Bi Lei, Gouesbet Gérard
Opt Express. 2022 Aug 1;30(16):29796-29810. doi: 10.1364/OE.465772.
A new formulation of the Debye series based on the Riccati-differential equations was developed to compute electromagnetic wave scattering by non-spherical particles. In this formulation, the T-matrix was expanded in terms of the Debye series. The zeroth-order term, which corresponds to a combination of diffraction and external reflection, is given by unity minus the external reflection matrix. The higher-order terms are generated from the transmission matrix from the medium to the particle, the internal reflection matrix within the particle and the transmission matrix from the particle to the medium. We demonstrate that the aforementioned four reflection-transmission matrices satisfy the Riccati-differential equations, which can be numerically solved by the fourth-order Runge-Kutta method. The present algorithm can be applied to generalized convex non-spherical particles. The differential equations were analytically validated in the case of a homogeneous sphere. Representative results were given in the case of spheroids. The impacts of the Debye series with various orders on the optical properties of spheroids were revealed with significant details.
基于里卡蒂微分方程开发了一种新的德拜级数公式，用于计算非球形粒子的电磁波散射。在该公式中，T矩阵以德拜级数展开。零阶项对应于衍射和外部反射的组合，由单位矩阵减去外部反射矩阵给出。高阶项由从介质到粒子的传输矩阵、粒子内部的反射矩阵以及从粒子到介质的传输矩阵生成。我们证明上述四个反射 - 传输矩阵满足里卡蒂微分方程，该方程可通过四阶龙格 - 库塔方法进行数值求解。本算法可应用于广义凸非球形粒子。在均匀球体的情况下对微分方程进行了解析验证。在椭球体的情况下给出了代表性结果。详细揭示了不同阶数的德拜级数对椭球体光学特性的影响。
