Visualized geometric phase of caustic geometric beams

Detecting Pancharatnam-Berry (PB) or geometric phases of light usually requires complex interferometry or diffraction through a specially designed truncated aperture. In this work, we present a simpler method that enables directly visualized measurement of geometric phases in certain complex structured light fields, without additional interferometry or beam truncation. Our approach exploits the PB phase present in SU(2) structured light. In these SU(2) modes, spatial wave packets naturally align with underlying caustic trajectories. By observing wave-packet evolution, i.e., the morphology of coupled caustics as the beam propagates, we can visually reveal both the geometric phase and the Gouy phase of the beam. This visual detection technique offers insights into the geometric phase of structured light and broadens the possibilities for designing optical devices that harness geometric phases.