# Round-trip gain

Round-trip gain

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 coupling of the cavity and its background loss.

Round-trip gain in geometric optics

Generally, the Round-trip gain may depend on the frequency, on the position and tilt of the ray, and even on the
polarization of light. Usually, we may assume that at some moment of time, at reasonable frequency of operation, the gain $~G\left(x,y,z\right)~$ is function of the Cartesian coordinates $~x~$,$~y~$, and $~z~$. Then, assuming that the geometrical optics is applyablethe round-trip gain $~g~$ can be expressed as follows: $~g=int G\left(x\left(a\right),y\left(a\right),z\left(a\right)\right)~\left\{ m d\right\}a~$, where $~a~$ is path along the ray, parametrized with functions $~x\left(a\right)~$, $~y\left(a\right)~$, $~z\left(a\right)~$; the integration is performed along the whole ray, which is supposed toform the closed loop.

In simple models, the flat-top distribution of pump andgain $~G~$ is assumed to be constant. In the case of simlest cavity, the round-trip gain$~g=2Gh~$, where $~h~$ is length of the cavity; the laser light is supposedto go forward and back, this leads to the coefficient 2 in the estimate.

In the steady-state continuous wave operation of a laser, the round-trip gain is determined by thereflectivity of the mirrors (in the case of stable cavity) and the magnification coefficient in thecase of unstable resonator (unstable cavity).

Coupling parameter

The coupling parameter $~ heta~$ of a laser resonator determines, what part of theenergy of the laser field in the cavity goes out at each round-trip. This output can be deermined by thetransmitivity of the output coupler, or the magnification coefficient in the case of unstable cavitycite 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
] .

Round-trip loss (background loss)

The background loss, of the round-trip loss determines, what part of the energy of the laser field becomes unusable at each round-trip; it can be absorbed or scattered.

At the self-pulsation, the gain lates to respond the variation of number of photons in the cavity. Within the simple model, the round-trip loss and the output coupling determine the damping parameters of the equivalent oscillator Todacite journal|url=http://worldcat.org/issn/0722-3277| author=G.L.Oppo|coauthors=A.Politi|title=Toda potential in laser equations
journal=Zeitschrift fur Physik B|volume=59|pages=111–115| year=1985|doi=10.1007/BF01325388
] cite journal|url=http://www.iop.org/EJ/abstract/-search=15823442.1/1751-8121/40/9/016| author=D.Kouznetsov|coauthors=J.-F.Bisson, J.Li, K.Ueda|title=Self-pulsing laser as oscillator Toda: Approximation through elementary functions|journal=Journal of Physics A|volume=40|pages=1–18| year=2007|doi=10.1088/1751-8113/40/9/016] .

At the steady-state operation, the round-trip gain $~g~$ exactly compensate both,the output coupling and losses:.Assuming, that the gain is small ($~g~ll 1~$), this relation can be written as follows:

Such as relation is used in analytic estimates of the performance of laserscite journal
author=D.Kouznetsov
coauthors=J.-F.Bisson, K.Takaichi, K.Ueda
title=Single-mode solid-state laser with short wide unstable cavity
url=http://josab.osa.org/abstract.cfm?id=84730
journal=JOSAB|volume=22| issue=8| pages=1605–1619
year=2005
doi=10.1364/JOSAB.22.001605
] . In particular, the round-trip loss may be one of important parameters which limit theoutput power of a disk laser; at the power scaling, the gain $~G~$ should be decreased(in order to avoid the exponential growth of the amplified spontaneous emission), and the round-trip gain$~g~$ should remain larger than the background loss ;this requires to increase of the thickness of the slab of the gain medium; at certain thickness, the
overheating prevents the efficient operationcite journal| author=D. Kouznetsov|coauthors= J.-F. Bisson, J. Dong, and K. Ueda| title=Surface loss limit of the power scaling of a thin-disk laser| journal=JOSAB| volume=23| issue=6| pages=1074–1082| year=2006| url=http://josab.osa.org/abstract.cfm?id=90157| accessdate=2007-01-26| doi=10.1364/JOSAB.23.001074; [http://www.ils.uec.ac.jp/~dima/disk.pdf] ] .

For the analysis of processes in active medium, the sum can be also called"loss"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
] . This notation leads to confusions as soon as one is interested, which part of theenergy is absorbed and scattered, and which part of such a "loss" is actually wanted and useful output of the laser.

References

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Round trip — has several uses including:*Round trip in travel means purchasing a ticket or traveling from one destination to another and then returning to the starting location. *Round tripping *Round trip delay time in communications *Round trip format… …   Wikipedia

• Gain (lasers) — Gain (or amplification) in laser physics is a process, where the medium transfers part of its energy to the emitted electromagnetic radiation, resulting in an increase in laser power. This is basic principle of all lasers.Quantitatively, the… …   Wikipedia

• Cumulative elevation gain — In running, cycling, and mountaineering, cumulative elevation gain refers to the sum of every gain in elevation throughout an entire trip. It is sometimes also known as cumulative gain or elevation gain, or often in the context of mountain travel …   Wikipedia

• Bergedorf Round Table — Unbound by political and economic agendas, the Körber Foundation with its international relations department in Berlin is committed to helping foster a better understanding of international politics. In confidential conferences and background… …   Wikipedia

• Disk laser — Not to be confused with Laserdisc. Fig.1. An optically pumped disk laser (active mirror). A disk laser or active mirror (Fig.1.) is a type of solid state laser characterized by a heat sink and laser output that are realized on opposite sides of a …   Wikipedia

• Coupling parameter — The coupling parameter of the resonator, specifies the part of the energy of the laser field, which is output at each round trip. The coupling parameter should not be confused with the round trip loss, which refers to the part of the energy of… …   Wikipedia

• Amplified spontaneous emission — (ASE) or superluminescence is light, produced by spontaneous emission, that has been optically amplified by the process of stimulated emission in a gain medium.Origins and problemsASE is produced when a laser gain medium is pumped to produce a… …   Wikipedia

• Equalization — Unreferenced|date=July 2007Equalization (or equalisation, EQ) is the process of changing the frequency envelope of a sound in audio processing. In passing through any channel, an audio signal will spread from its original qualities. The goal of… …   Wikipedia

• усиление при двукратном прохождении — — [Л.Г.Суменко. Англо русский словарь по информационным технологиям. М.: ГП ЦНИИС, 2003.] Тематики информационные технологии в целом EN round trip gain …   Справочник технического переводчика

• football — /foot bawl /, n. 1. a game in which two opposing teams of 11 players each defend goals at opposite ends of a field having goal posts at each end, with points being scored chiefly by carrying the ball across the opponent s goal line and by place… …   Universalium