Four-channel polarization-multiplexed metalens for 3D optical trapping

Polarization multiplexing offers an additional degree of freedom for parallel optical manipulation in compact systems. However, simultaneously generating spatially separated foci with prescribed local polarization states under a fixed incident polarization and establishing their three-dimensional trapping stability through optical-force analysis remains challenging. Here, we propose and numerically demonstrate a four-channel polarization-multiplexed Pancharatnam-Berry metalens operating in water at 532 nm. Under x-polarized illumination, the metalens simultaneously forms four off-axis foci in a common focal plane, with prescribed local polarization states corresponding to linear polarization at 30° and 120°, right-circular polarization, and left-circular polarization. The simulated mean FWHMs of the four channels yield ratios of 1.032-1.062 relative to the common scalar Airy FWHM benchmark. Within circular regions of radius 3×FWHM, the target-polarization-projected power accounts for 78.15% of the total encircled power, with an inter-channel power uniformity of 0.931. Maxwell stress tensor calculations for a 0.2-µm-radius SiO₂ sphere at an incident power of 100 mW reveal stable transverse and axial zero-force equilibria and trap depths exceeding 10 k_BT in all four channels. These results establish a direct connection between polarization-multiplexed focal-field engineering and channel-dependent optical-force responses, demonstrating a compact approach to parallel three-dimensional optical trapping with polarization-labeled channels.