Vectorial Analysis of the Gaussian Beams of Light

Abstract

The scalar theory of Gaussian beams is an approximation to describe narrow beams of light. A vectorial analysis is required to describe the electromagnetic fields in the focal region with a small spot size. Maxwell’s equations are solved to obtain the longitudinal as well as the transversal components of field vectors in a beam of light propagating along an axis. Solutions of the electromagnetic fields of either the plane-polarized-electric (and magnetic) or the transeverse-electric (and magnetic) modes are expressed in terms of Hermite-Gaussian functions. Magnitudes of the longitudinal field components in these modes are evaluated in particular.