Transverse Angular Momentum and Geometric Spin Hall Effect of Light

We present a novel fundamental phenomenon occurring when a polarized beam of light is observed from a reference frame tilted with respect to the direction of propagation of the beam. This effect has a purely geometric nature and amounts to a polarization-dependent shift or split of the beam intensity distribution evaluated as the time-averaged flux of the Poynting vector across the plane of observation. We demonstrate that such a shift is unavoidable whenever the beam possesses a nonzero transverse angular momentum. This latter result has general validity and applies to arbitrary systems such as, e.g., electronic and atomic beams.

Figure 1

(a) Geometry of the problem. (b) Components of the angular momentum density $\mathit{j}$ in the beam and in the laboratory frame $K^{\prime }$ and $K$, respectively. Note that the beam cross section on the observation plane $z=0$ is stretched along the $x$ direction while the geometric SHEL shift occurs along the $y$ axis.

Figure 2

(a) Plot of the $x^{\prime }$ component of the relative Poynting vector density $p_{x^{\prime }}^{\prime }(x^{\prime },y^{\prime },0)/p_{z^{\prime }}^{\prime }(0,0,0)$ ($\times {10}^3$). (b) Plot of the $z^{\prime }$ component of the relative Poynting vector density $p_{z^{\prime }}^{\prime }(x^{\prime },y^{\prime },0)/p_{z^{\prime }}^{\prime }(0,0,0)$. In both cases the polarization is right-circular.