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.