The properties of a pencil of light as defined approximately in the geometric optics ray tracing method are investigated. The vector Kirchhoff integral is utilized to accurately compute the electromagnetic near field in and around the pencil of light with various beam base sizes, shapes, propagation directions and medium refractive indices. If a pencil of light has geometric mean cross section size of the order p times the wavelength, it can propagate independently to a distance p² times the wavelength, where most of the beam energy diffuses out of the beam region. This is consistent with a statement that van de Hulst made in a classical text on light scattering. The electromagnetic near fields in the pencil of light are not uniform, have complicated patterns within short distances from the beam base, and the fields tend to converge to Fraunhofer diffraction fields far away from the base.

中文翻译：

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通过数值求解向量基尔霍夫积分确定几何光学射线跟踪的极限

研究了在几何光学光线追踪方法中大致定义的光笔的特性。向量基尔霍夫积分用于精确计算具有各种光束基础尺寸，形状，传播方向和中等折射率的光铅笔内部及其周围的电磁近场。如果一支铅笔的几何平均横截面大小约为波长的p倍，则它可以独立传播到距离p ²倍波长，其中大部分光束能量从光束区域扩散出去。这与范·德·赫尔斯特（van de Hulst）在经典著作中关于光散射的说法是一致的。光笔中的电磁近场不均匀，在距光束基座短距离内具有复杂的图案，并且这些场倾向于会聚到远离基座的Fraunhofer衍射场。