- Active laser medium
The active laser medium or gain medium is the source of optical
gain within alaser . The gain results from thestimulated emission of electronic or molecular transitions to a lower energy state from a higher energy statepreviously populated by a pump source.Examples of active laser media include:
*Certaincrystal s, typically doped with rare-earthion s (e.g.neodymium ,ytterbium , orerbium ) ortransition metal ions (titanium orchromium ); most oftenyttrium aluminium garnet (YAG),yttrium orthovanadate (YVO4), orsapphire (Al2O3); [Hecht, Jeff. "The Laser Guidebook: Second Edition." McGraw-Hill, 1992. (Chapter 22)]
*Glass es, e.g. silicate or phosphate glasses, doped with laser-active ions; [Hecht, Chapter 22]
*Gas es, e.g. mixtures ofhelium andneon (HeNe),nitrogen ,argon ,carbon monoxide ,carbon dioxide , or metal vapors; [Hecht, Chapters 7-15]
*Semiconductor s, e.g.gallium arsenide (GaAs),indium gallium arsenide (InGaAs), orgallium nitride (GaN); [Hecht, Chapters 18-21]In order to lase, the active gain medium must be in a nonthermal energy distribution known as a population inversion. The preparation of this state requires an external energy source and is known as
laser pumping . Pumping may be achieved with electrical currents (e.g. semiconductors, or gases via high-voltage discharges) or with light, generated bydischarge lamp s or by other lasers (semiconductor laser s). More exotic gain media can be pumped bychemical reactions ,nuclear fission , or with high-energyelectron beam s. [http://www.rp-photonics.com/gain_media.html Encyclopedia of laser physics and technology] ] .Example of a model of gain medium
A universal model valid for all laser types does not exist.cite book
url=http://www.uscibooks.com/siegman.htm
author=A.E.Siegman
title=Lasers
year=1986
publisher=University Science Books
id= ISBN 0-935702-11-3] The simplest model includes two systems of sub-levels: upper and lower. Within each level, the fast transitions lead to theBoltzmann distribution of excitations among sub-levels "(fig.1)". The upper level is assumed to bemetastable ,neither gain nor refractive index depend on a particular way of excitation.For good performance of the gain medium, the separation between sub-levels should be larger than working temperature; then, at pump frequency omega_{ m 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 laseroscillators , when amplified radiation is used to transfer energy rather than information. The model below seems to work well for most optically-pumpedsolid-state laser s.Cross-sections
The simple medium can be characterized with effective cross-sections of
absorption and emission at frequencies omega_{ m p}~ and omega_{ m s}~.
*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_{ m u}=frac{I_{ m p}sigma_{ m ap{ hbar omega_{ m p} }+frac{I_{ m s}sigma_{ m as{ hbar omega_{ m s} } ~ andThe rate of transitions back to the ground state can be expressed with W_{ m d}=frac{ I_{ m p} sigma_{ m as{ hbar omega_{ m p} }+frac{I_{ m s}sigma_{ m es{ hbar omega_{ m s} } +frac{1}{ au}~,where sigma_{ m as} ~ and sigma_{ m ap} ~ are effective cross-sections of absorption at the frequencies of the pump and the signal.
sigma_{ m es} ~ and sigma_{ m ep} ~ are the same for stimulated emission;
frac{1}{ au}~ is rate of the spontaneous decay of the upper level.
Then, the kinetic equation for relative populations can be written as follows: frac m d}n_2} m d}t}=W_{ m u} n_1 -W_{ m d} n_2~,
frac m d}n_1} m d}t}=-W_{ m u} n_1 + W_{ m 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_{ m pa} -N_2sigma_{ m pe} ~,G = N_2sigma_{ m se} -N_1sigma_{ m se} ~.
teady-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.The steady-state solution can be written: n_2=frac{W_{ m u{W_{ m u}+W_{ m d ~n_1=frac{W_{ m d{W_{ m u}+W_{ m d ~
The dynamic saturation intensities can be defined:I_{ m po}=frac{hbar omega_{ m p{(sigma_{ m ap}+sigma_{ m ep}) au} ~,I_{ m so}=frac{hbar omega_{ m s{(sigma_{ m as}+sigma_{ m es}) au} ~.
The absorption at strong signal:A_0=frac{ND}{sigma_{ m as}+sigma_{ m es~.
The gain at strong pump:G_0=frac{ND}{sigma_{ m ap}+sigma_{ m ep~,where D=sigma_{ m pa}sigma_{ m se}-sigma_{ m pe}sigma_{ m sa}~is determinant of cross-section.
Gain never exceeds value G_0~, and absorption never exceeds value A_0~.
At given intensities I_{ m p}~, I_{ m s}~ of pump and signal, the gain and absorptioncan be expressed as follows:A=A_0frac{U+s}{1+p+s}~,G=G_0frac{p-V}{1+p+s}~,
where p=I_{ m p}/I_{ m po}~ ,s=I_{ m s}/I_{ m so}~ ,U=frac{(sigma_{ m as}+sigma_{ m es})sigma_{ m ap{D}~ ,V=frac{(sigma_{ m ap}+sigma_{ m ep})sigma_{ m as{D}~ .
Identities
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 asE =frac{I_{ m s} G}{I_{ m p}A}~.
Within the same model, the efficiency can be expressed as follows:E =frac{omega_{ m s{omega_{ m 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 ofthe interference of counter-propagating waves.
ee also
*
Population inversion ,
*Laser construction ,
*Laser science ,
*List of laser types References and notes
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