A Chebyshev Spectral Method for Radiative Transfer Equations Applied to Electromagnetic Wave Propagation and Scattering in a Discrete Random Medium
A Chebyshev Spectral Method for Radiative Transfer Equations Applied to Electromagnetic Wave Propagation and Scattering in a Discrete Random Medium
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DOI：
10.1006/jcph.1999.6247
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发表时间：
1999-06
影响因子：
4.1
通讯作者：
A. Kim;A. Ishimaru
中科院分区：
文献类型：
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作者：
A. Kim;A. Ishimaru
在本文中，我们提出了一种数值方法求解辐射传输方程，模型电磁波传播的恒定背景，平面平行介质随机分布，相同大小的介质球。这项研究的应用包括光波在介质中，如生物组织和雾，以及毫米波在雨。在这些问题中，散射是高度各向异性的，这对于首先近似辐射传递方程的积分项以产生相关微分方程系统的标准方法是有问题的。在我们的方法中，我们使用切比雪夫谱近似的空间部分的4？1 Stokes参数的向量。然后，这种谱逼近产生一个耦合的线性积分方程组，该方程组具有有边的块稀疏结构，可以使用缩小块消去法有效地求解。通过将这种数值方法的焦点从导数算子调整到积分算子，我们发现我们可以有效地研究高度各向异性的散射介质。我们提出了一些米氏共振散射的例子，其中圆偏振平面波在平面平行介质中传播和散射，该介质包含随机分布的、相同大小的、半径与波长相当的电介质球。
In this paper, we present a numerical method for solving the radiative transfer equation that models electromagnetic wave propagation in a constant background, plane-parallel medium containing randomly distributed, identically sized, dielectric spheres. Applications of this study include optical waves in media such as biological tissue and fog as well as millimeter waves in rain. In these problems, the scattering is highly anisotropic, which is problematic for standard methods that approximate the integral term of the radiative transfer equation first to yield an associated system of differential equations. In our method, we use a Chebyshev spectral approximation of the spatial part of the 4?1 vector of Stokes parameters. This spectral approximation then yields a coupled, linear system of integral equations that has a bordered, block sparsity structure that can be efficiently solved using a deflated block elimination method. By readjusting the focus of this numerical method to the integral operators instead of the derivative operators, we find that we can effectively study highly anisotropic scattering media. We present some examples of Mie resonant scattering in which a circularly polarized plane wave propagates and scatters in a plane-parallel medium containing randomly distributed, identically sized, dielectric spheres whose radii are comparable to the wavelength.