Fraunhofer and Fresnel field distributions from the LP01 mode in a micro-sized hollow optical fibre

Abstract

The electric field distribution of a LP01 mode and properties of the evanescent-wave field in a micro-sized hollow optical fibre under the weakly guiding approximation are analysed. The far- and near-field distributions of the output beam from the LP01 mode and its propagation characteristics in free space are calculated numerically from Fraunhofer and Fresnel diffraction theory. We also derive an analytical expression of the far-field distribution of the LP01 mode and discuss its applicable conditions. Our study shows that the output beam of the LP01 mode in the hollow fibre is a dark hollow divergent beam whose near-field divergent angle is slightly smaller than the far-field divergent angle. The dark spot size (DSS) of the beam in the near field is about equal to the beam radius r 0, whereas the DSS in the far field is smaller than its beam radius. We analyse the dependences of the far-field divergent angle of the output beam from the LP01 mode on various fibre parameters and briefly discuss potential applications of the dark hollow beam in atomic physics and atomic optics.