Editing Laser (section)

== Laser physics ==
{{more citations needed section|date=May 2017}}
{{See also|Laser science}}

[[Electron]]s and how they interact with [[electromagnetic field]]s are important in our understanding of [[chemistry]] and [[physics]].

=== Stimulated emission ===
{{Main|Stimulated emission}}

[[File:Laser, quantum principle.ogv|thumb|upright=1.5|Animation explaining stimulated emission and the laser principle]]

In the [[Classical electromagnetism|classical view]], the energy of an electron orbiting an atomic nucleus is larger for orbits further from the [[atomic nucleus|nucleus]] of an [[atom]]. However, quantum mechanical effects force electrons to take on discrete positions in [[Atomic orbital|orbitals]]. Thus, electrons are found in specific energy levels of an atom, two of which are shown below:

[[File:Stimulated Emission.svg|frameless|center|upright=2]]

An electron in an atom can absorb energy from light ([[photon]]s) or heat ([[phonon]]s) only if there is a transition between energy levels that match the energy carried by the photon or phonon. For light, this means that any given transition will only [[Absorption (electromagnetic radiation)|absorb]] one particular [[wavelength]] of light. Photons with the correct wavelength can cause an electron to jump from the lower to the higher energy level. The photon is consumed in this process.

When an electron is [[excited state|excited]] from one state to that at a higher energy level with energy difference ΔE, it will not stay that way forever. Eventually, a photon will be spontaneously created from the vacuum having energy ΔE. Conserving energy, the electron transitions to a lower energy level that is not occupied, with transitions to different levels having different time constants. This process is called [[spontaneous emission]]. Spontaneous emission is a quantum-mechanical effect and a direct physical manifestation of the Heisenberg [[uncertainty principle]]. The emitted photon has a random direction, but its wavelength matches the absorption wavelength of the transition. This is the mechanism of [[fluorescence]] and [[thermal emission]].

A photon with the correct wavelength to be absorbed by a transition can also cause an electron to drop from the higher to the lower level, emitting a new photon. The emitted photon exactly matches the original photon in wavelength, phase, and direction. This process is called stimulated emission.

=== Gain medium and cavity ===
[[File:Laser DSC09088.JPG|thumb|A [[helium–neon laser]] demonstration. The glow running through the center of the tube is an electric discharge. This glowing plasma is the [[active laser medium|gain medium]] for the laser. The laser produces a tiny, intense spot on the screen to the right. The center of the spot appears white because the image is [[overexposure|overexposed]] there.]]
[[File:Helium neon laser spectrum.svg|thumb|Spectrum of a helium–neon laser. The actual bandwidth is much narrower than shown; the spectrum is limited by the measuring apparatus.]]

The gain medium is put into an [[excited state]] by an external source of energy. In most lasers, this medium consists of a population of atoms that have been excited into such a state using an outside light source, or an electrical field that supplies energy for atoms to absorb and be transformed into their excited states.

The gain medium of a laser is normally a material of controlled purity, size, concentration, and shape, which amplifies the beam by the process of stimulated emission described above. This material can be of any [[state of matter|state]]: gas, liquid, solid, or [[plasma (physics)|plasma]]. The gain medium absorbs pump energy, which raises some electrons into higher energy ("[[excited state|excited]]") [[quantum state]]s. Particles can interact with light by either absorbing or emitting photons. Emission can be spontaneous or stimulated. In the latter case, the photon is emitted in the same direction as the light that is passing by. When the number of particles in one excited state exceeds the number of particles in some lower-energy state, [[population inversion]] is achieved. In this state, the rate of stimulated emission is larger than the rate of absorption of light in the medium, and therefore the light is amplified. A system with this property is called an [[optical amplifier]]. When an optical amplifier is placed inside a resonant optical cavity, one obtains a laser.<ref>{{cite book |first = Anthony E. |last=Siegman |year=1986 |title=Lasers |url = https://archive.org/details/lasers0000sieg |url-access = registration |publisher=University Science Books |isbn= 978-0-935702-11-8 |page=[https://archive.org/details/lasers0000sieg/page/4 4]}}</ref>

For lasing media with extremely high gain, so-called [[superluminescence]], light can be sufficiently amplified in a single pass through the gain medium without requiring a resonator. Although often referred to as a laser (see, for example, [[nitrogen laser]]),<ref name="StrongLight">{{cite book
  |title=Light and Its Uses: Making and using lasers, holograms, interferometers, and instruments of dispersion
  |chapter=Nitrogen Laser
  |date=June 1974
  |isbn=978-0-7167-1185-8
  |pages=40–43
  |url=https://archive.org/details/lightitsusesmaki0000unse
  |url-access=registration
  |last1=Strong
  |first1=C.L.
  |publisher=W. H. Freeman
 }}</ref> the light output from such a device lacks the spatial and temporal coherence achievable with lasers. Such a device cannot be described as an oscillator but rather as a high-gain optical amplifier that amplifies its spontaneous emission. The same mechanism describes so-called [[astrophysical maser]]s/lasers.

The optical [[resonator]] is sometimes referred to as an "optical cavity", but this is a misnomer: lasers use open resonators as opposed to the literal cavity that would be employed at microwave frequencies in a [[maser]].
The resonator typically consists of two mirrors between which a coherent beam of light travels in both directions, reflecting on itself so that an average photon will pass through the gain medium repeatedly before it is emitted from the output aperture or lost to diffraction or absorption.
If the gain (amplification) in the medium is larger than the resonator losses, then the power of the recirculating light can rise [[exponential growth|exponentially]]. But each stimulated emission event returns an atom from its excited state to the ground state, reducing the gain of the medium. With increasing beam power, the net gain (gain minus loss) reduces to unity and the gain medium is said to be saturated. In a continuous wave (CW) laser, the balance of pump power against gain saturation and cavity losses produces an equilibrium value of the laser power inside the cavity; this equilibrium determines the operating point of the laser. If the applied pump power is too small, the gain will never be sufficient to overcome the cavity losses, and laser light will not be produced. The minimum pump power needed to begin laser action is called the ''[[lasing threshold]]''. The gain medium will amplify any photons passing through it, regardless of direction; but only the photons in a [[spatial mode]] supported by the resonator will pass more than once through the medium and receive substantial amplification.

=== 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.

=== Quantum vs. classical emission processes ===

The mechanism of producing radiation in a laser relies on [[stimulated emission]], where energy is extracted from a transition in an atom or molecule. This is a quantum phenomenon that was predicted by [[Albert Einstein]], who derived the relationship between the [[Spontaneous emission#Rate of spontaneous emission|''A'' coefficient]], describing spontaneous emission, and the [[Stimulated emission#Mathematical model|''B'' coefficient]] which applies to absorption and stimulated emission. In the case of the [[free-electron laser]], atomic energy levels are not involved; it appears that the operation of this rather exotic device can be explained without reference to [[quantum mechanics]].