非球形粒子光散射计算研究的进展综述

doi:10.11867/j.issn.1001-8166.2014.08.0903

介质的光散射在许多科学和工程领域中, 如光学、电磁学、工程物理、天体物理、大气科学、海洋学、生态学、生物物理学等都有重要的应用。由于其重要性、复杂性和困难性, 非球形粒子光散射已成为国际上光散射理论研究的焦点和前沿课题。就粒子光散射, 特别是非球形粒子光散射的计算方法及其研究进展进行扼要综述。首先, 从光散射的理论基础出发, 指出过去广泛应用的球形粒子光散射LorenzMie理论的局限性, 从粒子非球形性对散射模式影响的本质, 讨论球形粒子LorenzMie散射与非球形粒子光散射的不等效性。在此基础上扼要地阐述了现代非球形粒子光散射计算研究的进展, 包括精确的理论解法、一些重要的数值技术以及2个重要的近似解法, 即光学软粒子近似和几何光学近似。并指出, 近年来为了表示自然界中近于层状和更复杂粒子的光散射特性, 层状粒子模型和扩展边界条件法（EBCM）正在成为热门的研究领域, 是2个值得注意的发展动向。最后, 简要地讨论了非球形粒子光散射计算研究所面临的挑战及其未来的发展方向。

关键词: 光散射计算, 精确理论解和数值技术, 近似解法

Electromagnetic scattering by particles is a field of active research with high relevance for such diverse fields as atmospheric science, oceanography, astronomy, and engineering sciences, with specific applications in remote sensing, ecological environment, ocean optics, climate research, scattering by interplanetary dust grains, bio-optical imaging, antenna theory, particle sizing technology, and coating technology. Since its importance, complexity and difficulty, light scattering by nonspherical particles has become an international focus and frontiers of light scattering research and made a lot of studies. In the paper, some basic and important problems on light scattering calculations by nonspherical particles are briefly discussed and summarized. Based on the theoretical foundation of light scattering, the limitations of LorenzMie theory of spherical particles which have been widely used since the 1950 s are pointed out first. From the nature of the impact of nonsphericity of particles on scattering model, the nonequivalence of both the LorenzMie scattering by spherical particles and the light scattering by nonspherical particles is further discussed. Then, the research progresses of modern light scattering calculations by nonspherical particles are expounded and discussed, including accurate theoretical methods, some important numerical methods and two approximation algorithms, namely the approximations by optically soft particles and geometric optics approximation. We also point out that in order to express the light scattering characteristics by quasilayered and more complex particles in nature, the layered particle model and EBCM（Extended Boundary Condition Method）are becoming a hot research field in recent years, which are two noteworthy development trends. Finally, the challenge of the research on light scattering calculation methods by nonspherical particles and the future developments are briefly discussed.

Key words: Light scattering calculations, Accurate theoretical methods and numerical methods, Approximation algorithms.

中图分类号:

P422.3

图1 尘埃气溶胶粒子的扫描电子显微镜图像 ^{[

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Fig.1. Scanning electron photographs of dust particles ^{[

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图2 冰晶粒子图像:准球形、柱状、盘状和子弹玫瑰花状 ^{[

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]}

Fig.2 Ice crystal habits: quasi-spherical, column-type, plate-type, and bullet rosette particles ^{[

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表1 一些重要的非球形粒子光散射算法

Table 1 Some important optical scattering methods for nonspherical particles

计算方法	尺度参数x	粒子的形状和结构	优点	缺点
TMM (T-matrix method) T-矩阵法	<180	适于各种均匀对称粒子, 包括偏心夹杂物粒子、层状粒子和多球体集合等	是严格计算共振非球形粒子光散射最强有力和广泛使用的方法之一	当粒子x 180或用于任意粒子形状时, 存在数值稳定性和收敛性问题
FDTD (finite difference time domain method) 有限差分时域法	≤ 20	可用于任意粒子的形状和非均匀性粒子	概念简单、易于实现, 适用于形状复杂和非均匀小粒子的光散射	存在一系列局限性, 只适合于粒子x ≤ 20的光散射计算
SVM (separation of variables method) 分离变量法	<40	可用于长/扁椭球和更为复杂的粒子, 特别是层状粒子的光散射	能提供非常精确的计算结果	当粒子x或折射指数较大时, 易产生病态条件
PMM (point -matching method) 点匹配法		适用于比较简单的粒子的形状和结构	一般能提供比较精确的计算结果	在计算中会得到不精确或数值不稳定的结果。
GPMM(generalised PMM ) 广义PMM法		适用于形状和结构比较简单的粒子	解具有更清晰的收敛性, 结果更精确	对具有不同形状的粒子光散射, 缺乏灵活性和实用性
DDA (discrete dipole approxim. ) 离散偶极子近似, 或耦合偶极子法(CDM) [注]	适用于较小粒子的散射问题	可用到不同形状的散射体, 包括多粒子组合和具有覆盖层粒子等	物理概念简单, 散射条件能自动满足, 可用较少的未知量进行计算	存在数值精度、收敛速度慢、需要重复计算等问题
MoM (method of moments) 矩法	适用于较小粒子的散射问题	可用到不同形状的散射体, 包括具有覆盖层粒子和随机凹凸不平的球形粒子等	物理概念简单, 散射条件能自动满足, 可用较少的未知量进行计算	存在数值精度、收敛速度慢、需要重复计算等问题
ADA(anomalous diffraction approxim.) 异常衍射近似 MADA(modified anomalous diffraction approxim.) 改进异常衍射近似	x  1	可用到形状比较复杂的粒子的光散射	适用于大尺度光学软粒子的光散射, 具有算法快速和较精确等优点。 MADA具有计算更加简单和更加精确等优点
GOA (geometric optics approxima.) 几何光学近似	>>1	任意形状和大尺度粒子	精度随尺度与波长之比而增大	不适用于小粒子光散射
层状粒子模型和EBCM(extended boundary condition method) 扩展边界条件法		各种非球形和非均匀粒子	可处理各种非球形和非均匀粒子的光散射	实际的数值计算仍存在挑战

表1 一些重要的非球形粒子光散射算法

Table 1 Some important optical scattering methods for nonspherical particles

计算方法	尺度参数x	粒子的形状和结构	优点	缺点
TMM (T-matrix method) T-矩阵法	<180	适于各种均匀对称粒子, 包括偏心夹杂物粒子、层状粒子和多球体集合等	是严格计算共振非球形粒子光散射最强有力和广泛使用的方法之一	当粒子x 180或用于任意粒子形状时, 存在数值稳定性和收敛性问题
FDTD (finite difference time domain method) 有限差分时域法	≤ 20	可用于任意粒子的形状和非均匀性粒子	概念简单、易于实现, 适用于形状复杂和非均匀小粒子的光散射	存在一系列局限性, 只适合于粒子x ≤ 20的光散射计算
SVM (separation of variables method) 分离变量法	<40	可用于长/扁椭球和更为复杂的粒子, 特别是层状粒子的光散射	能提供非常精确的计算结果	当粒子x或折射指数较大时, 易产生病态条件
PMM (point -matching method) 点匹配法		适用于比较简单的粒子的形状和结构	一般能提供比较精确的计算结果	在计算中会得到不精确或数值不稳定的结果。
GPMM(generalised PMM ) 广义PMM法		适用于形状和结构比较简单的粒子	解具有更清晰的收敛性, 结果更精确	对具有不同形状的粒子光散射, 缺乏灵活性和实用性
DDA (discrete dipole approxim. ) 离散偶极子近似, 或耦合偶极子法(CDM) [注]	适用于较小粒子的散射问题	可用到不同形状的散射体, 包括多粒子组合和具有覆盖层粒子等	物理概念简单, 散射条件能自动满足, 可用较少的未知量进行计算	存在数值精度、收敛速度慢、需要重复计算等问题
MoM (method of moments) 矩法	适用于较小粒子的散射问题	可用到不同形状的散射体, 包括具有覆盖层粒子和随机凹凸不平的球形粒子等	物理概念简单, 散射条件能自动满足, 可用较少的未知量进行计算	存在数值精度、收敛速度慢、需要重复计算等问题
ADA(anomalous diffraction approxim.) 异常衍射近似 MADA(modified anomalous diffraction approxim.) 改进异常衍射近似	x  1	可用到形状比较复杂的粒子的光散射	适用于大尺度光学软粒子的光散射, 具有算法快速和较精确等优点。 MADA具有计算更加简单和更加精确等优点
GOA (geometric optics approxima.) 几何光学近似	>>1	任意形状和大尺度粒子	精度随尺度与波长之比而增大	不适用于小粒子光散射
层状粒子模型和EBCM(extended boundary condition method) 扩展边界条件法		各种非球形和非均匀粒子	可处理各种非球形和非均匀粒子的光散射	实际的数值计算仍存在挑战

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摘要

An Overview of the Advances in Computational Studies on Light Scattering by Nonspherical Particles