Tong Ruihuan, Dong Zhen, Chen Yahong, Wang Fei, Cai Yangjian, Setälä Tero
Opt Express. 2020 Mar 30;28(7):9713-9727. doi: 10.1364/OE.386187.
Focusing of a vectorial (electromagnetic) optical beam through a high numerical aperture can be investigated by means of the Richards-Wolf diffraction integral. However, such an integral extends from two-dimensional to four-dimensional, greatly increasing the computation time and therefore limiting the applicability, when light with decreased spatial coherence is considered. Here, we advance an effective protocol for the fast calculation of the statistical properties of a tightly focused field produced by a random electromagnetic beam with arbitrary state of spatial coherence and polarization. The novel method relies on a vectorial pseudo-mode representation and a fast algorithm of the wave-vector space Fourier transform. The procedure is demonstrated for several types of radially (fully) polarized but spatially partially coherent Schell-model beams. The simulations show that the computation time for obtaining the focal spectral density distribution with 512 × 512 spatial points for a low coherence beam is less than 100 seconds, while with the conventional quadruple Richards-Wolf integral more than 100 hours is required. The results further indicate that spatial coherence can be viewed as an effective degree of freedom to govern both the transverse and longitudinal components of a tightly focused field with potential applications in reverse shaping of focal fields and optical trapping control.
通过高数值孔径对矢量（电磁）光束进行聚焦，可以借助理查兹 - 沃尔夫衍射积分来研究。然而，当考虑空间相干性降低的光时，这样的积分从二维扩展到四维，极大地增加了计算时间，从而限制了其适用性。在此，我们提出一种有效的方案，用于快速计算由具有任意空间相干态和偏振态的随机电磁光束产生的紧聚焦场的统计特性。该新方法依赖于矢量伪模表示和波矢空间傅里叶变换的快速算法。针对几种类型的径向（完全）偏振但空间部分相干的谢尔模型光束演示了该过程。模拟结果表明，对于低相干光束，获取具有512×512空间点的焦谱密度分布的计算时间少于100秒，而使用传统的四重理查兹 - 沃尔夫积分则需要超过100小时。结果进一步表明，空间相干性可被视为一种有效的自由度，用于控制紧聚焦场的横向和纵向分量，在焦场的反向整形和光阱控制方面具有潜在应用。
