An intuitive approach to structuring the three electric field components of light

Abstract

This paper presents intuitive interpretations of tightly focused beams of light by drawing analogies with two-dimensional electrostatics, magnetostatics and fluid dynamics. We use a Helmholtz decomposition of the transverse electric field components in the transverse plane to introduce generalized radial and azimuthal polarization states. This reveals the interplay between transverse and longitudinal electric field components in a transparent fashion. Our approach yields a comprehensive understanding of tightly focused laser beams, which we illustrate through several insightful examples.