Geometric phase mechanism behind experimental observation of vector polarization in Hermite-Gaussian superposition states.

Superposition of orthogonal Hermite-Gaussian (HG) modes in orthogonal linear polarization states is one of the approaches used for the experimental realization of lower-order optical vector beams and vector vortex lattices. To date, it has generally been assumed that the vector characteristics observed in such systems originate from the spatial intensity distribution of the superposed HG modes. Here, we demonstrate that the experimentally observed vector features arising during the characterization of HG-mode superposition states result from the combined effects of the azimuthally inhomogeneous intensity distribution and the polarization-dependent Pancharatnam-Berry (PB) geometric phase of light. Analytical calculations reveal that these vector characteristics are not intrinsically encoded in the superposition state itself; rather, they become observable through the action of polarization-selective optical elements employed during the characterization process. Furthermore, we experimentally verify the emergence of the PB geometric phase during the projection of orthogonally polarized spatial modes onto a common polarization state using a linear polarizer. The experimental observations provide direct evidence for the involvement of the PB geometric phase in the polarization characterization of HG-mode superposition states. These findings offer a fundamental clarification of the physical origin of the vector features experimentally observed in HG-mode superposition and provide new insight into the interpretation of vector beam generation based on mode superposition techniques.