metric [35] This metric carries torsion but no curvature and describes a screw dislocated medium. We consider a monochromatic paraxial beam with definite values of the spin and orbital angular momentum, propagating in a weakly inhomogeneous isotropic medium where the refractive index n ( x ) varies adiabatically with position ( ∇ n → 0). With the screw axis z as the paraxial direction, the beam’s electric field can be represented as in a homogeneous medium according to Here k = k$_{0}$n is the wave number, the adiabatic variation of which has been neglected ( k$_{0}$ being the wave number in vacuum), with σ = ± 1 ( e$_{ρ}$ , e$_{ϕ}$ being the cylindrical unit vectors) are the orthonormal polarization vectors corresponding, respectively, to right/left circular polarization and R$_{l}$$_{|}$$_{m}$$_{|}$ ; with l = 0 , 1 , 2 , . . . and m = − l, − l +1 , . . . , l ; being the radial solution of the Helmholtz equation ( σ and m represent the helicity and the z -component of the orbital angular mo- mentum of the photon, respectively (¯ h = 1)). In the presence of screw dislocation, the Laplacian operator ∇ 2 appearing in the Helmholtz equation is to be replaced by which is the Laplacian associated with the metric (1) of the dislocated medium. The solution (2), therefore, acquires an additional phase factor due to the coupling of torsion with angular momentum, according to Furthermore, the relative permittivity tensor n $^{2}$δ$_{ij}$ acquires an anisotropic part Δ$_{ij}$ due to the strain field of the dislocation, where (see e.g. [36]) ds 2 = dρ 2 + ρ $^{2}$dϕ2 + ( dz + βdϕ ) $^{2}$. (1) E$_{σlm}$ ( ρ, ϕ, z ) = e$_{σ}$ E$_{lm}$ ( ρ, ϕ ) e $^{ikz}$. (2) e$_{σ}$ = 1 √$_{2}$ ( e$_{ρ}$ − iσ e$_{ϕ}$ ) E$_{lm}$ ( ρ, ϕ ) = R$_{l}$$_{|}$$_{m}$$_{|}$ ( ρ ) e imϕ ∂ 2 z + 1 ρ ∂$_{ρ}$ ( ρ∂$_{ρ}$ ) + 1 ρ $_{2}$( ∂$_{ϕ}$ − β∂$_{z}$ ) 2 E$_{lm}$ ( ρ, ϕ ) = R$_{l}$$_{|}$$_{m}$$_{|}$ ( ρ ) e i ( m + βk ) $^{ϕ}$. (3) Δ$_{ij}$ = − n $^{4}$p$_{ijkl}$ S$_{kl}$ 4