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

$z\_R\; =\; frac\{pi\; w\_0^2\}\{lambda\}$,

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 $sqrt\{2\}$.

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

$z\_R\; =\; frac\{b\}\{2\}$

See also

• Beam diameter
• Beam divergence
• Beam parameter product
• Gaussian function
• Electromagnetic wave equation
• John Strutt, 3rd Baron Rayleigh
• Robert Strutt, 4th Baron Rayleigh

References

• Rayleigh length RP Photonics Encyclopedia of Optics