Focusing behavior of Gaussian beam through a variable π-phase plate plus lens with long focal depth

We investigate the optical properties of Gaussian beams diffracted by a variable π-phase plate clinging tightly to the lens with long focal depth and its dependence on the size of the π-phase plate and the preset long focal depth of the lens. The numerical results show that the π-phase plate with appropriate size plus the multifunctional lens illuminated by Gaussian beam can produce bi-focus along the propagation direction and a center hollow light, and the distance between two focal planes along the longitudinal direction and the transverse and longitudinal spot size of the hollow beam will vary when changing the size of the π-phase plate or the preset long focal depth. This investigation indicates that the distance between the focal planes and the spot sizes of the hollow light can be controlled by the appropriately chosen size of the π-phase plate and the preset long focal depth of the lens. Furthermore, we compare the optical characteristics produced by three existing phase functions of the lens with long focal depth. It is expected that this investigation will provide useful information in various optical tweezers for operating and controlling.