- Gain (lasers)
Gain (or amplification) in
laser physicsis a process, where the medium transfers part of its energy to the emitted electromagnetic radiation, resulting in an increase in laser power. This is basic principle of all lasers.Quantitatively, the ability of a laser mediumto increase power of light is characterised withGain.
The gain can be defined as the derivative of logarithm of power as it passes through the medium: where is the coordinate in the direction of propagation.This equation neglects the effects of the transversal profile of beam.
quasi-monochromatic paraxial approximation, the gain can be taken into account with the following equation ,
where is variation of index of refraction (Which is supposed to be small),
is complex field, related to the physical electric field with relation , where is vector of polarization, is wavenumber, is frequency,is transversal Laplacian; means real part.
Gain in Quasi two-level system
In the simple quasi two-level system, the gain can be expressed in terms of populations and of lower and excited states:
where andare effective emission and absorption cross-sections. In the case of non-pumped medium, the gain is negative.
Round-trip gainmeans gain multiplied by the length of propagation of the laser emission during a single round-trip.In the case of gain varying along the length, the round-trip gain can be expressed with integral.This definition assumes either flat-top profile of the laser beam inside the laser, orsome effective gain, averaged across the beam cross-section.
The amplification coefficient can be defined as ratio of the output power input power :
. It is related with gain;.
The gain and the amplification coefficient should not be confused with the
magnification coefficient.The magnification characterizes the scale of enlarging of an image; such enlargement can be realized with passive elements, without gain medium. cite book
publisher=University Science Books
id= ISBN 0-935702-11-3]
Alternative terminology and notations
There is no established terminology about gain and absorption.Everyone is free to use own notations, and it is not possible to cover all the systems of notations in a Wikipedia article.
radiophysics, gain may mean logarithm of the amplification coefficient.
In many articles on laser physics, which do not use the amplification coefficient defined above,the gain is called "Amplification coefficient", in analogy with "Absorption coefficient", which is actually not a coefficient at all;one has to multiply it to the length of propagation (thickness), change the signum, take inverse of the exponential,and only then get the coefficient of attenuation of the sample.
Some publications use term
incrementinstead of gain and decrementinstead of absorption coefficientto avoid the ambiguitycite book
title=The transformation of the transverse structure of monochromatic light in the non-linear media.In book: -- Optics and Lasers. ed: G.G.Petrash
year=1995] , exploiting the analogy between paraxial propagaition of quasi-monochromatic waves and time evolution of a dynamic system.
Round-trip gain, gain multiplied by the length of propagation of the laser emission during a single round-trip
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