Vortices in multipole radiation

The Poynting vector for electric and magnetic multipole radiation of arbitrary order (ℓ, m) has been obtained, and an expression for the field lines of this vector field has been derived. It is shown that the field lines lie on a cone, and that, for m ≠ 0, they exhibit a vortex structure with a dimension of about a wavelength around the multipole. The field lines wind around the z-axis in the neighborhood of the multipole, and outside this vortex region the field lines run approximately radially outward. We have also derived the asymptotic limit of a field line.