双零阶贝塞尔波束的传播及对单轴各向异性球的散射特性

Propagation of double zero-order Bessel beam and its scattering properties to uniaxial anisotropic spheres

基于广义洛伦兹Mie理论,研究了单轴各向异性球形粒子对两束具有任意传播和极化方向的零阶贝塞尔波束的传播和散射特性,并与单零阶贝赛尔波束入射单轴各向异性球形粒子时的传播和散射特性进行了对比研究.利用球矢量波函数的正交关系及坐标旋转定理,导出了任意传播和极化方向零阶贝塞尔波束的球矢量波函数的展开形式,通过矢量叠加得到了总入射场的展开系数.基于傅里叶变换方法和切向连续的边界条件,得到了单轴各向异性球内部电磁场的球矢量波函数展开式,并导出了散射系数解析表达式.将零阶贝塞尔波束退化成平面波,通过将其入射到单轴各向异性球形粒子的雷达散射截面角分布与文献结果进行对比,验证了本文理论及程序的正确性.数值分析了入射角、锥角及极化角等参数对雷达散射截面角分布的影响.本文理论和数值结果希望能应用于多波束入射下各向异性粒子、生物细胞等复杂粒子体系的散射、粒径分析以及光学俘获等特性的研究中.

Based on the generalized Lorenz Mie theory,the propagation and scattering properties of a uniaxial anisotropic spherical particle illuminated separately by double zero-order Bessel beam with arbitrary propagation direction and polarization direction are studied.The propagation and scattering characteristics are compared with those of a uniaxial anisotropic spherical particle illuminated by a single zero-order Bessel beam.Using the orthogonal relation of the spherical vector wave function and coordinate rotation theorem,the expanded forms of double zero-order Bessel beams with arbitrary propagation direction and polarization direction are derived.The analytical expressions of the expansion coefficients are derived by the integral method.The expansion coefficients of total incident field are obtained through the vector superposition principle.Based on the Fourier transform and tangentially continuous boundary conditions,the internal electromagnetic field of the uniaxial anisotropic sphere is expanded in terms of the spherical vector wave function and the scattering coefficients are derived.By comparing the angular distribution of the radar cross section of the particle illuminated by single and double zero-order Bessel beam when degenerating into plane waves with those results given by the literature,the correctness of the theory and the program in this paper are both verified.The effects of the incidence angle,conic angle and polarization angle on angle distribution of the radar cross section are numerically analyzed.The theoretical and numerical results in this paper are expected to be used to study the scattering properties,particle size analysis and optical trapping for anisotropic particles,biological cells and other particles illuminated by multi-beams.