Editing Laser (section)

=== The light emitted ===

[[File:Lasers.JPG|thumb|Red (660 & 635&nbsp;nm), green (532 & 520&nbsp;nm), and blue-violet (445 & 405&nbsp;nm) lasers]]In most lasers, lasing begins with spontaneous emission into the lasing mode. This initial light is then amplified by stimulated emission in the gain medium. Stimulated emission produces light that matches the input signal in direction, wavelength, and polarization, whereas the [[phase (waves)|phase]] of the emitted light is 90 degrees in lead of the stimulating light.<ref name=Pollnau2018>{{cite journal |last1 = Pollnau |first1 = M. |year = 2018 |title = Phase aspect in photon emission and absorption |journal = Optica |volume = 5 |issue = 4 |pages = 465–474 |doi = 10.1364/OPTICA.5.000465 |bibcode = 2018Optic...5..465P |url = https://www.osapublishing.org/DirectPDFAccess/C50A8E4B-9698-1EAB-90F88B72D53AEB42_385547/optica-5-4-465.pdf?da=1&id=385547&seq=0&mobile=no |doi-access = free |access-date = June 28, 2020 |archive-date = February 8, 2023 |archive-url = https://web.archive.org/web/20230208064609/https://opg.optica.org/static307.htm?da=1&id=385547&seq=0&mobile=no |url-status = live}}</ref> This, combined with the filtering effect of the optical resonator gives laser light its characteristic coherence, and may give it uniform polarization and monochromaticity, depending on the resonator's design. The fundamental [[laser linewidth]]<ref name=Pollnau2020>{{cite journal |last1 = Pollnau |first1 = M. |last2 = Eichhorn |first2 = M. |year = 2020 |title = Spectral coherence, Part I: Passive resonator linewidth, fundamental laser linewidth, and Schawlow-Townes approximation |journal = Progress in Quantum Electronics |volume = 72 |pages = 100255 |doi = 10.1016/j.pquantelec.2020.100255 |bibcode = 2020PQE....7200255P |doi-access = free}}</ref> of light emitted from the lasing resonator can be orders of magnitude narrower than the linewidth of light emitted from the passive resonator. Some lasers use a separate [[injection seeder]] to start the process off with a beam that is already highly coherent. This can produce beams with a narrower spectrum than would otherwise be possible.

In 1963, [[Roy J. Glauber]] showed that coherent states are formed from combinations of [[photon number]] states, for which he was awarded the [[Nobel Prize in Physics]].<ref name=Glauber1963>{{cite journal |last1 = Glauber |first1 = R.J. |year = 1963 |title = Coherent and incoherent states of the radiation field |journal = Phys. Rev. |volume = 131 |issue = 6 |pages = 2766–2788 |doi = 10.1103/PhysRev.131.2766 |bibcode = 1963PhRv..131.2766G |url = http://conf.kias.re.kr/~brane/wc2006/lec_note/Glauber-2.pdf |access-date = February 23, 2021 |archive-date = May 8, 2021 |archive-url = https://web.archive.org/web/20210508173506/http://conf.kias.re.kr/~brane/wc2006/lec_note/Glauber-2.pdf |url-status = live}}</ref>  A coherent beam of light is formed by single-frequency quantum photon states distributed according to a [[Poisson distribution]].  As a result, the arrival rate of photons in a laser beam is described by Poisson statistics.{{sfn|Pearsall|2020|p=276}}

Many lasers produce a beam that can be approximated as a [[Gaussian beam]]; such beams have the minimum divergence possible for a given beam diameter. Some lasers, particularly high-power ones, produce multimode beams, with the [[transverse mode]]s often approximated using [[Hermite polynomials|Hermite]]–[[Gaussian function|Gaussian]] or [[Laguerre polynomials|Laguerre]]-Gaussian functions. Some high-power lasers use a flat-topped profile known as a "[[tophat beam]]". Unstable laser resonators (not used in most lasers) produce fractal-shaped beams.<ref>{{cite journal |last1 = Karman |first1 = G.P. |last2 = McDonald |first2 = G.S. |last3 = New |first3 = G.H.C. |last4 = Woerdman |first4 = J.P. |author-link4 = Han Woerdman |title = Laser Optics: Fractal modes in unstable resonators |journal = Nature |volume = 402 |issue = 6758| page = 138 |doi=10.1038/45960| bibcode = 1999Natur.402..138K |date = November 1999 |s2cid = 205046813 |doi-access = free}}</ref> Specialized optical systems can produce more complex beam geometries, such as [[Bessel beam]]s and [[optical vortex]]es.

Near the "waist" (or [[focus (optics)|focal region]]) of a laser beam, it is highly ''[[collimated light|collimated]]'': the wavefronts are planar, normal to the direction of propagation, with no [[beam divergence]] at that point. However, due to [[diffraction]], that can only remain true well within the [[Rayleigh range]]. The beam of a single transverse mode (gaussian beam) laser eventually diverges at an angle that varies inversely with the beam diameter, as required by [[diffraction]] theory. Thus, the "pencil beam" directly generated by a common [[helium–neon laser]] would spread out to a size of perhaps 500 kilometers when shone on the Moon (from the distance of the Earth). On the other hand, the light from a [[semiconductor laser]] typically exits the tiny crystal with a large divergence: up to 50°. However even such a divergent beam can be transformed into a similarly collimated beam employing a [[lens (optics)|lens]] system, as is always included, for instance, in a [[laser pointer]] whose light originates from a [[laser diode]]. That is possible due to the light being of a single spatial mode. This unique property of laser light, [[spatial coherence]], cannot be replicated using standard light sources (except by discarding most of the light) as can be appreciated by comparing the beam from a flashlight (torch) or spotlight to that of almost any laser.

A [[laser beam profiler]] is used to measure the intensity profile, width, and divergence of laser beams.

[[Diffuse reflection]] of a laser beam from a matte surface produces a [[speckle pattern]] with interesting properties.