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The far-field intensity distribution characteristics of fundamental mode of the annular core optical fibers (ACF) are calculated theoretically based on the weak waveguide approximation in this paper. The simulation results demonstrate that provided the parameters of the ACF are designed properly, the ACF can realize single-mode operation. Besides, the beam will concentrate to the principal maximum position to form a central bright spot indicating great enhancement for the energy focusability of beam, which is valuable for the energy-demand applications in the far-field. These theoretical results possess great significance in designing and manufacturing ACF.