The nonparaxial propagation of the TEM_(ol)~(*) doughnut beam with the orbital angular momentum in the far field

摘要

The analytical expression for nonparaxial electric field amplitude of the TEM_(0l)~(*) doughnut beam with the orbital angular momentum quantum number l is derived in the far field by means of the angular spectrum representation and the stationary phase method. It is shown that the divergent angle of the far field of TEM_(0l)~(*) doughnut beam will be smaller with the decreasing of the orbital angular momentum quantum number I or the increasing of the beam waist width w of the initial beam. And the maximal radial intensity of the beam is decreased with its propagation at different rates for different l and w.