In laser-driven inertial confinement fusion (ICF) facilities, nonuniform laser irradiation can cause significant challenges, such as hydrodynamics instability and laser plasma instability, which hinder the success of fusion. This article presents a new idea for improving the uniformity of far-field laser irradiation through a method of single-beam polarization smoothing. The method involves modulating full Poincaré beams using stress-engineered optics made from fused silica. We designed a stress birefringence system and conducted opto-mechanical modeling and analysis on it. The article elaborates on the mechanism and principles of generating large-aperture full Poincaré beams by stress birefringence, as well as the mechanism of polarization smoothing by full Poincaré beams. Near-field polarization measurements were conducted to verify these mechanisms, and the effectiveness of this method in improving the uniformity of laser irradiation in the target area was evaluated through far-field optical tests.