content_image/348521.jpg content_image/348527.jpg content_image/348528.jpg
<img src='content_image/348521.jpg'>

describing the vector field structure. Here, the fixed unit vector u lies in the plane zox and makes an angle θ with the propagation axis, and 

<img src='content_image/348527.jpg'>

where − π/ 2 ≤ θ ≤ + π/ 2. Note that this fixed unit vector is not a purely mathematical concept [11, 12]. In fact, a perpendicular u to the propagation axis corresponds to the uniformly polarized beam in the paraxial approximation [13], and a parallel u corresponds to the cylindrical vector beam [14]. The axis u that is neither perpendicular nor parallel to the propagation axis was observed by Hosten and Kwiat in a recent experiment [8]. 

In order to accurately describe the optical Magnus effect, we introduce the scaler Whit- taker potentials [5] to represent the vectorial field. Consequently, the angular spectrum can be decomposed along the two vectors and we have 

<img src='content_image/348528.jpg'>

