Particle-in-Cell (PIC) simulations are fundamental to plasma physics but often suffer from limited scalability due to particle-grid interaction bottlenecks and particle redistribution costs. Specifically, the particle-grid interaction computations have not taken full advantage of the emerging Matrix Processing Units (MPUs), the particle motion introduces irregular memory accesses, and the bulk-synchronous redistribution further destroys long-term data locality thereby limiting parallel efficiency. To address these inefficiencies, we present POLAR-PIC, a co-designed framework for large-scale PIC simulations that (i) reformulates Field Interpolation into an MPU-friendly outer-product form, (ii) maintains a physically ordered particle layout to preserve memory contiguity, and (iii) overlaps particle communication with Deposition to hide redistribution overhead. The evaluation on the pilot system of an Exascale supercomputer demonstrates that POLAR-PIC accelerates the entire particle-processing phase by up to 10.9x in uniform plasma and 4.4x in real-world laser-ion acceleration scenarios compared to the native WarpX reference pipeline on LX2. Ablation studies reveal that the speedups achieved by Interpolation and Deposition are 8.0x and 13.2x, respectively, and the asynchronous communication design sustains a 99.1% overlap ratio. In cross-platform comparisons, POLAR-PIC achieves 13.2% of theoretical peak efficiency on the CPU-based LS system, while WarpX reaches 9.6% on NVIDIA A800 GPUs. Notably, the scalability evaluation demonstrates that POLAR-PIC maintains 67.5% weak scaling efficiency on over 2 million cores under high-migration dynamic workloads, highlighting the importance of holistic co-design for future matrix-centric HPC systems.