Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect

We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.

Figure 1

The parallel transport of the cross structure of a beam (${\mathrm{HG}}_{31}$ mode here) propagating along a helical trajectory.

Figure 2

Transverse transport of rays (vortex cores) in an inhomogeneous medium. The rays are marked with values of $\sigma +l$. The dashed arrow points to the direction of the intrinsic angular momentum current.