Manipulating the magnetic energy density and energy flux by cylindrically symmetric state of polarization

Using the Richards and Wolf formulas for an arbitrary cylindrical vector (CV) beam, we obtain explicit expressions for all components of the electric and magnetic field strength vectors near the focus, as well as expression for the energy flux in an aplanatic optical system. Based on such analytical models, it reveals that the intensity pattern of the magnetic field at the focus can be tailored by appropriately adjusting the initial phase, peak-centered, doughnut, and flat-topped magnetic fields can be achieved using this method. For the energy flows, in contrast, they are almost the same for arbitrary CV beams, which exhibit hollow shaped patterns for both the transverse and longitudinal components. Unlike the longitudinal component, however, the hollow shaped pattern of the transverse component is separated into two regions, arriving from the null transverse energy flow in the focal plane. Besides, the directions of the transverse energy flow are reversed between these two regions, which are directed inwardly and outwardly along the radial direction, respectively.