Gain in laser physics

Laser Physics

Laser Physics is an international scientific journal published by Nauka/Interperiodica. It is distributed through the Springer.-Topics covered:The journal specializes in laser physics, but also publishes papers about:...

 is a process, where the medium transfers part of its energy to the emitted electromagnetic radiation

Electromagnetic radiation

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

, resulting in an increase in laser power. This is basic principle of all lasers.
Quantitatively, the ability of a laser medium to increase power of light is characterised with
Gain.
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.

In the quasi-monochromatic paraxial approximation

Paraxial approximation

In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system ....

, 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.
In the simple quasi two-level system,
the gain can be expressed in terms of populations
and
of lower and excited states:

where
and

are effective emission and absorption cross-sections.