Focused Fields of given Power with Maximum Electric Field Components
  Closed formulas are derived for the field in the focal region of a diffraction limited lens, such that the electric field component in a given direction at the focal point is larger than that of all other focused fields with the same power in the entrance pupil of the lens. Furthermore, closed formulas are derived for the corresponding optimum field distribution in the lens pupil. Focused fields with maximum longitudinal or maximum transverse are considered in detail. The latter field is similar, but not identical, to the focused linearly polarized plane wave. 
H.P. Urbach S.F. Pereira