Numerical calculation of beam shifts for higher-order Laguerre-Gaussian beams upon transmission

We study numerically the spatial and angular contributions to Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts for higher-order (|l|≥1) Laguerre-Gaussian (LG) beams upon transmission from a planar interface separating two media. Two kinds of spin-orbit interaction and their role in beam shifts are discussed. Firstly, the interaction between the spin and intrinsic orbital angular momentum (OAM) of the LG beam that produces polarization dependent angular shift which is further coupled to the angular momentum structure of the beam and gives rise to spatial shift in orthogonal direction. Secondly, the interaction between the intrinsic and extrinsic OAM of the beam which produces polarization independent transverse shift, called orbital-Hall effect (OHE). Since the angular and spatial shifts are coupled and the angular shift is dependent on the beam waist, the beam shifts can be tuned to maximize or reduce the resultant shifts for LG beams.