FIG. 1: (color online) Schematic illustrating the geometry of the vector field structure. The fixed unit vector u lies in the plane zox and makes an angle θ with the propagation axis z . The propagation axis z perpendicular to the plane of xoy , and the wavevector k for an arbitrary angular spectrum component is perpendicular to the plane of I$_{1}$oI$_{2}$ 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 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 4 u = sin θ e$_{x}$ + cos θ e$_{z}$ , (4) ˜ E ( k$_{x}$, k$_{y}$ ) = ˜ V$_{1}$ ( k$_{x}$, k$_{y}$ ) I$_{1}$ + ˜ V$_{2}$ ( k$_{x}$, k$_{y}$ ) I$_{2}$ . (5)