Fig. 1. Polarization rotation of light beam in total internal reflection at glass–air interface and in partial reflection at air–glass interface. (a) and (c) Polarization rotation in momentum space. (b) and (d) Polarization rotation in position space. The incident angle is chosen as θi=45°. To make the polarization rotation characteristics more noticeable, we amplify the rotation angles by 100 times.

Fig. 2. Experimental setup for observation of the spin-dependent splitting in photonic SHE with complex weak values. The He–Ne laser inputs a linearly polarized Gaussian beam; prisms have refractive index n=1.515 (BK7 at 632.8 nm); the half-wave plate (HWP) for adjusting the intensity of light beam; the lenses L1 and L2 have 50 and 280 mm focal lengths, respectively; the GLP1 and GLP2 and the QWP together provide the preselected and postselected states; and the CCD will be used for capturing the intensity profiles. The inset represent the preselected and postselected angles on a Poincaré sphere. Note that the experiment setup is slightly different from those in Refs. [5,6]; in the present case the QWP has been introduced to modulate the preselected state.

Fig. 3. Transverse spatial displacement of initial and final displacement when the polarization states of the incident light beam are |H⟩ and |V⟩, namely Φ=0 and Φ=π. (a) and (c) show the amplified shift of |H⟩ and |V⟩, respectively. (b) and (d) are the corresponding initial spin-dependent splitting in position space. Insets in (a) and (c) represent the preselected and postselected angles on Poincaré spheres, respectively.

Fig. 4. Transverse angular displacement of initial and final displacement as a function of preselection angle. (a) and (c) show the amplified shift of |H⟩ and |V⟩, respectively. (b) and (d) are the corresponding initial spin-dependent splitting in momentum space. Insets in (a) and (c) represent the preselected and postselected angles on the Poincaré spheres.