across the direction of propagation. This is the optical Hall effect in the dislocated medium and generalizes the result of [27]. Because the beam’s singular vortex core can be observed with great accuracy, measurement of the displacements is very reliable. Measuring δ r for opposite values of m and σ provides an indirect method for determining the Burgers vector as well as the elasto-optic coefficients (or rather their difference p$_{11}$ − p$_{12}$ ) of the medium. We conclude by describing a simple situation that demonstrates the application of the result (7) in determining the magnitude of the Burgers vector. Silicon, being transparent in the near infrared, has attracted extensive attention in op- toelectronic devices. Waveguides in silicon can serve as optical interconnects in silicon integrated circuits, or distribute optical clock signals in a microprocessor. Fabrication of such waveguides requires a core with a higher refractive index than that of crystalline sili- con. Amorphous silicon, with a higher refractive index in the near infrared, thus provides an interesting candidate for the core material [44]. Let us, therefore, consider an amorphous silicon cylindrical waveguide with screw dislocation along its axis z . For a beam propagating inside the waveguide along its circular cross section, the trajectory C in (7) is a circle of radius k = 2 π/λ in the xy -plane ( θ = π/ 2). Thus, I = 0 and D ′ 3 = D$_{3}$ = 1 so that (7) yields, for every one revolution of the beam, where, of course, e$_{z}$ is the unit vector in the z -direction and b = 2 πβ is the magnitude of the Burgers vector. Therefore, for two beams of opposite polarization and orbital angular momentum, we have a displacement (per unit revolution) in the negative z-direction given by While δz + > 0, δz − can take any value (including zero) by suitably tuning λ and | m | . Thus one can have the oppositely polarized beams emerging from the same end of the waveguide, with one lagging behind the other, or from opposite ends (see FIG. 1). Keeping the emerging direction of the right-handed beam as the reference direction, the emerging direction of the left handed beam changes at the threshold value λ ( | m | +1) = b . With λ in the near infrared, δz ± = b ± λ ( | m | + 1) . δ r = − [ b + λ ( m + σ )] e$_{z}$ IV. EXAMPLE: CIRCULAR WAVEGUIDE 9