Pancharatnam Berry Phase as the Origin of Vector Nature Observed in Hermite Gaussian Superposition States

Superposition of orthogonal Hermite Gaussian (HG) modes in orthogonal linear polarization states is one of the techniques used for the experimental realization of lower order optical vector beams and vector vortex lattices. To date, it has been widely believed that the vector nature arising from this technique originates from the spatial intensity distribution of the superposed HG modes. Here, we report that the vector characteristics observed during the characterization of vector modes generated via HG mode superposition arise from the azimuthally inhomogeneous intensity distribution and the polarization-dependent Pancharatnam Berry (PB) phase. Our analytical calculations confirm that the vector nature is not inherently present in the superposition state; rather, it becomes observable due to polarization-based optical elements used in the characterization process. This insight provides a fundamental clarification of the physical origin of the experimentally observed vector nature in HG-mode superposition.