Editing Gaussian beam (section)

===Evolving beam width===
[[File:Gaussian Beam FWHM.gif|thumb|upright=1.5|The [[Gaussian function]] has a {{math|1/''e''<sup>2</sup>}} diameter ({{math|2''w''}} as used in the text) about 1.7 times the [[FWHM]].]]
At a position {{mvar|z}} along the beam (measured from the focus), the spot size parameter {{mvar|w}} is given by a [[Hyperbola#Equation|hyperbolic relation]]:<ref name="svelto153" />
<math display="block">w(z) = w_0 \, \sqrt{ 1+ {\left( \frac{z}{z_\mathrm{R}} \right)}^2 },</math>
where<ref name="svelto153" />
<math display="block">z_\mathrm{R} = \frac{\pi w_0^2 n}{\lambda}</math>
is called the [[Rayleigh range]] as further discussed below, and <math>n</math> is the refractive index of the medium.

The radius of the beam {{math|''w''(''z'')}}, at any position {{mvar|z}} along the beam, is related to the [[full width at half maximum]] (FWHM) of the intensity distribution at that position according to:<ref name=zemax>{{cite web |url=http://www.zemax.com/support/resource-center/knowledgebase/how-to-convert-fwhm-measurements-to-1-e-squared-ha |title=How to Convert FWHM Measurements to 1/e-Squared Halfwidths |first=Dan |last=Hill |date=April 4, 2007 |work=Radiant Zemax Knowledge Base |access-date=June 7, 2016 |archive-date=March 4, 2016 |archive-url=https://web.archive.org/web/20160304035034/http://www.zemax.com/support/resource-center/knowledgebase/how-to-convert-fwhm-measurements-to-1-e-squared-ha |url-status=dead }}</ref>
<math display="block">w(z)={\frac {\text{FWHM}(z)}{\sqrt {2\ln2}}}.</math>