Analytic results for the electrostatic T-matrix and polarizability of finite cylinders

IF 2.3 3区 物理与天体物理 Q2 OPTICS
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Abstract

The T-matrix for electromagnetic scattering is most commonly computed using the Extended Boundary Condition Method (EBCM), but this approach is numerically unstable for finite cylinders of high aspect ratio. In the electrostatics limit, we show that this instability is caused by catastrophic cancellations in the numerical calculations of oscillatory integrals. We find that the problematic integrals can instead be evaluated by integrating over the complement surface that extends from the cylinder to infinity. The resulting integrals are stable and we are then able to compute the electrostatic T-matrix accurately. The polarizability of the finite cylinder is then derived from this T-matrix and validated against results obtained via discretization. As an alternative, we also investigate the T-matrix on a basis of spheroidal harmonics, which is stable on its own and converges more quickly than on the spherical basis. Since the integrals are analytic, we moreover derive a simple analytic approximation based on truncation of the T-matrix on this basis. Beyond the direct benefits of analytic expressions for the electrostatic cylinder polarizability, this work should pave the way for a stable formulation of the full-wave T-matrix/EBCM approach for cylinders.
有限圆柱体静电 T 矩阵和极化性的解析结果
电磁散射的 T 矩阵最常用扩展边界条件法(EBCM)来计算,但这种方法对于高纵横比的有限圆柱体在数值上是不稳定的。在静电极限中,我们证明这种不稳定性是由振荡积分数值计算中的灾难性抵消引起的。我们发现,可以通过对从圆柱体延伸到无穷远的补余面进行积分来计算有问题的积分。由此得到的积分是稳定的,这样我们就能精确计算静电 T 矩阵。有限圆柱体的极化性就是根据这个 T 矩阵推导出来的,并与离散化得到的结果进行了验证。作为替代方案,我们还在球面谐波的基础上研究了 T 矩阵,它本身是稳定的,而且比球面基础收敛得更快。由于积分是解析的,我们还根据在此基础上对 T 矩阵的截断推导出一个简单的解析近似值。除了静电圆柱体极化率解析表达式的直接益处之外,这项工作还将为圆柱体全波 T 矩阵/EBCM 方法的稳定表述铺平道路。
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来源期刊
CiteScore
5.30
自引率
21.70%
发文量
273
审稿时长
58 days
期刊介绍: Papers with the following subject areas are suitable for publication in the Journal of Quantitative Spectroscopy and Radiative Transfer: - Theoretical and experimental aspects of the spectra of atoms, molecules, ions, and plasmas. - Spectral lineshape studies including models and computational algorithms. - Atmospheric spectroscopy. - Theoretical and experimental aspects of light scattering. - Application of light scattering in particle characterization and remote sensing. - Application of light scattering in biological sciences and medicine. - Radiative transfer in absorbing, emitting, and scattering media. - Radiative transfer in stochastic media.
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