaussian beam. The main contributions and results of thethesis are as follows:
1. The expansion formats and expansion coefficients of two polarization modelsplane wave with an arbitrary propagating direction are derived. The angulardistributions of radar cross section (RCS) of larger particle size parameter are analyzednumerically when the plane wave incident along the primary optical axis. The effects ofpermittivity and permeability tensor elements, lossy and lossless dielectric, incidentangle and azimuth angle on the RCS of a uniaxial anisotropic sphere illuminated by anarbitrary direction incident plane wave are numerically analyzed in detail.
2. Scattering of an off-axis Gaussian beam by a uniaxial anisotropic sphere isstudied. Applying orthogonal and recursive relationships of associated Legendrefunction and trigonometric function, analytical expressions of the transverse and axialradiation forces exerted on a uniaxial anisotropic dielectric spherical particle by anoff-axis incident Gaussian beam are derived. The effects of permittivity tensor elementson axis radiation forces are numerically analyzed by an on-axis Gaussian beam. Theinfluences of the anisotropic absorbing dielectric, sphere radius, beam waist width,distance between sphere center and beam waist center on the axial and transverseradiation forces exerted on a uniaxial anisotropic dielectric sphere by an off-axisGaussian beam are discussed in detail.
3. Using spherical vector wave functions (SVWFs) and their coordinate rotation theory, the field of a Gaussian beam with an arbitrary propagating direction expanded interms of the SVWFs is derived. The beam shape coefficients and its convergenceproperty are discussed in detail. Analytical expressions of the transverse and axialradiation forces exerted on a uniaxial anisotropic dielectric spherical particle by anoff-axis obliquely incident Gaussian beam are derived. The changes of axial, transverseand resultant radiation forces with the incident angle and azimuth angle are numericallyanalyzed. Applying orthogonal and recursive relationships of associated Legendrefunction and trigonometric function, analytical expressions of the transverse and axialradiation torque exerted on a uniaxial anisotropic dielectric spherical particle by anoff-axis obliquely incident Gaussian beam are derived. The effects of location of beamcenter and incident angle on the radiation torque exerted on a uniaxial anisotropic by anoff-axis obliquely incident Gaussian beam are numerically discussed.
4. Based on generalized multi-spheres Mie theory (GMM), scattering of anarbitrary direction incident plane wave and Gaussian beam by a random aggregate ofhomogeneous isotropic spherical particles is investigated. The interactive scatteringcoefficients and total scattering coefficients are derived by using the addition theorem ofSVWFs. The angular distributions of total scattering intensity of several kinds ofaggregate spherical particles with different configurations are calculated. The effects ofbeam waist width, sphere separation distance, sphere number, beam center positioningand incident angle for a Gaussian beam with two polarization models incident onvarious shaped clusters spherical particles are numerically analyzed. The scatteringcharacteristics of two kinds of shaped red blood cells and soot aggregation particlesilluminated by an arbitrary direction incident Gaussian beam with two polarizationmodels are numerically discussed in detail.
5. The scattering of two interacting homogeneous uniaxial anisotropic spheres withparallel primary optical axes illuminated by a plane wave propagating parallel to theoptical axes is investigated. The analytical expressions of scattering coefficients arederived through the continuous boundary conditions on which the interaction of thebispheres is considered. The effects of the size parameter, the uniaxial anisotropicabsorbing dielectric and the sphere separation distance on the scattering characteristicare numerically analyzed. Based on scattering results of uniaxial anisotropic bispheres,an exact analytical solution is obtained for the scattering of a plane wave with arbitrarypropagation directions by a random aggregate of interacting homogeneous uniaxialanisotropic spherical particles with parallel primary optical axes. The interactivescattering coefficients and total scattering coefficients are derived. The effects of the incident angle and azimuth angle on RCSs of several types of collective uniaxialanisotropic spheres are numerically analyzed in detail. The characteristics of theforward and backward RCSs in relation to the incident wavelength are also numericallystudied.
6. The scattering of a uniaxial anisotropic rotation dielectric spheroid illuminatedby a plane wave propagating parallel to the primary optical axis is firstly investigated intheory. Utilizing the expansion method of internal fields of a uniaxial anisotropic spherein terms of SVWFs and complete relationship of SVWFs and spheroidal vector wavefunctions, the expansion formats of the electromagnetic fields in a uniaxial anisotropicprolate rotation spheroid in terms of prolate spheroidal vector wave functions arederived. The corresponding expansion coefficients of internal fields are given.Expansion formats and coefficients of the incident plane wave field in terms of prolatespheroidal vector wave functions are also derived by using the expansion of a planewave field in terms of SVWFs and the relationship of SVWFs and spheroidal vectorwave functions. Applying a smart method dealing with boundary condition of spheroidwhich is proposed by Asano et al., the equation set on the scattering coefficients andunknown expansion coefficient are obtained. The analytical expressions of thescattering coefficients are derived by solving this equation set.
引文
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