Propagation properties of hollow conical double half-Gaussian beams

In this paper, we present a new hollow beams - hollow conical double half-Gaussian beams - and deduce the analytical equation of propagation and transformation of these through the paraxial optical system by using the Collins formula. By using the formula deduced, we calculate and analyze the propagation properties of these in free space. In an experiment, we have obtained hollow conical double half-Gaussian beams, which are cone-angle controllable by using the combinational optical system of the spherical reflector, reflecting positive-axis cone and zoom lens, and we obtain the beam loop of far field in different distances. The results show good coherence between theory and experiment. This paper will play a guiding role in the practical application of hollow conical double half-Gaussian beams.