beam contains an optical dislocation, namely the optical vortex along its axis, which is a topological object on the wavefront the beam [30]. Regarding the medium as a continuum, we use the differential geometric theory of defects which is isomorphic to three dimensional gravity [31, 32]. In this geometric approach, the effect of defects on the three dimensional geometry of the medium is incorporated into a metric. The effect of the screw dislocation on the beam’s orbital angular momentum is, thus, shown to change the optical vortex strength, rendering vortex annihilation (for left-handed helical modes) or generation of non-integral vortices [33] possible. This is useful in generating fast switchable helical modes for optical information encoding [9, 34]. Furthermore, the dislocation is shown to induce a weak biaxial anisotropy in the medium due to the elasto-optic effect. This anisotropy, which is felt more strongly by beams that propagate close to the dislocation line, changes the beam’s spin angular momentum as well as causing precession of the polarization. Finally, we derive the equations of motion of the beam and demonstrate how beams with different values of spin and/or angular momentum split in the dislocated medium (the optical Hall effect). Because the beam’s singular vortex core can be observed with great accuracy, measurement of the splittings is very reliable. Measuring beam splittings for opposite values of the polarization and orbital angular momentum provides an indirect method for determining the Burgers vector as well as the elasto-optic coefficients of the medium. Determination of the former is demonstrated in a simple example. 

## II. EFFECT OF SCREW DISLOCATION ON THE BEAM 

Dislocation is a defect caused by the action of internal stress, which changes the physical properties of the medium, in particular, its optical properties. The displacement vector field, u , associated with a screw dislocation line oriented along the z -axis of the cylindrical coordinates ( ρ, ϕ, z ) is u = (0 , 0 , βϕ ), where β is the magnitude of Burgers vector divided by 2 π . The corresponding strain tensor field S$_{ij}$ = 1 $_{2}$( ∂$_{i}$u$_{j}$ + ∂$_{j}$u$_{i}$ ) is, thus, given by S$_{ϕz}$ = S$_{zϕ}$ = β/ 2 ρ , other components being zero. Regarding the medium as a continuum, we can use the differential geometric theory of defects which is isomorphic to three dimensional gravity [31, 32]. In this geometric approach, the effect of defects on the three dimensional geometry of the medium is incorporated into a metric. In particular, a screw dislocation, which corresponds to a singular torsion along the defect line, is described by the following 

