Poincaré Beams at the Tight Focus: Inseparability, Radial Spin Hall Effect, and Reverse Energy Flow

The family of Poincaré beams has three parameters, including two real-valued angular which specify a definite polarization state on the sphere, and third integer parameter n specifying beam singularity order. We show theoretically through numerical simulation that, while being inseparable not allowing for separation orbital degrees freedom in general case, display remarkable properties when tightly focused. find that at = 2, reverse energy flow occurs near optical axis, is mathematically expressed as negative projection Poynting vector. also reveal given certain parameters beams, rotates around axis due to spin–orbital conversion. radial Hall effect tight focus on-axis components spin momentum vector have different signs different-radius circles centered focal spot center.