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## Active laser medium
Within a laser, the Examples of active laser media include: - certain crystals, typically doped with some rare-earth ions (e.g. of neodymium, ytterbium, or erbium) or transition metal ions (e.g. of titanium or chromium), most often yttrium aluminium garnet (YAG), yttrium orthovanadate (YVO4), or sapphire (Al
_{2}O_{3}); - glasses, e.g. silicate or phosphate glasses, also doped with some 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);
- liquid solutions of certain dyes (see dye laser);
- a beam of electrons (see free electron laser).
Pumping of gain media (i.e., the supply of energy) can be achieved with electrical currents (e.g. in semiconductors, or in gases via high-voltage discharges) or with light, which may be generated with discharge lamps or with other lasers (often semiconductor lasers, see DPSS laser). More exotic gain media can be pumped by chemical reactions (see chemical laser), nuclear fission (see nuclear pumped laser), or with high-energy electron beams. ## Additional recommended knowledge
## Example of a model of gain medium
There is no universal model, which would be valid for all types of lasers The simplest model includes two systems of sublevels, upper (2) and lower (1). Within each level the fast transitions
lead to the Boltzman distribution of excitations among sublevels (fig.1). The upper level is assumed to be metastable.
In this approximation, neither gain, nor refractive index depend on the particular way of excitation. For good performance of the
gain medium, the separation between sublevels should be larger than working temperature, then, at the pump frequency
,
the absorption dominates, and the emission (preferably, stimulated emission is dominant at the laser frequency
. In the case of amplification of optical signals, the lasing frequency is called
The model below seems to work well for most of optically-pumped solid-state lasers. For other types of lasers, (for example, chemical lasers or gas-dynamical lasers) more complicated analysis is required. ## Cross-sectionsThe simple medium can be characterized with effective cross-sections of absorption and emission at frequencies and . Let be concentration of active centers. This is typical state in the solid-state lasers. Let be concentration of active centers in the ground state and Let be concentration of excited centers; Let . The relative concentrations can be defined as and . The rate of transitions of an active center from ground state to the excited state can be expressed with and The rate of transitions back to the ground state can be expressed with , where and are effective cross-sections of the absorption at the frequencies of the pump and the signal, and and are the same for stimulated emission; is rate of the spontaneous decay of the upper level. Then, the kinetic equation for relative populations can be written as follows: ,
However, these equations keep . The absorption at the pump frequency and the gain at the signal frequency can be written as follows: , . ## Steady-state solutionIn many cases, the gain medium works in continuous-wave or quasi-contiunuous regime, then the time derrivatives of populations are negligible. The steady-state solution can be written
The dynamic saturation intensities can be defined with , . _ The absorption at strong signal . The gain at strong pump , where is determinant of cross-section. For the efficient gain medium, this determinant should be pretty positive. Gain never exceeds value , and absorption never exceeds value . At given intensities , of pump and sigmal, the gain and absorption can be expressed as follows: , , where ,
## IdentitiesThe following identities
, . The state of gain medium can be characterized with a single parameter. Such a parameter can be population of the upper level, gain or absorption; other parameters can be expressed with the relations above. ## Efficiency of the gain mediumThe efficiency of a . Without loss of laser cavity, this efficiency would be optical to optical efficiency of the laser. Within the same model, the efficiency can be expressed as follows: . For the efficient operation, both intensities, pump and signal should exceed their saturation intensities; , and . The estimates above are valid for the medium uniformly filled with pump and signal light. The spatial hole burning may slightly reduce the efficiency, because some region are pumped well, but the pump is not efficiently withdrawn by the signal in the nodes of the interference of counter-propagating waves. ## See also## 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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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Active_laser_medium". A list of authors is available in Wikipedia. |