In
laser physics
Laser science or laser physics is a branch of optics that describes the theory and practice of lasers.
Laser science is principally concerned with quantum electronics, laser construction, optical cavity design, the physics of producing a popul ...
, gain or amplification is a process where the medium transfers part of its energy to the emitted
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
, resulting in an increase in optical power. This is the basic principle of all
lasers
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
.
Quantitatively, ''gain'' is a measure of the ability of a
laser medium
The active laser medium (also called gain medium or lasing medium) is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from a h ...
to increase optical power.
Definition
The gain can be defined as the derivative of logarithm of power
as it passes through the medium. The factor by which an input beam is amplified by a medium is called the gain and is represented by G.
:
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
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens).
A paraxial ray is a ray which makes a small angle (''θ'') to the optical ...
, 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
and
are effective emission and absorption cross-sections. In the case of non-pumped medium, the gain is negative.
Round-trip gain Round-trip gain refers to the laser physics, and laser cavities (or laser resonators). It is gain, integrated along a ray, which makes a round-trip in the cavity.
At the continuous-wave operation, the round-trip gain exactly compensates both the ...
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.
The amplification coefficient
can be defined as ratio of the
output power
to the
input power
:
:
.
It is related with gain;
.
The gain and the amplification coefficient should not be confused with the
magnification coefficient
Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in siz ...
.
The magnification characterizes the scale of enlarging of an image; such enlargement
can be realized with
passive elements
Passive may refer to:
* Passive voice, a grammatical voice common in many languages, see also Pseudopassive
* Passive language, a language from which an interpreter works
* Passivity (behavior), the condition of submitting to the influence of o ...
, without
gain medium
The active laser medium (also called gain medium or lasing medium) is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from a ...
.
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 Radiophysics (also modern writing "radio physics") is a branch of physics focused on the theoretical and experimental study of certain kinds of radiation, its emission, propagation and interaction with matter.
The term is used in the following majo ...
, 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
The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient valu ...
to avoid the
ambiguity
Ambiguity is the type of meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations plausible. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement ...
,
[
]
exploiting the analogy between paraxial propagation of quasi-monochromatic waves and time evolution of a dynamic system.
See also
*
Round-trip gain Round-trip gain refers to the laser physics, and laser cavities (or laser resonators). It is gain, integrated along a ray, which makes a round-trip in the cavity.
At the continuous-wave operation, the round-trip gain exactly compensates both the ...
, gain multiplied by the length of propagation of the laser emission during a single round-trip
*
Disk laser
A disk laser or active mirror (Fig.1) is a type of diode pumped solid-state laser characterized by a heat sink and laser output that are realized on opposite sides of a thin layer of active gain medium.
Despite their name, disk lasers do not ha ...
*
Effective cross-sections
*
McCumber relation
References
{{lasers
Laser science