Editing Gaussian beam (section)

{{short description|Monochrome light beam whose amplitude envelope is a Gaussian function}}

[[Image:Gaussian beam w40mm lambda30mm.png|thumb|right|''Instantaneous'' absolute value of the real part of electric field amplitude of a TEM<sub>00</sub> gaussian beam, focal region. Showing <math>|\mathcal{Re}(E(t_1))|</math> thus with ''two'' peaks for each positive [[wavefront]].]]
[[Image:Laser gaussian profile.svg|thumb|right|Top: transverse intensity profile of a Gaussian beam that is propagating out of the page. Blue curve: electric (or magnetic) field amplitude vs. radial position from the beam axis. The black curve is the corresponding intensity.]]
[[Image:Green laser pointer TEM00 profile.JPG|thumb|right|A 5 mW green laser pointer beam, showing the TEM<sub>00</sub> profile]]

In [[optics]], a '''Gaussian beam''' is an idealized [[Light beam|beam]] of [[electromagnetic radiation]] whose [[Envelope (waves)|amplitude envelope]] in the transverse plane is given by a [[Gaussian function]]; this also implies a Gaussian [[irradiance|intensity]] (irradiance) profile. This fundamental (or TEM<sub>00</sub>) [[transverse mode|transverse]] Gaussian mode describes the intended output of many [[laser]]s, as such a beam diverges less and can be focused better than any other. When a Gaussian beam is refocused by an ideal [[lens (optics)|lens]], a new Gaussian beam is produced. The [[Electric field|electric]] and [[magnetic field]] amplitude profiles along a circular Gaussian beam of a given [[wavelength]] and [[polarization (waves)|polarization]] are determined by two parameters: the [[#Beam waist|waist]] {{math|''w''<sub>0</sub>}}, which is a measure of the width of the beam at its narrowest point, and the position {{mvar|z}} relative to the waist.<ref name="svelto153">Svelto, pp. 153–5.</ref>

Since the Gaussian function is infinite in extent, perfect Gaussian beams do not exist in nature, and the edges of any such beam would be cut off by any finite lens or mirror. However, the Gaussian is a useful approximation to a real-world beam for cases where lenses or mirrors in the beam are significantly larger than the spot size ''w''(''z'') of the beam.

Fundamentally, the Gaussian is a solution of the paraxial [[Helmholtz equation]], the wave equation for an electromagnetic field. Although there exist other solutions, the Gaussian families of solutions are useful for problems involving compact beams.