Hollow vortex beams

Hollow beam formation of radially and azimuthally polarized vortex beams, which has arbitrary topological charge, is analytically discussed under the strong focusing condition. The expressions for the electric fields of the focused vector-vortex beams are obtained based on a vector diffraction theory. The order of the Bessel function of the first kind appearing in the expressions indicates the ability to form hollow beams. Similar discussion is applied for different vortex beams, which are expressed by linear combination of radially and azimuthally polarized beams. Calculations of intensity profiles across the focus are also presented.