Structuring the Three Electric Field Components of Light

Unless the beam's transverse electric field components are divergence-free in the two-dimensional transverse plane [1], tightly focused light typically leads to a non-negligible longitudinal electric field component [2], where the terms longitudinal and transverse electric field components refer to the components of the electric field that are parallel or perpendicular, respectively, to the direction of the mean Poynting flux. Having a longitudinal electric field component does not add a new degree of freedom, in the sense that all components of the electric and magnetic fields are still fixed by prescribing two electric field components in a plane. However, it is the electric field component parallel to the direction of the Poynting flux that makes it somewhat special.