Spin separations in the spin Hall effect of light

In the spin Hall effect of light (SHEL) with an incident linear polarization, the left circularly polarized (LCP) and the right circularly polarized (RCP) spin components are transversely shifted to opposite sides of the incident plane. We find that each spin component of the reflected or the refracted light is actually the coherent superposition of a pair with the same handedness. The two parts in a pair are generated by both the incident LCP and RCP components, respectively, and have different transverse shifts. Their weighted shifts lead to the overall displacement of the corresponding spin component. This perspective can successfully elucidate the dependence of the SHEL spin separations on the angle of polarization of the incident electric field.

Figure 1

(a) L-LCP ($\left|+\right.〉$) and (b) L-RCP ($\left|-\right.〉$) component intensity profiles of the reflected light with an LCP beam incident at ${\theta }_I={50}^{\circ }$.

Figure 2

Schematic of the relative shifts of spin separation and IF shift with exaggeration for LCP incident beam.

Figure 3

Spin separation in IF shift for an LCP incident light with and without neglecting the in-plane wave vector spread $\mathrm{\Delta }{k}_{x_I}$. (a) Transverse shift of the reflected LCP and its power weight; (b) IF shift as the function of incident angle.

Figure 4

IF shift in the total internal reflection (TIR) for an LCP incident light.

Figure 5

Schematic of spin separations in SHEL for an arbitrary linear polarization incident beam with exaggeration of the separation. The notations are as follows: I-LCP = $\frac{1}{\sqrt{2}}\left(cos{\gamma }_I-isin{\gamma }_I\right)\left|+\right.〉$, I-RCP = $\frac{1}{\sqrt{2}}\left(cos{\gamma }_I+isin{\gamma }_I\right)\left|-\right.〉$, L-LCP = $E_{{\left|+\right.〉}_R}^{{\left|+\right.〉}_I}\propto g_{{\left|+\right.〉}_R}^{{\left|+\right.〉}_I}\left|+\right.〉$, R-LCP = $E_{{\left|+\right.〉}_R}^{{\left|-\right.〉}_I}\propto g_{{\left|+\right.〉}_R}^{{\left|-\right.〉}_I}\left|+\right.〉$, LCP = L-LCP+R-LCP, L-RCP = $E_{{\left|-\right.〉}_R}^{{\left|+\right.〉}_I}\propto g_{{\left|-\right.〉}_R}^{{\left|+\right.〉}_I}\left|-\right.〉$, R-RCP = $E_{{\left|-\right.〉}_R}^{{\left|-\right.〉}_I}\propto g_{{\left|-\right.〉}_R}^{{\left|-\right.〉}_I}\left|-\right.〉$, and RCP = L-RCP+R-RCP.

Figure 6

Intensity profiles of incident and reflected light beams at air-glass interface with $\left|P\right.〉$ linear polarization incident state at ${\theta }_I={56}^{\circ }$. The spin separations $\delta$ are also presented. The intensities of the reflected light are multiplied by a factor indicated in the images.

Figure 7

The influence of the in-plane wave vector spread ($\mathrm{\Delta }{k}_{x_I}$) on the SHEL shift for $\left|P\right.〉$ incident polarization (${\delta }_{\left|+\right.〉}^{\left|P\right.〉}$).

Figure 8

Power weight of LCP in the transmitted beam for an LCP incident light.

Figure 9

Spin shifts as the function of the incident angle. (a) Transverse shift of the transmitted LCP (red) and RCP (black) components for an LCP incident beam; (b) the transmitted LCP component shift in SHEL for $\left|P\right.〉$ (black) and $\left|S\right.〉$ (red) incident polarization. Solid lines and dotted lines correspond to without and with neglecting the in-plane wave vector spread $\mathrm{\Delta }{k}_{x_I}$, respectively.