x / y / -20 -10 0 10 20 -20 -10 0 10 20 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 (c) x / y / -20 -10 0 10 20 -20 -10 0 10 20 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 (f) x / y / -20 -10 0 10 20 -20 -10 0 10 20 (a) x / y / -20 -10 0 10 20 -20 -10 0 10 20 (b) x / y / -20 -10 0 10 20 -20 -10 0 10 20 (d) x / y / -20 -10 0 10 20 -20 -10 0 10 20 (e) FIG. 3: (color online) The momentum currents for the model [W] under the condition θ = π/ 2. First row: Left circularly polarized wavepacket σ = +1. Second row: Right circularly polarized wavepacket σ = − 1. The background distribution is depicted as the longitudinal currents and the green arrows is described as the transverse currents. [(a), (d)] Orbital momentum currents p [W] O . [(b), (e)] Spin momentum currents p [W] S . [(c), (f)] Total momentum currents p [W] O + p [W] S . The cross section is chosen as z = z$_{R}$ and the intensity is plotted in normalized units. III. OPTICAL MAGNUS EFFECT To illustrate the polarization-dependent rotation effect, we now determine the shift of wavepacket centroid, which is given by 〈 r 〉 [M] = 〈 x 〉 $^{[M]}$e$_{x}$ + 〈 y 〉 $^{[M]}$e$_{y}$ , with First let us examine the polarization-dependent rotation in the model [W]. By substituting Eqs. (10), (11) and (15) into Eq. (19), we obtain the shifts as where z$_{R}$ = kw 2 $_{0}$/ 2 is the Rayleigh length. We find that the wavepacket centroid shifts a distance away from the propagation axis in xoy plane. The shift 〈 x 〉 [W] is polarization independent, while the shift 〈 y 〉 [W] depends on the polarization state σ . Note that the shift 9 〈 r 〉 [M] = ∫ ∫ r p [M] z ( x, y, z )d x d y p [M] z ( x, y, z )d x d y . (19) 〈 x 〉 [W] = − z sin 2 θ 2(cos 2 θ + kz$_{R}$ sin 2 θ ) , (20) 〈 y 〉 [W] = − σz$_{R}$ sin 2 θ 2(cos 2 θ + kz$_{R}$ sin 2 θ ) , (21)