# Plane Electromagnetic Waves and Gaussian Beams

## Abstract

Plane electromagnetic waves are solutions of the Maxwell equations that are unbounded in the plane perpendicular to the direction of propagation. They approximately describe local properties of the real field far from the source of radiation. They can also be used as building blocks from which a general solution of Maxwell’s equations in free space can be constructed. An important practical example of electromagnetic radiation that finds many applications in accelerator physics and elsewhere is a focused laser beam. The distribution of the electromagnetic field in such light is characterized by Gaussian modes which can be considered as a superposition of plane waves propagating at small angles to the direction of the beam. Gaussian beams correctly describe the field structure near the focus and the diffraction of the beam as it propagates away from the focal region. In this chapter, we will briefly summarize the main properties of plane electromagnetic waves, and then derive the field in a Gaussian beam.