- Gain (lasers)
**Gain**(or amplification) inlaser physics is a process, where the medium transfers part of its energy to the emittedelectromagnetic radiation , resulting in an increase in laser power. This is basic principle of alllasers .Quantitatively, the ability of alaser medium to increase power of light is characterised with**Gain**.**Definition**The gain can be defined as the derivative of logarithm of power $~P~$as it passes through the medium: $G\; =\; frac$ m d m d}z}ln(P)=frac{ { m d}P /{ m d} z}{P}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 , the gain can be taken into account with the following equation $2ikfrac\{partial\; E\}\{partial\; z\}=Delta\_\{perp\}E\; +\; 2\; u\; E\; +\; i\; G\; E$,where $~\; u~$ is variation of index of refraction (Which is supposed to be small),

$~E~$ is complex field, related to the physical electric field$~E\_\{\; m\; phys\}~$ with relation $~E\_\{\; m\; phys\}=\{\; m\; Re\}left(\; vec\; e\; E\; exp(ikz-iomega\; t)\; ight)~$, where$~vec\; e~$ is vector of polarization,$~k~$ is wavenumber,$~omega~$ is frequency,$~Delta\_\{\; m\; perp\}=left(frac\{partial\; ^2\}\{partial\; x^2\}+frac\{partial\; ^2\}\{partial\; y^2\}\; ight)~$is transversal Laplacian;$~\; m\; Re\; ~$ 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: $~\; G\; =\; sigma\_\{\; m\; e\}N\_2\; -\; sigma\_\{\; m\; a\}N\_1~$

where $~\; sigma\_\{\; m\; e\}~$ and$~\; sigma\_\{\; m\; a\}~$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$g=int\; G\; \{\; m\; d\}\; z$.This definition assumes either flat-top profile of the laser beam inside the laser, orsome effective gain, averaged across the beam cross-section.The amplification coefficient $~K~$ can be defined as ratio of the output power $~\; K=P\_\{\; m\; in\}/P\_\{\; m\; out\}$input power $~\; K=P\_\{\; m\; in\}/P\_\{\; m\; out\}$:

$~\; K=P\_\{\; m\; in\}/P\_\{\; m\; out\}$. It is related with gain;$~K=expleft(int\; G\; \{\; m\; d\}\; z\; ight)~$.

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 withpassive elements , withoutgain medium . cite book

url=http://www.uscibooks.com/siegman.htm

author=A.E.Siegman

title=Lasers

year=1986

publisher=University Science Books

id= ISBN 0-935702-11-3]**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 a Wikipedia article.

In

radiophysics , 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 anddecrement instead ofabsorption coefficient to avoid theambiguity cite book

url=

author=D.Yu.Kuznetsov

title=The transformation of the transverse structure of monochromatic light in the non-linear media.In book: -- Optics and Lasers. ed: G.G.Petrash

year=1995] , exploiting the analogy between paraxial propagaition of quasi-monochromatic waves and time evolution of a dynamic system.**ee also***gain medium

*Round-trip gain , gain multiplied by the length of propagation of the laser emission during a single round-trip

*disk laser

*effective cross-sections

*McCumber relation **References**

*Wikimedia Foundation.
2010.*

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**Gain (disambiguation)**— Gain may refer to: * Gain, an electronics and signal processing term * Gain (lasers), derivative of the logarithm of power with respect to length of propagation. * Gain (finance) * Gain (information retrieval) * Gain (novel), a novel by American… … Wikipedia**LASERS**— Les lasers (le mot «laser» est formé des initiales des mots anglais light amplification by stimulated emission of radiations , signifiant: amplification de lumière par émission stimulée de rayonnement) sont des sources nouvelles de rayonnement,… … Encyclopédie Universelle**gain**— [ gɛ̃ ] n. m. • XIIe; de gagner 1 ♦ Littér. Action de gagner. Le gain d une bataille. ⇒ succès, victoire. Le gain d un procès. Cour. Avoir, obtenir gain de cause. Absolt Chances égales de gain et de perte. 2 ♦ Ce qu on gagne; profit, bénéfice… … Encyclopédie Universelle**Round-trip gain**— refers to the laser physics, and laser cavitys (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 gain exactly compensate both, the output… … Wikipedia**Laser**— For other uses, see Laser (disambiguation). United States Air Force laser experiment … Wikipedia**Laser diode**— Top: a packaged laser diode shown with a penny for scale. Bottom: the laser diode chip is removed from the above package and placed on the eye of a needle for scale … Wikipedia**THERMONUCLÉAIRE (ÉNERGIE)**— Jusqu’au milieu du XXe siècle, l’énergie nécessaire à la survie et au développement du monde vivant a été assurée, directement ou indirectement, par la transformation du rayonnement solaire arrivant sur la planète. Dans un premier temps, la… … Encyclopédie Universelle**Optical amplifier**— An optical amplifier is a device that amplifies an optical signal directly, without the need to first convert it to an electrical signal. An optical amplifier may be thought of as a laser without an optical cavity, or one in which feedback from… … Wikipedia**Quantum cascade laser**— Quantum cascade lasers (QCLs) are semiconductor lasers that emit in the mid to far infrared portion of the electromagnetic spectrum and were first demonstrated by Jerome Faist, Federico Capasso, Deborah Sivco, Carlo Sirtori, Albert Hutchinson,… … Wikipedia**Fiber laser**— A fiber laser or fibre laser is a laser in which the active gain medium is an optical fiber doped with rare earth elements such as erbium, ytterbium, neodymium, dysprosium, praseodymium, and thulium. They are related to doped fiber amplifiers,… … Wikipedia