content_image/338433.jpg content_image/338432.jpg content_image/338430.jpg content_image/338431.jpg content_image/338429.jpg content_image/338428.jpg content_image/338427.jpg
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 

<img src='content_image/338433.jpg'>

other components being zero. The principle refractive indices are, therefore, 

<img src='content_image/338432.jpg'>

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 $^{3}$. 

<img src='content_image/338430.jpg'>

<img src='content_image/338431.jpg'>

<img src='content_image/338429.jpg'>

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] 

<img src='content_image/338428.jpg'>

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 

<img src='content_image/338427.jpg'>

