The fact that its value has changed from m to m + βk owes itself to the torque exerted by the strain field of the dislocation. The effect of the screw dislocation on the orbital angular momentum, therefore, is to change the optical vortex strength, rendering vortex annihilation (for negative values of m , i.e., 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]. Moreover, the z -component of the beam’s spin angular momentum is [38] As expected [38], the spin component varies along the paraxial direction due to the induced elasto-optic birefringence. Therefore, a screw dislocated medium exerts torques that change both the spin and orbital parts of the beam’s angular momentum. The spin change, being attributed to the elasto-optic effect, is more pronounced for beams that propagate close to the dislocation line. Note that, the z -component of the beam’s total angular momentum, reduces to the constant value σ + m in the absence of the screw dislocation ( β = 0), as it should. The adiabatic variation of the wave number k , caused by the weak inhomogeneity, has negligible dynamical effect and was, therefore, ignored. However, the adiabatic variation of the beam direction (given by its wave vector k ) plays a geometric role with nontrivial consequences for the beam dynamics. To incorporate this variation, we treat the coordinate frame used in the previous section as a local frame following the beam direction. As usual, the variation gives rise to a parallel transport law in the momentum space, defined by the Berry connection (gauge potential) Using (2) to (4), we obtain 6 A$_{σσ}$ ′ = [ jδ$_{σσ}$ ′ + iσ ( δ$_{σσ}$ ′ − 1) sin( γ cot θ )] cot θ k e$_{ϕ}$ A$_{σσ}$ ′ ( k ) = ( E$_{σlm}$ | − i ∇ k | E$_{σ}$ ′ $_{lm}$) . j = σ cos( γ cot θ ) + m + βk III. PARAXIAL BEAM DYNAMICS IN THE DISLOCATED MEDIUM ∫ ∫ − i e$_{z}$ · E ⋆ σlm × E$_{σlm}$ ρdρdϕ = − i e$_{z}$ · e ⋆ σ × e$_{σ}$ = σ cos( γ cot θ ) .