光学学报, 2007, 27 (10): 1846, 网络出版: 2007-10-24
在轴高斯波束入射无限长多层圆柱散射的德拜级数解
Debye Series of Scattering by an Infinite Multi-Layered Cylinder in an on-Axis Gaussian Beam
物理光学 多层圆柱散射 德拜级数解 高斯波束 physical optics scattering by an infinite multi-layered cylinder Debye-series solution Gaussian beam
摘要
不均匀柱形粒子的光散射特性研究对复杂结构粒子参量的反演具有重要意义。基于德拜理论,对在轴高斯波束垂直入射无限长多层圆柱的散射特性进行了讨论。获得了散射系数的德拜级数展开式;并利用该公式分别计算了均匀和双层圆柱的总散射强度角分布,德拜级数单阶散射强度角分布;总散射强度结果与广义米氏理论(GLMT)进行了比较,两者吻合很好。分析表明圆柱散射强度不同散射角区间的值来自德拜级数不同阶的散射强度贡献;双层圆柱各层半径和折射率的值对德拜级数二阶散射强度角分布中峰值的出现起决定作用。当双层圆柱的外层较薄时,在120°~150°之间会出现两个明显峰值,即出现双重一阶彩虹峰值;反之,当外层厚度大于内层时,只有一个峰值存在。
Abstract
Scattering characteristic of an inhomogeneous cylindrical particle plays an important role in the measurement of parameters of complicated particles. Based on Debye theory, scattering by an infinite multi-layered cylinder in an on-axis Gaussian beam is discussed in detail. Scattering coefficient formulas of Debye series are obtained. With the formulas, distributions of total scattering intensities, Debye component scattering intensities by a homogeneous and a two-layered cylinder are calculated. And the results of total scattering intensities are in line with those of generalized Lorentz Mie theory. It is indicated that the different scattering angle interval of total scattering intensities comes from the contribution of different-order scattering intensities. Presence of two maximums in two order scattering intensities of Debye series is determined by radius and refractive index of a two-layered cylinder. For a two layered cylinder with a thin shell, there are two maximums between 120° and 150°, which is called dual first-order rainbow. Otherwise, when the external layer is thicker than the inner one, there is only one maximum.
李海英, 吴振森. 在轴高斯波束入射无限长多层圆柱散射的德拜级数解[J]. 光学学报, 2007, 27(10): 1846. 李海英, 吴振森. Debye Series of Scattering by an Infinite Multi-Layered Cylinder in an on-Axis Gaussian Beam[J]. Acta Optica Sinica, 2007, 27(10): 1846.