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.
Quantitatively, gain is a measure of the ability of a laser medium to increase optical power.
However, overall a laser consumes energy.
The gain can be defined as the derivative of logarithm of power
The factor by which an input beam is amplified by a medium is called the gain and is represented by G. where
This equation neglects the effects of the transversal profile of the beam.
In the 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),
In the simple quasi two-level system, the gain can be expressed in terms of populations
are effective emission and absorption cross-sections.
In the case of non-pumped medium, the gain is negative.
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
This definition assumes either flat-top profile of the laser beam inside the laser, or some effective gain, averaged across the beam cross-section.
can be defined as ratio of the output power
The magnification characterizes the scale of enlarging of an image; such enlargement can be realized with passive elements, without gain medium.
[1] There is no established terminology about gain and absorption.
In 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 increment instead of gain and decrement instead of absorption coefficient to avoid the ambiguity,[2] exploiting the analogy between paraxial propagation of quasi-monochromatic waves and time evolution of a dynamic system.