In laser physics, gain or amplification is a process where the medium transfers part of its energy to the emitted electromagnetic radiation, resulting in an increase in optical power. This is the basic principle of all lasers. Quantitatively, gain is a measure of the ability of a laser medium to increase optical power.
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Definition
The gain can be defined as the derivative of logarithm of power
where
In the quasi-monochromatic paraxial approximation, the gain can be taken into account with the following equation
where
Gain in Quasi two-level system
In the simple quasi two-level system, the gain can be expressed in terms of populations
where
Round-trip gain means 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
The amplification coefficient
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.
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 this article.
In radiophysics, gain may mean logarithm of the amplification coefficient.
In many articles on laser physics, which do not use the amplification coefficient
Some publications use term increment instead of gain and decrement instead of absorption coefficient to avoid the ambiguity, exploiting the analogy between paraxial propagaition of quasi-monochromatic waves and time evolution of a dynamic system.