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Encyclopedia > Active laser medium

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The active laser medium or gain medium is the material that exhibits optical gain within a laser. The gain is generated by stimulated emission on electronic or molecular transitions to a lower energy state from a higher energy state previously stimulated by a pump source. Image File history File links Question_book-3. ... In electronics, gain is usually taken as the mean ratio of the signal output of a system to the signal input of the system. ... For other uses, see Laser (disambiguation). ... In optics, stimulated emission is the process by which, when perturbed by a photon, matter may lose energy resulting in the creation of another photon. ... Laser pumping is the act of energy transfer from an external source into the laser gain medium. ...

Examples of active laser media include:

Certain crystals, typically doped with rare-earth ions (e.g. neodymium, ytterbium, or erbium) or transition metal ions (titanium or chromium); most often yttrium aluminium garnet (YAG), yttrium orthovanadate (YVO4), or sapphire (Al₂O₃);
Glasses, e.g. silicate or phosphate glasses, doped with laser-active ions;
Gases, e.g. mixtures of helium and neon, nitrogen, argon, carbon monoxide, carbon dioxide, or metal vapors;
Semiconductors, e.g. gallium arsenide (GaAs), indium gallium arsenide (InGaAs), or gallium nitride (GaN);

Pumping gain media (i.e., supply of energy) can be achieved with electrical currents (e.g. semiconductors, or gases via high-voltage discharges) or with light, generated with discharge lamps or with other lasers (semiconductor lasers). More exotic gain media can be pumped by chemical reactions, nuclear fission, or with high-energy electron beams.^[1]. For other uses, see Crystal (disambiguation). ... Rare earth ore Rare earth elements and rare earth metals are trivial names sometimes applied to a collection of 17 chemical elements in the periodic table, namely scandium, yttrium, and the lanthanides. ... This article is about the electrically charged particle. ... General Name, Symbol, Number neodymium, Nd, 60 Chemical series lanthanides Group, Period, Block n/a, 6, f Appearance silvery white, yellowish tinge Standard atomic weight 144. ... Yb redirects here; for the unit of information see Yottabit General Name, Symbol, Number ytterbium, Yb, 70 Chemical series lanthanides Group, Period, Block n/a, 6, f Appearance silvery white Standard atomic weight 173. ... General Name, Symbol, Number erbium, Er, 68 Chemical series lanthanides Group, Period, Block n/a, 6, f Appearance silvery white Standard atomic weight 167. ... In chemistry, the term transition metal (sometimes also called a transition element) has two possible meanings: It commonly refers to any element in the d-block of the periodic table, including zinc, cadmium and mercury. ... General Name, symbol, number titanium, Ti, 22 Chemical series transition metals Group, period, block 4, 4, d Appearance silvery metallic Standard atomic weight 47. ... REDIRECT [[ Insert text]]EWWWWWWWWWWWWW YO General Name, symbol, number chromium, Cr, 24 Chemical series transition metals Group, period, block 6, 4, d Appearance silvery metallic Standard atomic weight 51. ... Yttrium aluminium garnet (YAG, Y3Al5O12) is a synthetic crystalline material of the garnet group, used as the active laser medium in various solid-state lasers. ... Yttrium orthovanadate (YVO4) is a transparent crystal. ... For other uses, see Sapphire (disambiguation). ... This article is about the material. ... For other uses, see Gas (disambiguation). ... General Name, symbol, number helium, He, 2 Chemical series noble gases Group, period, block 18, 1, s Appearance colorless Standard atomic weight 4. ... For other uses, see Neon (disambiguation). ... General Name, symbol, number nitrogen, N, 7 Chemical series nonmetals Group, period, block 15, 2, p Appearance colorless gas Standard atomic weight 14. ... General Name, symbol, number argon, Ar, 18 Chemical series noble gases Group, period, block 18, 3, p Appearance colorless Standard atomic weight 39. ... Carbon monoxide, with the chemical formula CO, is a colorless, odorless, and tasteless gas. ... Carbon dioxide (chemical formula: ) is a chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom. ... A semiconductor is a solid material that has electrical conductivity in between that of a conductor and that of an insulator; it can vary over that wide range either permanently or dynamically. ... This article is about the chemical compound. ... Indium gallium arsenide (InGaAs) is a semiconductor composed of indium, gallium and arsenic. ... Gallium nitride (GaN) is a wide bandgap semiconductor material used in optoelectronic, high-power and high-frequency devices. ... now. ... Germicidal lamps are simple low pressure mercury vapor discharges in a fused quartz envelope. ... A laser diode is a laser where the active medium is a semiconductor p-n junction similar to that found in a light-emitting diode. ... Chemical reactions are also known as chemical changes. ... For the generation of electrical power by fission, see Nuclear power plant. ... A charged particle beam is a group of electrically charged particles that have approximately the same kinetic energy and move in approximately the same direction. ...

1 Example of a model of gain medium
2 See also
3 References and notes

Example of a model of gain medium

Fig.1. Simplified scheme of levels a gain medium.

A universal model valid for all laser types does not exist.^[2] The simplest model includes two systems of sub-levels: upper and lower. Within each level, the fast transitions lead to the Boltzman distribution of excitations among sub-levels (fig.1). The upper level is assumed to be metastable, neither gain nor refractive index depend on a particular way of excitation. Image File history File links Size of this preview: 396 Ã— 600 pixelsFull resolution (660 Ã— 1000 pixel, file size: 35 KB, MIME type: image/png) Scheme of an idealized laser with two systems of sublevels Domitori 11:49, 4 April 2007 (UTC) File history Legend: (cur) = this is the current file... Image File history File links Size of this preview: 396 Ã— 600 pixelsFull resolution (660 Ã— 1000 pixel, file size: 35 KB, MIME type: image/png) Scheme of an idealized laser with two systems of sublevels Domitori 11:49, 4 April 2007 (UTC) File history Legend: (cur) = this is the current file... The Maxwellâ€“Boltzmann distribution is a probability distribution with applications in physics and chemistry. ... Metastability is the ability of a non-equilibrium state to persist for a long period of time. ...

For good performance of the gain medium, the separation between sub-levels should be larger than working temperature and the emission; then, at pump frequency $~omega_{rm p}~$ , the absorption dominates. In the case of amplification of optical signals, the lasing frequency is called signal frequency. However, the same term is used even in the laser oscillators, when amplified radiation is used to transfer energy rather than information. The model below seems to work well for most optically-pumped solid-state lasers. Generally, amplification is a basic process sometimes seen in nature, and often used in processes which involve a signal which must be made stronger. ... A solid-state laser is a laser that uses a gain medium that is a solid, rather than a liquid such as dye lasers or a gas such as gas lasers. ...

Cross-sections

The simple medium can be characterized with effective cross-sections of absorption and emission at frequencies $~omega_{rm p}~$ and $~omega_{rm s}~$ . In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. ... Look up absorption in Wiktionary, the free dictionary. ... In physics, emission is the process by which the energy of a photon is released by another entity, for example, by an atom whose valence electrons make a transition between two electronic energy levels. ...

Let $~N~$ be concentration of active centers in the solid-state lasers.
Let $~N_1~$ be concentration of active centers in the ground state.
Let $~N_2~$ be concentration of excited centers.
Let $~N_1+N_2=N~$ .

The relative concentrations can be defined as $~n_1=N_1/N~$ and $~n_2=N_2/N~$ .

The rate of transitions of an active center from ground state to the excited state can be expressed with $~ W_{rm u}= frac{I_{rm p}sigma_{rm ap}}{ hbar omega_{rm p} }+frac{I_{rm s}sigma_{rm as}}{ hbar omega_{rm s} } ~$ and The rate of transitions back to the ground state can be expressed with $~W_{rm d}=frac{ I_{rm p} sigma_{rm as}}{ hbar omega_{rm p} }+frac{I_{rm s}sigma_{rm es}}{ hbar omega_{rm s} } +frac{1}{tau}~$ , where $~sigma_{rm as} ~$ and $~sigma_{rm ap} ~$ are effective cross-sections of absorption at the frequencies of the pump and the signal. Electromagnetic radiation may be characterised by its wavelength. ...

$~sigma_{rm es} ~$ and $~sigma_{rm ep} ~$ are the same for stimulated emission;

$~frac{1}{tau}~$ is rate of the spontaneous decay of the upper level.

Then, the kinetic equation for relative populations can be written as follows: $~ frac {{rm d}n_2} {{rm d}t} = W_{rm u} n_1 - W_{rm d} n_2 ~$ ,

$~ frac{{rm d}n_1}{{rm d}t}=-W_{rm u} n_1 + W_{rm d} n_2 ~$ However, these equations keep $~ n_1+n_2=1 ~$ .

The absorption $~ A ~$ at the pump frequency and the gain $~ G ~$ at the signal frequency can be written as follows: $~ A = N_1sigma_{rm pa} -N_2sigma_{rm pe} ~$ , $~ G = N_2sigma_{rm se} -N_1sigma_{rm se} ~$ .

Steady-state solution

In many cases the gain medium works in a continuous-wave or quasi-continuous regime, causing the time derivatives of populations to be negligible. In math, a quasi-continuous function is a function in which it is continuous only for a limited range of input values. ... In mathematics, the derivative of a function is one of the two central concepts of calculus. ...

The steady-state solution can be written: $~ n_2=frac{W_{rm u}}{W_{rm u}+W_{rm d}} ~$ $~ n_1=frac{W_{rm d}}{W_{rm u}+W_{rm d}} ~$

The dynamic saturation intensities can be defined: $~ I_{rm po}=frac{hbar omega_{rm p}}{(sigma_{rm ap}+sigma_{rm ep})tau} ~$ , $~ I_{rm so}=frac{hbar omega_{rm s}}{(sigma_{rm as}+sigma_{rm es})tau} ~$ .

The absorption at strong signal: $~ A_0=frac{ND}{sigma_{rm as}+sigma_{rm es}}~$ .

The gain at strong pump: $~ G_0=frac{ND}{sigma_{rm ap}+sigma_{rm ep}}~$ , where $~ D= sigma_{rm pa} sigma_{rm se} - sigma_{rm pe} sigma_{rm sa} ~$ is determinant of cross-section.

Gain never exceeds value $~G_0~$ , and absorption never exceeds value $~A_0~$ .

At given intensities $~I_{rm p}~$ , $~I_{rm s}~$ of pump and signal, the gain and absorption can be expressed as follows: $~A=A_0frac{U+s}{1+p+s}~$ , $~G=A_0frac{p-V}{1+p+s}~$ ,

where $~p=I_{rm p}/I_{rm po}~$ , $~s=I_{rm s}/I_{rm so}~$ , $~U=frac{(sigma_{rm as}+sigma_{rm es})sigma_{rm ap}}{D}~$ , $~V=frac{(sigma_{rm ap}+sigma_{rm ep})sigma_{rm as}}{D}~$ .

Identities

The following identities ^[3] take place:

$~U-V=1~$ , $~A/A_0 +G/G_0=1~$ .

The state of gain medium can be characterized with a single parameter, such as population of the upper level, gain or absorption.

Efficiency of the gain medium

The efficiency of a gain medium can be defined as $~ E =frac{I_{rm s} G}{I_{rm p}A}~$ .

Within the same model, the efficiency can be expressed as follows: $~E =frac{omega_{rm s}}{omega_{rm p}} frac{1-V/p}{1+U/s}~$ .

For the efficient operation both intensities, pump and signal should exceed their saturation intensities; $~frac{p}{V}gg 1~$ , and $~frac{s}{U}gg 1~$ .

The estimates above are valid for a medium uniformly filled with pump and signal light. The spatial hole burning may slightly reduce the efficiency because some regions are pumped well, but the pump is not efficiently withdrawn by the signal in the nodes of the interference of counter-propagating waves.

References and notes

^ Encyclopedia of laser physics and technology
^ A.E.Siegman (1986). Lasers. University Science Books. ISBN 0-935702-11-3.
^ D.Kouznetsov; J.F.Bisson, K.Takaichi, K.Ueda (2005). "Single-mode solid-state laser with short wide unstable cavity". JOSAB 22 (8): 1605-1619.

Categories: Lasers | Laser gain media

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The Journal of the Optical Society of America B is a scientific journal, published by the Optical Society of America. ...

Results from FactBites:

Active laser medium - Wikipedia, the free encyclopedia (199 words)
	Within a laser, the active laser medium is the material that exhibits optical gain.
	This gain is generally generated by stimulated emission on electronic or molecular transitions to a lower energy state, starting from a higher energy state to which it had been previously stimulated by means of a pump source.
	in semiconductors, or in gases via high-voltage discharges) or with light, which may be generated with discharge lamps or with other lasers.

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Contents

Cross-sections

Steady-state solution

Identities

Efficiency of the gain medium

See also

References and notes