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## III. OPTICAL MAGNUS EFFECT 

<img src='content_image/354603.jpg'>

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 

<img src='content_image/354610.jpg'>

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 

<img src='content_image/354611.jpg'>

<img src='content_image/354612.jpg'>

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 

