# Laser A **laser** is a device that produces light by optical amplification through [[Stimulated_emission|stimulated emission]], feeding the amplified light back through the amplifier with mirrors until the device oscillates. The name is an acronym for *light amplification by stimulated emission of radiation*. What distinguishes laser light from the light of a lamp is not brightness but order: because every stimulated [[Photon|photon]] copies the one that caused it, the emitted beam is close to a single frequency, close to a single direction, and coherent across its width, so it can be focused to a spot of the order of its own wavelength and kept narrow over long distances.[^openstax-lasers] In the microsim below the reader turns a laser on. Two coupled rate equations for a four-level medium — `dN2/dt = R_p - N2/tau - sigma*c*N2*phi` for the upper-level population and `dphi/dt = sigma*c*N2*phi - phi/tau_c` for the photon density in the cavity — are integrated while a single control raises the pump rate R_p. Below a critical pump the cavity holds only fluorescence and φ decays away; above it the photon number climbs in proportion to the excess pump, so the output-against-pump curve shows the sharp kink every real laser shows, and the upper-level population stops rising because gain has become equal to loss. Stepping the pump makes the two variables chase each other into relaxation oscillations before settling. The parameters are ILLUSTRATIVE, chosen to make threshold and oscillations visible on one screen rather than to model a particular medium. On the [[Physics]] flagship this article serves Part IV — Branches and fields, section *The laser* (row P60). Its dense Wikitube child is [[Ring_laser_gyroscope]], which uses a laser cavity as an instrument rather than a source, and its nearest neighbours on the spine are [[Population_inversion]] and [[Quantum_optics]]. ## Terminology The word entered English as an acronym in the late 1950s, on the pattern of *maser* — *microwave amplification by stimulated emission of radiation* — which named the device that worked first. It is now an ordinary noun, and has produced the verb *to lase*. Strictly the amplifier and the oscillator differ: a gain medium with no mirrors is a laser *amplifier*, and only amplifier plus cavity is a laser in the usual sense. In practice the word covers the whole instrument, pump supply and cooling included. ## Fundamentals Three things are needed, and the third is easy to miss. There must be a gain medium — [[Atom|atoms]], ions, molecules or electrons with two [[Energy_level|energy levels]] whose spacing matches the wavelength wanted. There must be a pump that puts energy into it. And there must be more population in the upper level than the lower, a [[Population_inversion|population inversion]], because stimulated emission and absorption have the same coefficient: a photon passing a population mostly in the lower level is more likely to be absorbed than copied, and the medium attenuates instead of amplifying. An inversion cannot be produced by shining light on a two-level system. The Portal Book works out the excited fraction of a two-level [[Atomic_physics|atom]] driven on resonance: 25 % when the intensity equals the saturation intensity, with a ceiling of 50 % however hard the atom is driven, because the field that excites the atom also stimulates it back down.[^raven-sat] Real lasers therefore use three or four levels, arranging for the lower laser level to empty into a level the pump does not touch. ## Design A laser is built as an optical resonator with the gain medium inside it. Two mirrors face each other; one is as reflective as can be made, the other transmits a few per cent and is the output coupler. Light makes many round trips, amplified on each pass, and the device oscillates when round-trip gain exceeds round-trip loss from output coupling, scattering and absorption. The geometry of the mirrors selects the transverse shape of the beam, and the length of the cavity selects the frequencies that fit an integer number of half-wavelengths between them. The pump can be a flashlamp, another laser, an electric discharge or, in a diode, a current injected across a [[P–n_junction|p–n junction]]. Cooling matters as much as optics, since pump energy that does not leave as light leaves as heat, and heat in the medium bends the beam by changing the refractive index across the rod. The output coupler's transmission is itself a design compromise: too little and the stored light is wasted inside the cavity, too much and the round-trip gain no longer reaches threshold. ## Theory of operation The behaviour of a laser is captured with surprising completeness by two coupled ordinary differential equations, one for the excited population and one for the photons. Their steady states account for threshold, for the linearity of output against pump above it, and for the clamping of the inversion; their transients account for the spiking seen when the pump is switched on. ### Stimulated emission [[Albert_Einstein|Einstein]] introduced stimulated emission in 1917 in deriving the [[Black-body_radiation|blackbody]] spectrum from a balance of three processes: spontaneous emission, absorption, and a third process in which an incident photon induces an excited atom to emit.[^einstein1917] The induced photon matches the one that caused it in frequency, phase, polarisation and direction, which is why amplification by this mechanism preserves coherence while amplification by spontaneous emission does not. The absorption and stimulated-emission coefficients are equal, so the net gain of a medium is proportional to the population difference N₂ − N₁ rather than to N₂ alone.[^openstax-lasers] ### Simple model Write N₂ for the upper-level population density and φ for the photon density in the cavity mode. Pumping adds R_p per unit time, spontaneous decay removes N₂/τ, and stimulated emission removes σ·c·N₂·φ, where σ is the stimulated-emission cross-section; the same stimulated term adds photons, and the cavity loses them with a lifetime τ_c. That is the pair of equations the microsim integrates.[^rate-eqs] Set the derivatives to zero. With φ ≈ 0 the upper level fills to N₂ = R_p·τ, and the photon equation grows only if σ·c·N₂ > 1/τ_c. The threshold inversion is therefore `N2_th = 1/(sigma*c*tau_c)` and the threshold pump is `R_p,th = N2_th/tau` (derived). Above threshold the photon equation forces σ·c·N₂ = 1/τ_c exactly, so N₂ is pinned at N2_th no matter how hard the medium is pumped, and every additional pump quantum goes into the beam: `phi = tau_c*(R_p - R_p,th)` (derived).[^rate-eqs] This is the kink the microsim draws — fluorescence rising with pump, then a corner, then a straight line of photons — and it is the reason a laser has a well-defined threshold at all. The clamping also explains why the fluorescence from the side of a laser rod stops brightening once the rod lases. Because the two equations are coupled and neither variable responds instantly, the approach to the steady state is oscillatory: an excess of photons burns the inversion below its clamp, the photons decay, the pump rebuilds the inversion, and the cycle repeats with falling amplitude. These relaxation oscillations appear whenever the pump is stepped, and their damping is what settles into continuous operation. ### Gain medium and cavity Gain per unit length is σ·(N₂ − N₁), and the cavity turns that into a round-trip condition. The cavity lifetime τ_c collects every loss — output coupling, scattering, absorption — into one number, while the cavity's resonances select the frequencies. A cavity of length L supports [[Standing_wave|standing waves]] spaced c/2L apart, which for a 0.30 m cavity is 500 MHz (derived); the gain bandwidth usually spans many such modes, and whether one or many oscillate is a question of how they compete for the same inversion. ### The light emitted The beam's directionality is set by [[Wave_interference|diffraction]], not by the mirrors: a beam of diameter D cannot be collimated better than an angle of order λ/D, the same limit that governs the resolution of a telescope through the Rayleigh criterion θ_R = 1.22·λ/D.[^openstax-diffraction] A 1 mm beam at 633 nm spreads by about 0.8 mrad, roughly 0.8 m per kilometre (derived) — enough to look like a straight line, not enough to be called parallel. The narrow [[Spectral_line|spectral]] width gives a long coherence length, which makes interferometry and holography practical, and coherence across the beam produces speckle. ### Quantum vs. classical emission processes Spontaneous and stimulated emission are the same interaction seen without and with photons already in the mode, the stimulated rate being proportional to the number already there. The output of a laser well above threshold is close to a coherent state: its field behaves like a classical wave of definite amplitude and phase while its photon number fluctuates, so laser light is neither a classical wave nor a simple stream of independent photons. Below threshold the same device emits ordinary thermal fluorescence, and the change of statistics at threshold is a standard subject of [[Quantum_optics|quantum optics]].[^openstax-lasers] ## Modes of operation A laser can be run so that the pump, the inversion and the output are all constant in time, or so that the energy is stored and released in bursts. The choice is made in the cavity, not in the medium. ### Continuous-wave operation With a steady pump above threshold the rate equations reach the steady state described above, and the output power rises linearly with pump power along a line whose slope is the slope efficiency and whose intercept on the pump axis is the threshold. Continuous-wave operation is what most measurement, communication and alignment uses require, and it is the regime in which the sim's straight line above the kink applies. The practical limits are thermal: the waste heat deposited in the medium distorts it, and beyond some pump power the beam quality degrades faster than the power grows. ### Pulsed operation Storing energy and releasing it quickly raises peak power far above anything the medium could sustain continuously. Holding the cavity lossy while the pump builds the inversion and then restoring it suddenly — Q-switching — dumps the stored inversion in one giant pulse, the relaxation oscillation of the simple model driven deliberately. Locking the phases of many longitudinal modes instead gives a train of pulses whose length is roughly the inverse of the gain bandwidth. The arithmetic of peak power makes the regime useful: 1 mJ in 100 fs is 10 GW while it lasts, although the average power at a kilohertz repetition rate is only 1 W (derived, ILLUSTRATIVE). ## History The laser is one of the few technologies whose theoretical basis preceded its construction by four decades, and whose first working device had no application waiting for it. The sequence below runs from a term in a radiation law, through a microwave oscillator, to an optical device, and then to the two refinements that made the short intense pulse a laboratory instrument. ### Foundations Einstein's 1917 paper on the quantum theory of radiation contained stimulated emission as the term required to make the radiation law consistent, but it described a process, not a machine.[^einstein1917] The intervening decades supplied what was missing: the quantum description of [[Atomic_orbital|atomic structure]] that fixes where the levels are, and the microwave technology of the 1940s that supplied sources, cavities and detectors.[^openstax-lasers] ### Maser The first working device amplified microwaves rather than light. In 1954 Gordon, Zeiger and Townes at Columbia reported a molecular oscillator using a beam of ammonia molecules sorted by state to produce an inversion, obtaining both amplification and self-sustained oscillation.[^gordon1954] Townes shared the 1964 Nobel Prize in Physics with Basov and Prokhorov for the work on the maser–laser principle.[^nobel1964] ### Laser Schawlow and Townes set out the extension to optical wavelengths in 1958, showing that an open resonator formed by two mirrors could select a small number of modes out of the enormous number available at optical frequencies.[^schawlow1958] Maiman built the first working optical device in 1960, using a ruby rod pumped by a flashlamp, and reported it in *Nature* as stimulated optical radiation in ruby.[^maiman1960] Gas, [[Semiconductor|semiconductor]] and other media followed within a few years. ### Recent innovations Two later advances changed what lasers are used for. Chirped pulse amplification, which stretches a pulse before amplifying it and recompresses it afterwards, made table-top terawatt peak powers possible and took a share of the 2018 Nobel Prize in Physics.[^nobel2018] Driving atoms with such fields generates bursts on the attosecond scale, the subject of the 2023 Nobel Prize, which put electron motion within reach of measurement.[^nobel2023] ## Types and operating principles Lasers are classified by what is inverted. Gas lasers run a discharge through helium–neon, carbon dioxide or an excimer mixture, covering the ultraviolet to the far infrared. Solid-state lasers use ions doped into a crystal or glass host — ruby, then neodymium and titanium-doped media — pumped by lamps or diodes; fibre lasers put the same medium in a long thin waveguide, which makes heat easy to remove. [[Photonic_crystal|Photonic-crystal]] lasers use a periodic dielectric structure as the resonator instead of mirrors. Semiconductor diode lasers invert the population across a forward-biased [[Doping_(semiconductor)|doped]] junction and are, by count, almost all the lasers in the world. Dye lasers use a flowing organic solution whose broad gain bandwidth makes them tunable; free-electron lasers dispense with bound states, extracting light from a relativistic electron beam in a magnet array. Exotic media extend the list to X-ray and Raman devices, and astrophysical masers show the mechanism needs no laboratory: clouds in the [[Interstellar_medium|interstellar medium]] emit amplified microwave lines. ## Field of study Laser science sits inside [[Atomic,_molecular,_and_optical_physics|atomic, molecular and optical physics]], overlapping [[Quantum_optics|quantum optics]] and [[Optical_engineering|optical engineering]]. Its characteristic questions are how to get gain from a new medium, how to keep a cavity stable, how to make a pulse shorter, and how to define a frequency more exactly. The last has fed metrology, where a stabilised laser is a length and frequency standard, and [[Doppler_broadening|Doppler-free]] spectroscopy, where a narrow tunable source resolves structure thermal motion would bury. ## Uses The laser is used wherever light must be delivered in a known direction, at a known frequency or at a known instant. Optical-fibre communication carries nearly all long-distance data traffic on diode lasers. Manufacturing cuts, marks and joins with them, and additive processes such as [[Selective_laser_melting|selective laser melting]] and [[Laser_metal_deposition|laser metal deposition]] build parts by melting powder along a scanned path, while [[Photolithography|photolithography]] prints circuits with ultraviolet sources. Measurement uses them in interferometers, rangefinders and the [[Ring_laser_gyroscope|ring laser gyroscope]]; medicine to cut, coagulate and reshape tissue; research to cool atoms, trap particles and compress fuel in [[Inertial_confinement_fusion|inertial confinement fusion]]. Directed-energy weapons are in service at the kilowatt scale, and hobby and consumer uses — pointers, printers, disc drives, light shows — account for most units sold. The powers in routine use span more than fifteen orders of magnitude, from microwatt pointers to the petawatt peaks of chirped-pulse systems.[^nobel2018] ## Safety The hazard of a laser is not its total [[Power_(physics)|power]] but its irradiance, and the eye makes that distinction sharply. A collimated visible or near-infrared beam entering the pupil is focused onto the retina, and because a millimetre-wide beam is brought to a spot of the order of ten micrometres, the irradiance rises by roughly four orders of magnitude (derived, ILLUSTRATIVE). A beam harmless on the skin can therefore destroy retinal tissue in less time than the blink reflex takes. Lasers are graded for this reason into classes running from those safe under all reasonably foreseeable conditions to those hazardous even as diffuse reflections, under an international equipment-classification standard.[^iec60825] Wavelength governs where the energy lands: ultraviolet and far-infrared light is absorbed in the cornea and lens rather than reaching the retina. ## See also - [[Stimulated_emission]] - [[Population_inversion]] - [[Quantum_optics]] - [[Ring_laser_gyroscope]] - [[Doppler_broadening]] - [[Spectral_line_shape]] - [[Atomic,_molecular,_and_optical_physics]] ## References [^openstax-lasers]: Sanny, Jeff; Ling, Samuel J.; et al. (2016). *University Physics Volume 3*. OpenStax. Ch. 8, "Atomic Structure," pp. 347–392; the section on lasers, stimulated emission and population inversion (printed page to pin). Portal Book 079. https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3 [^openstax-diffraction]: Sanny and Ling, *University Physics Volume 3* (2016), Ch. 4 "Diffraction," pp. 145–182, the Rayleigh criterion θ_R = 1.22·λ/D at pp. 162–166. Portal Book 079. [^raven-sat]: Raven, Will (2025). *Atomic Physics for Everyone*. Ch. 3, pp. 60–70 (saturation intensity, the scattering rate r = πγs/(1 + s + 4δ²/γ²), the excited fraction of 25 % at s = 1 on resonance and its ceiling of 50 %, and the power-broadened width γ√(1 + s)). Portal Book 046. https://open.umn.edu/opentextbooks/textbooks/atomic-physics-for-everyone-an-introduction-to-atomic-physics-quantum-mechanics-and-precision-spectroscopy-with-no-college-level-prerequisites [^rate-eqs]: The four-level rate equations dN₂/dt = R_p − N₂/τ − σ·c·N₂·φ and dφ/dt = σ·c·N₂·φ − φ/τ_c are the standard textbook form; they are not printed in the Portal Books read for this page (page to pin). Their steady states, quoted here as *derived*, follow by inspection: N₂ = R_p·τ below threshold, N2_th = 1/(σ·c·τ_c), R_p,th = N2_th/τ, and φ = τ_c·(R_p − R_p,th) above threshold, with N₂ clamped at N2_th. The microsim's σ, τ and τ_c are ILLUSTRATIVE. [^einstein1917]: Einstein, Albert (1917). "Zur Quantentheorie der Strahlung." *Physikalische Zeitschrift* 18: 121–128. [^gordon1954]: Gordon, J. P.; Zeiger, H. J.; Townes, C. H. (1954). "Molecular Microwave Oscillator and New Hyperfine Structure in the Microwave Spectrum of NH₃." *Physical Review* 95 (1): 282–284. [^schawlow1958]: Schawlow, A. L.; Townes, C. H. (1958). "Infrared and Optical Masers." *Physical Review* 112 (6): 1940–1949. [^maiman1960]: Maiman, T. H. (1960). "Stimulated Optical Radiation in Ruby." *Nature* 187 (4736): 493–494. [^nobel1964]: Nobel Prize Outreach. "The Nobel Prize in Physics 1964 — Charles Hard Townes, Nicolay Gennadiyevich Basov and Aleksandr Mikhailovich Prokhorov." https://www.nobelprize.org/prizes/physics/1964/summary/ [^nobel2018]: Nobel Prize Outreach. "The Nobel Prize in Physics 2018 — Arthur Ashkin, Gérard Mourou and Donna Strickland" (optical tweezers; chirped pulse amplification). https://www.nobelprize.org/prizes/physics/2018/summary/ [^nobel2023]: Nobel Prize Outreach. "The Nobel Prize in Physics 2023 — Pierre Agostini, Ferenc Krausz and Anne L'Huillier" (attosecond pulses of light). https://www.nobelprize.org/prizes/physics/2023/summary/ [^iec60825]: International Electrotechnical Commission. *IEC 60825-1, Safety of laser products — Part 1: Equipment classification and requirements* (edition and clause to pin). The class boundaries themselves are not quoted on this page. ## Further reading ### Books - Sanny, Ling et al., *University Physics Volume 3* (OpenStax, 2016), Ch. 8 "Atomic Structure," pp. 347–392 — Portal Book 079, https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3 - Raven, *Atomic Physics for Everyone* (2025), Part I "Atom–Light Interactions," pp. 13–117 — Portal Book 046, https://open.umn.edu/opentextbooks/textbooks/atomic-physics-for-everyone-an-introduction-to-atomic-physics-quantum-mechanics-and-precision-spectroscopy-with-no-college-level-prerequisites ### Periodicals - *Physical Review* and its successors, where the maser and optical-maser papers of 1954 and 1958 appeared. - *Nature*, where the first ruby laser was reported in 1960. ## External links - [University Physics Volume 3](https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3), the Open Textbook Library record for Portal Book 079 - [Atomic Physics for Everyone](https://open.umn.edu/opentextbooks/textbooks/atomic-physics-for-everyone-an-introduction-to-atomic-physics-quantum-mechanics-and-precision-spectroscopy-with-no-college-level-prerequisites), the Open Textbook Library record for Portal Book 046 - The Wikipedia pair's external links list manufacturer, museum and tutorial resources not duplicated here <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Laser.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Laser* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Laser.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Laser.html" data-title="Laser"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Laser) : [Wikitube](https://en.wikitube.io/wiki/Laser) · pinned revision [1373868442](https://en.wikipedia.org/w/index.php?oldid=1373868442) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Physics]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Physics row P60 · sim pending (matter/Laser).*