## I. INTRODUCTION 

Paraxial beams with non-zero orbital angular momentum, which are exact eigenmodes of the paraxial wave equation [1], have been of considerable interest [2–4]. In addition to spin angular momentum (polarization), paraxial beams carry an intrinsic orbital angular momentum that depends on their spatial structure. While the transfer of spin angular momentum to matter has long been reported for optically anisotropic media [5], the transfer of orbital angular momentum has newly triggered a wide range of applications. A notable example is particle trapping [6], whereby particles are set into rotation by coupling with the beam’s orbital angular momentum and are thus trapped. Such a coupling of the orbital angular momentum with matter is possible in optically inhomogeneous isotropic media [7]. Thus, a simultaneous independent coupling of both spin and orbital angular momentum with matter is to be expected in a medium which is both optically inhomogeneous and anisotropic [8, 9]. 

In the past decades, the geometric Berry phase [10] acquired by an optical beam (as the Pancharatnam phase [11] or a spin redirection phase [12, 13]) has attracted extensive attention. In particular, Bliokh et. al. [14–16] developed a modified geometrical optics approximation for optically weakly inhomogeneous isotropic media, which contained the Rytov-Vladimirskii rotation law [17, 18] and the optical Magnus effect [19, 20] (also called the optical Hall effect) as manifestations of Berry effects. Such geometric Berry effects have been also derived via the semiclassical wave packet approximation [21–23], which was originally developed for the study of electronic spin transport in solids [24–26]. 

By studying the propagation of paraxial beams in optically weakly inhomogeneous isotropic media, Bliokh [27] demonstrated that the optical Hall effect becomes more pro- nounced because of the contribution of the orbital angular momentum Hall effect due to the orbit-orbit interaction. Here, we generalize his results for screw dislocated (amorphous) optical media. Mechanical deformation can result in dislocations that change the optical properties of a medium due to the elasto-optic effect. Such dislocations can be induced by the focused beam itself (see e.g. [28, 29]). The study of beam transport provides an indirect way to determine the dislocations as well as the elasto-optical properties of the medium. In the present work, we study paraxial beam propagation parallel to the screw axis of a dislocated amorphous medium that is optically weakly inhomogeneous and isotropic. The paraxial 

