p$_{ijkl}$ being the elasto-optic coefficients of the medium. For amorphous media, where only two independent elasto-optic coefficients (customarily denoted by p$_{11}$ and p$_{12}$ ) exist, the screw dislocation yields other components being zero. The principle refractive indices are, therefore, to first order in the perturbation, which is generally sufficiently small. Hence, the elasto-optic perturbation induces a weak biaxial anisotropy in the medium, which is felt more strongly by beams that propagate close to the dislocation line (small ρ ). Propagation of the beam through the dislocated medium, thus, introduces the phases k$_{0}$n$_{ρ}$z and k$_{0}$n$_{ϕ}$z in the linear polarization states represented by e$_{ρ}$ and e$_{ϕ}$ , respectively. Hence, in (2), the polarization vector should be rewritten as where is the induced birefringence. Equivalently, where cot θ = z/ρ and γ = 1 $_{2}$βk$_{0}$ ( p$_{11}$ − p$_{12}$ ) n $^{3}$. Equations (2) to (4) form our expression for the field of a paraxial beam propagating in an optically weakly inhomogeneous and isotropic amorphous medium with screw dislocation. With the beam scalar product defined by [37] these beams form a complete orthonormal set, in terms of which an arbitrary field distri- bution can be constructed. The paraxial beam contains an optical dislocation, namely the optical vortex of strength m along its axis, which is a topological object on the wavefront the beam [30]. The z -component of the beam’s orbital angular momentum (per photon) is given by the expectation value 5 ∫ ∫ E ⋆ $_{lm}$( − i∂$_{ϕ}$ ) E$_{lm}$ ρdρdϕ = m + βk. ( E$_{σlm}$ | E$_{σ}$ $^{′}$l$^{′}$m′ ) = ∫ ∫ E † $_{σlm}$E$_{σ}$ $^{′}$l$^{′}$m′ ρdρdϕ = δ$_{σσ}$ ′ δ$_{mm}$ ′ ∫ R ⋆ l | m $_{|}$R$_{l}$ ′ | m | 2 πρdρ e$_{σ}$ = 1 √$_{2}$ ( e$_{ρ}$ − iσe iγ cot $^{θ}$e$_{ϕ}$ ) (4) e$_{σ}$ = 1 √ 2 ( e$_{ρ}$ − iσe ik 0 Δ $^{nz}$e$_{ϕ}$ ) Δ n ( ρ ) = n$_{ϕ}$ − n$_{ρ}$ = β ( p$_{11}$ − p$_{12}$ ) 2 ρ n 3 n$_{ρ}$ = n, n$_{ϕ}$ = n + β ( p$_{11}$ − p$_{12}$ ) 2 ρ n $^{3}$, n$_{z}$ = n − β ( p$_{11}$ − p$_{12}$ ) 2 ρ n 3 Δ$_{ϕz}$ = Δ$_{zϕ}$ = − β ( p$_{11}$ − p$_{12}$ ) ρ n 4