Monochromatic electromagnetic fields with maximum focal energy density

The monochromatic electromagnetic fields that achieve maximum focal energy density for a given input power and directional spread are found through a variational approach. It is found that the polarization of the fields at the focal point must be perpendicular to the main direction of propagation. Parametric expressions relating the directional spread and focal energy density of these fields (and others that achieve stationary focal irradiance) are found both in the optical (electric field only) and in the electromagnetic cases.