Generation of twisted Hermite-Gaussian correlated radially polarized beams and their propagation characteristics in vacuum and turbulence

In this study, we introduce a special kind of partially coherent vector beams, called twisted Hermite-Gaussian correlated radially polarized (THGCRP) beams, which possess a twist phase, special spatial coherence structure and radial polarization simultaneously. The second-order statistics such as spectral density, polarization state and degree of polarization (DOP) of such beams propagating in vacuum and atmospheric turbulence are examined in detail through numerical examples. It reveals that both the twist phase and correlation function play significant roles in determining the second-order statistical properties. The twist phase is responsible for the rotation of beam spot around the propagation axis and the correlation function mainly affects the spectral density evolution. By adjusting the initial beam parameters such as the twist factor and beam order, we find that the spectral density can remain the four petal-like profile invariant during propagation, even in the present of turbulence. Further, we establish a compact and flexible experimental setup for the generation of THGCRP beams with controllable parameters. The polarization state, DOP and spectral density are investigated in detail and we find a good agreement between the theory and experiment.