## Gaussian beam

#### Gaussian beam

A beam of electromagnetic radiation whose wave front is approximately spherical at any point along the beam and whose transverse field intensity over any wave front is a Gaussian function of the distance from the axis of the beam. A Gaussian function is a mathematical function like the one below that expresses the circular cross section amplitude:

$E\left(r\right)=E\left(0\right){e}^{{\left(r/w\right)}^{2}}$,

where E(r) is the amplitude of the electric field at a radial distance r from the center of the beam, E(0) is the amplitude at the center of the beam (usually maximum amplitude), and w is the radial distance at which the amplitude of the electric field is 1/e ≈ 1/2.71828 of its value on the axis. The variable w is usually called the beam width.