Jiang Keli, Han Xiang'e, Ren Kuan Fang
J Opt Soc Am A Opt Image Sci Vis. 2013 Aug 1;30(8):1548-56. doi: 10.1364/JOSAA.30.001548.
The scattered waves of a shaped beam by an infinite cylinder in the far field are, stricto sensu, neither cylindrical nor spherical, so the asymptotic form of special functions involved in the theories based on the rigorous solution of Maxwell equations cannot be used to evaluate scattered intensities, even in the most simple case of Gaussian beam scattering by an infinite circular cylinder. Thus, although theories exist for the scattering of a shaped beam by infinite cylinders with circular and elliptical sections, the numerical calculations are limited to the near field. The vectorial complex ray model (VCRM) developed by Ren et al. describes waves by rays with a new property: the curvature of the wavefront. It is suitable to deal with the scattering of an arbitrarily shaped beam by a particle with a smooth surface of any form. In this paper, we apply this method to the scattering of an infinite elliptical cylinder illuminated by a Gaussian beam at normal incidence with an arbitrary position and orientation relative to the symmetric axis of the elliptical section of the cylinder. The method for calculating the curvature of an arbitrary surface is given and applied in the determination of the two curvature radii of the Gaussian beam wavefront at any point. Scattered intensities for different parameters of the beam and the particle as well as observation distance are presented to reveal the scattering properties and new phenomena observed in the beam scattering by an infinite elliptical cylinder.
严格来讲，无限长圆柱对成形光束的远场散射波既不是柱面波也不是球面波，因此，即使在高斯光束被无限长圆柱散射这种最简单的情况下，基于麦克斯韦方程组严格解的理论中所涉及的特殊函数的渐近形式也不能用于计算散射强度。所以，尽管存在关于成形光束被具有圆形和椭圆形截面的无限长圆柱散射的理论，但数值计算仅限于近场。Ren等人提出的矢量复射线模型（VCRM）用具有一种新特性（波前曲率）的射线来描述波。它适用于处理任意形状的光束被具有任意形状光滑表面的粒子散射的问题。在本文中，我们将此方法应用于高斯光束垂直入射到无限长椭圆圆柱的散射问题，该圆柱相对于其椭圆截面的对称轴具有任意位置和取向。给出了计算任意曲面曲率的方法，并将其应用于确定高斯光束波前在任意点的两个曲率半径。给出了光束、粒子的不同参数以及观测距离下的散射强度，以揭示无限长椭圆圆柱对光束散射的散射特性和新现象。
