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 (d) 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 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 (f) x / y / -20 -10 0 10 20 -20 -10 0 10 20 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 (c) x / y / -20 -10 0 10 20 -20 -10 0 10 20 (e) FIG. 7: (color online) The distribution of the longitudinal angular momentum density for the model [II]. First row: Left circular polarization σ = +1. Second row: Right circular polarization σ = − 1. [(a) and (d)] Orbital angular momentum density j [II] $_{Oz}$. [(b) and (e)] Spin angular momentum density j [II] Sz . [(c) and (f)] Total angular momentum density j [II] Oz + j [II] Sz . The cross section is chosen as z = 0 and the intensity is plotted in normalized units. Other parameters are the same as those in Fig. 5. In this case, the polarization-dependent rotation of the centroid is unavoidable since the wavepacket possesses transverse angular momentum. For the model [I], we obtain This is the reason why the model [I] only exhibits a transverse shift. For the model [II], however Thus, the wavepacket centroid no longer presents the polarization-dependent rotation. The physics underlying this phenomenon is the absence of the transverse angular momentum. It should be noted that the SHEL can be noticeably enhanced when the wavepacket carries orbital angular momentum [39–41]. Further work is needed to uncover the optical Magnus effect of such a wavepacket in the free space. It should be mentioned that the recent advent of negative index metamaterials, also known as left-handed materials (LHMs) [42, 43], can induce a reversed polarization- dependent rotation of the trajectory of the wavepacket centroid. Because of the negative index, we can expect a negative Rayleigh length in LHMs [44, 45]. It will be interesting for 16 J [II] x = 0 , J [II] y = 0 . (42) J [I] x = − πσ cot θ k $^{2}$z$_{R}$ , J [I] y = 0 . (41)