High-purity polarization focusing through multimode fibers based on a vectorial transmission matrix

In multimode fiber (MMF) endoscopy, fiber-induced polarization scrambling and intermodal coupling severely degrade the linear polarization purity (LPP) of excitation probes. To overcome this fundamental limitation, we propose a vectorial light-field control strategy based on low-transmittance space projection. By performing singular value decomposition on the orthogonal-polarization sub-matrix of the MMF, we construct a projection basis from low-transmittance eigenchannels. Operating at an optimal 85% spatial degree-of-freedom retention ratio, this method suppresses cross-polarization leakage while preserving target focal intensity. Experiments demonstrate a LPP enhancement from 0.740 to 0.999 at the center and spatially uniform suppression (LPP > 0.97) during wide-field scanning. The method provides a compact vectorial wavefront-shaping strategy for high-purity polarized probe delivery through multimode fibers.