复杂粒子体系对波束的散射及其应用
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摘要
粒子对波束的电磁(光)散射作为国际研究热点领域之一,在粒度分析、生物医学、环境检测、宇宙遥感等领域中广泛应用。对平面波和三维高斯波束入射各向同性球和圆柱的散射研究已有大量报道。但是,粒子或多粒子对其它类型波束散射,以及各向异性介质粒子对波束散射仍然值得进一步研究。
本文围绕复杂粒子体系对有形波束散射这一具有重要理论意义及应用前景的课题开展研究。主要成果如下:
1.导出了多层圆柱对二维高斯波束的散射系数Debye series解,理论证明了该方法与广义米理论(GLMT)散射系数数学公式的一致性关系;分析了Debye series分量描述的双层圆柱的彩虹散射强度。数值计算了圆柱和波束参数对散射强度分布的影响;利用Debye series分量讨论了双层圆柱的折射率和半径对双一阶彩虹的影响。
2.详细推导了球和圆柱坐标系中两种矢量波函数的相互转化关系;导出了在轴和离轴二维高斯波束在球坐标系中的波形因子,该方法避免了复杂积分,提高了计算效率。利用二维高斯波束入射场,内场和散射场的球矢量波函数展开,结合边界条件,获得了散射系数的表达式。以水滴和有核血细胞为例,数值计算了分层球对二维高斯波束的散射,分析了粒子和波束参数对散射强度的影响。
3.研究了高斯波束入射各向异性球粒子的散射特性。采用傅立叶变换和球矢量波函数表示了内场和散射场;结合边界条件,推导了波束入射情况下散射系数的表达式,以及各向异性球内场各特征波场分量的表述式。数值计算了在轴和离轴高斯波束入射各向异性球时散射强度、内场和表面场的空间分布,讨论了波束参数、介电参数对其分布的影响。将该方法推广到导体各向异性涂层球的散射研究,计算了涂有磁化等离子体层的导体球散射强度分布。
4.研究了厄米高斯波束入射多层球和圆柱的散射特性。推导并证明了旁轴波动方程的解与复源点方法之间的一致性关系。基于复源点方法描述的多模高斯波束场,结合球和圆柱矢量波函数展开方法,导出了二维和三维高阶厄米波束的波形因子;数值计算了多层球和圆柱对厄米高斯波束的散射特性,讨论了球、圆柱参数和波束参数对高阶(多模)场散射强度角分布的影响。
5.基于矢量波函数展开和蒙特卡罗(MC)方法,研究了高斯波束入射单个和多个带电球粒子的散射传输特性。详细推导了单个带电球粒子的散射系数;并采用矢量波函数展开方法结合矢量波函数的加法定理导出了高斯波束入射多个带电/不带电球粒子的散射系数;提出了用MC模拟高斯波束的抽样方法。以星际空间带电Carbon粒子和极区中层的带电冰晶粒子为例,讨论了带电量对粒子体系散射特性的影响。
Electromagnetic(optical) scattering of shaped beams by particles is an important international research topic, and widely applied in the areas of grain size analysis, biomedical engineering, environmental testing, and remote sensing of the universe. The scattering characteristics of an isotropic sphere and an isotropic infinite cylinder illustrated by a plane wave and a three dimension(3D) Gaussian beam have been vastly reported. However, the scattering characteristics of other shaped beams, and the anisotropic media as well, still require further discussion.
Regarding the topic of the scattering properties of shaped beam by complex particle systems has great value and wide application, some work in this paper is done. The main work and results are as follows:
1. The scattering coefficient formulas of Debye series of an infinite multi-layered cylinder in a 2D Gaussian beam are derived. With the recurrence relations of the Bessel functions and applying induction, the consistency between our results by Debye series and those by GLMT is proved. Numerical calculations are given. The effects of particle and beam parameters on the scattering intensities, and the relationship between Debye series and twin primary rainbow of a two-layered cylinder are discussed.
2. Starting with the transform relations of spherical vector wave functions and cylindrical vector wave functions, based on the beam shape coefficients of a 2D Gaussian beam in the cylindrical coordinates, the on-axis and off-axis beam shape coefficients are deduced respectively. The method we provide avoids the complex integral calculation and greatly improves the computational efficiency. The incident, internal and scattering fields are all expanded in terms of the spherical vector wave functions. Combining with boundary conditions, scattering coefficients are obtained. Taking a droplet and a cell as examples, numerical calculations are given. The effects of the beam and particle parameters on the scattering properties are studied.
3. The scattering characteristics of a Gaussian beam by an anisotropic sphere are explored. Based on the Fourier transform and spherical vector wave functions, the scattering and internal fields are expressed. Using the boundary condition, both the scattering and internal field coefficients are derived. Numerical calculations are presented for both on-axis and off-axis Gaussian beams respectively. The angular distributions of the scattering intensities are calculated and the effects of beam parameters and dielectric constant on the scattering properties are analyzed. The internal and near-surface field components are also discussed in detail. On the basis of this method, the scattering characteristics of a plasma-coated conducting sphere are analyzed as well.
4. The scattering characteristics of a multi-layered sphere and a multi-layered cylinder are developed, respectively. The derivation of the relationship between the paraxial wave equation and the complex source points is given and proved. Based on the complex source points expressions of the multi-mode Gaussian beam field, with the spherical and cylindrical vector wave functions, the beam shape coefficients of the 2D and 3D Hermite Gaussian beams are obtained, and the scattering properties of a multi-layered sphere and a multi-layered cylinder are studied. The effects of particle and beam parameters on the angular distributions of scattering intensities in multi-mode Gaussian beam field are analyzed.
5. On the basis of spherical vector wave functions and Monto Carlo(MC) method, the characteristics of scattering and transmission by a single charged sphere and multiple charged spheres are involved. The scattering coefficients of a single charged sphere are deduced. And with spherical vector wave functions and addition theorem, the scattering coefficients of multiple charged and uncharged spheres are derived. The sampling method of simulating a Gaussian beam in use of MC is provided. As an application, scattering characteristics of charged Carbon particles and ice crystals are calculated, and the effects of the charge quantity on the properties of scattering and transmission are discussed.
本文围绕复杂粒子体系对有形波束散射这一具有重要理论意义及应用前景的课题开展研究。主要成果如下:
1.导出了多层圆柱对二维高斯波束的散射系数Debye series解,理论证明了该方法与广义米理论(GLMT)散射系数数学公式的一致性关系;分析了Debye series分量描述的双层圆柱的彩虹散射强度。数值计算了圆柱和波束参数对散射强度分布的影响;利用Debye series分量讨论了双层圆柱的折射率和半径对双一阶彩虹的影响。
2.详细推导了球和圆柱坐标系中两种矢量波函数的相互转化关系;导出了在轴和离轴二维高斯波束在球坐标系中的波形因子,该方法避免了复杂积分,提高了计算效率。利用二维高斯波束入射场,内场和散射场的球矢量波函数展开,结合边界条件,获得了散射系数的表达式。以水滴和有核血细胞为例,数值计算了分层球对二维高斯波束的散射,分析了粒子和波束参数对散射强度的影响。
3.研究了高斯波束入射各向异性球粒子的散射特性。采用傅立叶变换和球矢量波函数表示了内场和散射场;结合边界条件,推导了波束入射情况下散射系数的表达式,以及各向异性球内场各特征波场分量的表述式。数值计算了在轴和离轴高斯波束入射各向异性球时散射强度、内场和表面场的空间分布,讨论了波束参数、介电参数对其分布的影响。将该方法推广到导体各向异性涂层球的散射研究,计算了涂有磁化等离子体层的导体球散射强度分布。
4.研究了厄米高斯波束入射多层球和圆柱的散射特性。推导并证明了旁轴波动方程的解与复源点方法之间的一致性关系。基于复源点方法描述的多模高斯波束场,结合球和圆柱矢量波函数展开方法,导出了二维和三维高阶厄米波束的波形因子;数值计算了多层球和圆柱对厄米高斯波束的散射特性,讨论了球、圆柱参数和波束参数对高阶(多模)场散射强度角分布的影响。
5.基于矢量波函数展开和蒙特卡罗(MC)方法,研究了高斯波束入射单个和多个带电球粒子的散射传输特性。详细推导了单个带电球粒子的散射系数;并采用矢量波函数展开方法结合矢量波函数的加法定理导出了高斯波束入射多个带电/不带电球粒子的散射系数;提出了用MC模拟高斯波束的抽样方法。以星际空间带电Carbon粒子和极区中层的带电冰晶粒子为例,讨论了带电量对粒子体系散射特性的影响。
Electromagnetic(optical) scattering of shaped beams by particles is an important international research topic, and widely applied in the areas of grain size analysis, biomedical engineering, environmental testing, and remote sensing of the universe. The scattering characteristics of an isotropic sphere and an isotropic infinite cylinder illustrated by a plane wave and a three dimension(3D) Gaussian beam have been vastly reported. However, the scattering characteristics of other shaped beams, and the anisotropic media as well, still require further discussion.
Regarding the topic of the scattering properties of shaped beam by complex particle systems has great value and wide application, some work in this paper is done. The main work and results are as follows:
1. The scattering coefficient formulas of Debye series of an infinite multi-layered cylinder in a 2D Gaussian beam are derived. With the recurrence relations of the Bessel functions and applying induction, the consistency between our results by Debye series and those by GLMT is proved. Numerical calculations are given. The effects of particle and beam parameters on the scattering intensities, and the relationship between Debye series and twin primary rainbow of a two-layered cylinder are discussed.
2. Starting with the transform relations of spherical vector wave functions and cylindrical vector wave functions, based on the beam shape coefficients of a 2D Gaussian beam in the cylindrical coordinates, the on-axis and off-axis beam shape coefficients are deduced respectively. The method we provide avoids the complex integral calculation and greatly improves the computational efficiency. The incident, internal and scattering fields are all expanded in terms of the spherical vector wave functions. Combining with boundary conditions, scattering coefficients are obtained. Taking a droplet and a cell as examples, numerical calculations are given. The effects of the beam and particle parameters on the scattering properties are studied.
3. The scattering characteristics of a Gaussian beam by an anisotropic sphere are explored. Based on the Fourier transform and spherical vector wave functions, the scattering and internal fields are expressed. Using the boundary condition, both the scattering and internal field coefficients are derived. Numerical calculations are presented for both on-axis and off-axis Gaussian beams respectively. The angular distributions of the scattering intensities are calculated and the effects of beam parameters and dielectric constant on the scattering properties are analyzed. The internal and near-surface field components are also discussed in detail. On the basis of this method, the scattering characteristics of a plasma-coated conducting sphere are analyzed as well.
4. The scattering characteristics of a multi-layered sphere and a multi-layered cylinder are developed, respectively. The derivation of the relationship between the paraxial wave equation and the complex source points is given and proved. Based on the complex source points expressions of the multi-mode Gaussian beam field, with the spherical and cylindrical vector wave functions, the beam shape coefficients of the 2D and 3D Hermite Gaussian beams are obtained, and the scattering properties of a multi-layered sphere and a multi-layered cylinder are studied. The effects of particle and beam parameters on the angular distributions of scattering intensities in multi-mode Gaussian beam field are analyzed.
5. On the basis of spherical vector wave functions and Monto Carlo(MC) method, the characteristics of scattering and transmission by a single charged sphere and multiple charged spheres are involved. The scattering coefficients of a single charged sphere are deduced. And with spherical vector wave functions and addition theorem, the scattering coefficients of multiple charged and uncharged spheres are derived. The sampling method of simulating a Gaussian beam in use of MC is provided. As an application, scattering characteristics of charged Carbon particles and ice crystals are calculated, and the effects of the charge quantity on the properties of scattering and transmission are discussed.
引文
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