Optimized weak measurement for spatial spin-dependent shifts at Brewster angle

As Brewster law goes, the polarization selectivity when a light beam reflected at Brewster angle is feasible. We find that this polarization selectivity is still effective incorporated with weak measurement. So we realize an optimized weak measurement technique without preselection polarizer. This scheme is exploited to observe the spatial spin-dependent shifts when a linearly polarized beam is reflected at Brewster angle. The theoretical and experimental results show that by changing the polarization orientation of incident beam, the in-plane spin-dependent shift direction can be reversed, while the out-of-plane spin-dependent shift direction keeps unchanged. Our results may enrich the application of weak measurement.