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The principle of optical trapping is conventionally based on the interaction of optical fields with linear induced polarizations. However, the optical force originating from the nonlinear polarization becomes significant when nonlinear optical nanoparticles are trapped by ultrafast laser pulses. Herein we establish the time-averaged optical forces on a nonlinear optical nanoparticle using high-repetition-rate ultrafast laser pulses, based on the linear and nonlinear polarization effects. We investigate the dependence of the optical forces on the magnitudes and signs of the refractive nonlinearities. It is found that the self-focusing effect enhances the trapping ability, whereas the self-defocusing effect leads to the splitting of potential well at the focal plane and destabilizes the optical trap. Our results show good agreement with the reported experimental observations and provide a theoretical support for capturing nonlinear optical particles., Comment: 5 pages and 3 figures

Discovery of atomically thin black phosphorus (called phosphorene) holds promise to be used as an alternative two-dimensional material to graphene and transition metal dichalcogenides especially as an anode material for lithium-ion batteries (LIBs). However, at present bulk black phosphorus (BP) still suffers from rapid capacity fading that results in poor rechargeable performance. Here, for the first time, we use in situ transmission electron microscopy (TEM) to construct nanoscale phosphorene LIBs and visualize the capacity fading mechanism in thick multilayer phosphorene by real time capturing delithiation-induced structural decomposition that reduces electrical conductivity and thus causes irreversibility of lithiated Li3P phase. We further demonstrate that few-layer phosphorene successfully circumvents the structural decomposition and holds superior structural restorability, even subjected to multi-cycle lithiation/delithiation processes and concomitant huge volume expansion. This finding affords new experimental insights into thickness-dependent lithium diffusion kinetics in phosphorene. Additionally, a scalable liquid-phase shear exfoliation route has been developed to produce high-quality ultrathin (monolayer or few-layer) phosphorene, only by a high-speed shear mixer or even a household kitchen blender with the shear rate threshold, which will pave the way for potential large-scale applications in LIBs once the rechargeable phosphorene nanoscale batteries can be transferred to industrialized enlargement in the future.