水平界面上方球体的电磁散射

      Electromagnetic scattering by a sphere above a plane interface

      • 摘要: 研究水平界面上方球体的电磁散射可以为诸多应用提供一个合适的理论模型,为此本文提出了一种精确求解此电磁散射问题的半解析方法。该方法应用适当的球矢量波函数来展开球体的散射场和内场,并且考虑到球体与水平界面之间的耦合散射,应用了球和圆柱矢量波函数之间的转换关系。水平界面对入射电磁波的反射场和球体的散射场均采用投影法计算。以平面波、高斯波束和拉盖尔-高斯波束照射硅基底上方的聚苯乙烯球为例,计算了归一化的微分散射截面。数值结果表明对于入射的平面波和高斯波束在反射波方向附近散射最强,另外随着球体离水平界面距离的增加而前向散射变大。

         

        Abstract: The study the electromagnetic scattering by a sphere above a plane interface provides a proper theoretical model in many applications, thus we present an exact semi-analytical solution in this paper. This technique utilizes appropriate spherical vector wave functions to expand the scattered field by and internal field within the sphere, and to treat the coupling scattering between the sphere and plane interface, and the transformation relations of spherical vector wave functions to cylindrical ones are applied. The reflected wave off the interface and scattered field by the sphere are both calculated with a projection scheme. By taking incident plane wave, Gaussian beam and Laguerre-Gaussian beam on a polystyrene sphere above a silicon substrate as three typical examples, normalized differential scattering cross sections are evaluated. Numerical results show that for a plane wave and Gaussian beam the maximum scattering occurs in the angle regions around the direction of reflection, and the forward scattering becomes larger with the increase of the distance between the sphere and plane interface.

         

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