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Using exact solutions of Maxwell equations based on the vector model, we calculate the diffracted near- and far-field distributions of the HEi1-mode output beam from a micron-sized hollow optical fibre under the Fresnel approximation, and compare the differences between the HE11- and LP01-mode output beams. Our study shows that it is unsuitable to calculate the diffracted near-field distribution of the hollow fibre by using weakly waveguiding approximation, and the near- and far-field intensity distributions of the HE11-mode output beam are doughnut-like, which can be used to form a simple atomic funnel as it is blue-detuned.