Orbital angular momentum density characteristics of tightly focused polarized Laguerre–Gaussian beam

The orbital angular moment (OAM) of light has been proved to be useful in plenty of applications. By transmitting the OAM of the focused light field to a particle, it will be orbited around the optical axis. Therefore, it is necessary to study the OAM distribution of the focused light field used to manipulate the particles. In this application, the widely used paraxial approximation is no longer sufficient due to the tightly focused beam. We employ the higher-order Poincaré sphere to represent the Laguerre-Gaussian (LG) beams with arbitrary polarization. Then the Rayleigh-Sommerfeld integral method and the q-parameter method are used to derive the analytical expression of the light field on the focal plane. Based on this, the OAM density expression of the tightly focused LG beam is derived. In the numerical simulation, we study and analyze the unique intensity distributions and OAM distributions of tightly focused linear polarized, radial polarized, and circular polarized LG beams. The results could be leveraged to further explore the applications of the polarized vortex beam.