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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 ~P~ 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. :G = \frac\ln(P)=\frac where ~z~ 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 optica ...
, the gain can be taken into account with the following equation : 2ik\frac= \Delta_E + 2 \nu E + i G E, where ~\nu~ is variation of index of refraction (Which is supposed to be small), ~E~ is complex field, related to the physical electric field ~E_~ with relation ~E_=\left( \vec e E \exp(ikz-i\omega t)\right)~, where ~\vec e~ is vector of polarization, ~k~ is wavenumber, ~\omega~ is frequency, ~\Delta_=\left( \frac+ \frac \right) ~ is transversal Laplacian; ~ \rm Re ~ 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 ~N_1~ and ~N_2~ of lower and excited states: :~ G = \sigma_N_2 - \sigma_N_1 ~ where ~ \sigma_~ and ~ \sigma_~ 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 g=\int G z . 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 ~K~ can be defined as ratio of the output power ~ P_ to the input power ~P_: :~ K=P_/P_. It is related with gain; ~K=\exp\left(\int G z\right)~. The gain and the amplification coefficient should not be confused with the
magnification coefficient Magnification is the process of enlarging the angular diameter, 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 ...
. 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 ~K~ 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 The McCumber relation (or McCumber theory) is a relationship between the effective cross-sections of absorption and emission of light in the physics of solid-state lasers.D.E.McCumber. Einstein relations connecting broadband emission and absorption ...
* McCumber relation


References

{{lasers Laser science