  When light propagates through the edge or middle part of 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 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 this
rule scientifically. Based on the correlation between light
convergence-divergence and the slope of emergent light, combined with the
relationship between 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
perspective, 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 contrast 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 photonic hook (PH) and the modulation
of PNJ/PH in a new manner.
