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Summary form only given. A novel design of optical resonator for generating donut-like beam is proposed. We found that the w-axicon configuration is quite suitable for generating an atom trap beam, because the beam is annular inherently throughout the beam pathway. A w-axicon works as azimuthal mode selector to obtain single azimuthal order of Laguerre-Gaussian mode. The azimuthal order selection is obtained by moving the central cone to forward or backward along the optical axis. A two-dimensional, vector electric field resonator simulation code is developed to prove the proposed idea, and optimize the resonator design.