Circular Lorentz-Gauss beams with the power-exponent-phase vortex

Circular Lorentz-Gauss beams with the power-exponent-phase vortex are introduced in this paper. Based on the Collins formula, an analytical expression for a circular Lorentz-Gauss beam with the power-exponent-phase vortex passing through a paraxial ABCD optical system is derived. By using the obtained expression of the optical field, one can calculate the orbital angular momentum density of a circular Lorentz-Gauss beam passing through a paraxial ABCD optical system. As a numerical example, the propagation properties of a circular Lorentz-Gauss beam with the power-exponent-phase vortex are demonstrated in free space. The evolution laws of the normalized intensity and the orbital angular momentum density distributions are investigated during the beam propagation. Since a circular Lorentz-Gauss beam with different topological charge and power order has the same intensity distribution in the source plane, the effects of the topological charge and the power order on the normalized intensity and the orbital angular momentum density distributions in the non-source plane are examined.