When light propagates through the edge or middle part of a microparticle’s incoming interface, there is a basic rule that light converges and diverges rapidly or slowly at the output port. These two parts are referred to as the region of rapid change (RRC) and region of slow change (RSC), respectively. Finding the boundary point between RRC and RSC is the key to reveal and expound upon this rule scientifically. Based on the correlation between light convergence–divergence and the slope of emergent light, combined with the relationship between a natural logarithm and growth in physical reality and the second derivative of a function in practical significance, we determine the boundary point between RRC and RSC, namely, the inflection point. From such a perspective, a photonic nanojet (PNJ) and near-field focusing by light irradiation on RSC and RRC, as well as the position of the inflection point under different refractive index contrasts and the field distribution of light focusing, are studied with finite-element-method-based numerical simulation and ray-optics-based theoretical analysis. By illuminating light of different field intensity ratios to the regions divided by the inflection point, we demonstrate the generation of a photonic hook (PH) and the modulation of PNJ/PH in a new manner.

中文翻译：

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拐点：光子纳米喷射的透视

当光通过微粒进入界面的边缘或中间部分传播时，有一个基本规则，即光在输出端口会聚和发散的速度很快或很慢。这两个部分分别被称为快速变化区域（RRC）和缓慢变化区域（RSC）。找到RRC和RSC的分界点是科学揭示和阐述这一规律的关键。基于光会聚-发散度与出射光斜率的相关性，结合自然对数与物理现实增长的关系以及具有实际意义的函数的二阶导数，我们确定了RRC和RSC之间的边界点，即拐点。从这个角度来看，光子纳米喷射（PNJ）和近场聚焦在 RSC 和 RRC 上通过光照射，采用基于有限元方法的数值模拟和基于射线光学的理论分析，研究了不同折射率对比下的拐点位置和光聚焦场分布。通过将不同场强比的光照射到由拐点划分的区域，我们以一种新的方式展示了光子钩 (PH) 的产生和 PNJ/PH 的调制。