Symmetric Olver beams

This paper presents an innovative form of the symmetric and autofocusing beam in theory and experiment. These symmetric Olver beams (SOBs) originate from the spectral symmetry phase of the Olver beams. We find that the properties of these beams are related to the Olver integral's order. The even-order SOBs have an autofocusing major lobe in the preliminary stage of the propagation and symmetrically split into two symmetric off-axis parabolic lobes after autofocusing. In contrast, the odd-order SOBs do not split after focusing. For the odd-order SOBs, as the order increases, the energy at the focal point becomes higher, and the power gets more concentrated. Additionally, we use optical vortices to manipulate the propagation trajectories of the SOBs. The experimental results show that the symmetric Olver vortex beams have a self-focusing phenomenon, and the center of the beams presents a hollow structure due to the existence of the axial vortex. The orbital angular momentum carried by the vortex structure makes the beam rotate in the initial plane. It is also proved that multiple off-axis vortices can be inserted in the SOBs. More importantly, we experimentally demonstrate the capture capability of the SOBs and the vortex symmetric Olver beams. Therefore, we expect the proposed SOBs and the vortex symmetric Olver beams to provide potential optical communication and manipulation applications.