Rayleigh length

Parameters at the focus of a Gaussian beam. is the smallest radius that the light field occupies. is the opening angle with which the light is focused and at which it leaves the focus again. is the Rayleigh length. ${\displaystyle w_{0}}$ ${\displaystyle \Theta }$ ${\displaystyle z_{\mathrm {R} }}$

The Rayleigh length (after Lord Rayleigh ) is the distance along the optical axis that a laser beam needs until its cross-sectional area, starting from the beam waist or focus , doubles. The radius of the beam is larger there by a factor  than at the waist or the focus. ${\displaystyle z_{\mathrm {R} }}$ ${\displaystyle {\sqrt {2}}}$

If you consider the approximation of a Gaussian beam , which is usually permissible for lasers , the Rayleigh length can be expressed as follows:

${\displaystyle z_{\mathrm {R} }={\frac {n\cdot \pi \cdot w_{0}^{2}}{\lambda _{0}}}}$

in which

• ${\displaystyle n}$the refractive index of the medium
• ${\displaystyle w_{0}}$ the radius of the beam in focus
• ${\displaystyle \lambda _{0}}$is the vacuum wavelength of the light used.

This means: if red light (e.g. 650 nm wavelength) is bundled with ultraviolet light (e.g. 325 nm) on the same surface in the focus of a lens or a parabolic mirror , the red light is only halfway there of the ultraviolet is already spread out so far that it illuminates twice the original area.

Taking into account the beam quality , the formula changes to: ${\displaystyle {\frac {1}{M^{2}}}}$

${\displaystyle z_{\mathrm {R} }={\frac {1}{M^{2}}}\cdot {\frac {n\cdot \pi \cdot w_{0}^{2}}{\lambda _{0}}}}$

Web links

• Rayleigh length in the Encyclopedia of Laser Physics and Technology (Engl.)