Tight focusing of mixed-polarization beams and its impact on focal plane electric field distributions

Abstract Mixed-polarization beams, characterized by spatially varying polarization states, have multiple and arbitrary polarization states in different regions of the beam, directly governing the electric field distributions after tight focusing. While their potential in optical physics and manipulation is significant, systematic analysis of their tightly focused fields remains unexplored. We generalize the Richards-Wolf diffraction integrals by incorporating position-dependent polarization parameters, enabling rigorous calculation of tightly focused fields for arbitrary mixed-polarization beams [1]. We show how complex polarization patterns (e.g., hybrid linear, circular, elliptical regions) drastically reshape focal-plane fields. Numerical and experimental results reveal that the distributions of mixed polarization states in incident beams dictate the electric-field distributions on the focal plane. Simulated and measured intensity profiles exhibit a structural similarity exceeding 85%, confirming our method’s validity. These findings enable rational design of tightly focused beams for optical microfabrication and micromanipulation.