Definitions

# Rayleigh length

In optics and especially laser science, the Rayleigh length or Rayleigh range is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled.

For a Gaussian beam, the Rayleigh length is given by

$z_R = frac\left\{pi w_0^2\right\}\left\{lambda\right\}$,
where $w_0$ is the radius of the beam at the waist. At distance $z_R$ from the beam waist, the beam radius is increased by a factor $sqrt\left\{2\right\}$.

A related parameter is the confocal parameter b, which is just two times the Rayleigh length:

$z_R = frac\left\{b\right\}\left\{2\right\}$