Harnessing of inhomogeneously polarized Hermite–Gaussian vector beams to manage the 3D spin angular momentum density distribution

We propose vector modes based on inhomogeneously polarized Hermite–Gaussian (HG) vector beams, providing complete structural conservation of the beams during propagation. Like uniformly polarized mode beams, these beams provide structural stability (or invariance) of both the intensity and the polarization state, in turn ensuring the stability of other field characteristics, including the angular momentum. We determine the conditions imposed on the HG mode composition in the transverse components of the electromagnetic field in order to control the three-dimensional characteristics of the field, such as intensity, polarization, and spin angular momentum (SAM). For the visual analysis of the polarization state of inhomogeneously polarized beams, we use the transverse distribution of the vector of three Stokes parameters. The correspondence of the third Stokes parameter to the distribution of the longitudinal component of the SAM is used for experimental measurements. The theoretical analysis is clearly illustrated by numerical simulations and confirmed by experimental results.