- Round-trip gain
**Round-trip gain**refers to thelaser physics , andlaser cavity s (orlaser resonator s).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 thepolarization of light . Usually, we may assume that at some moment of time, at reasonable frequency of operation, the gain $~G(x,y,z)~$ is function of theCartesian coordinates $~x~$,$~y~$, and $~z~$. Then, assuming that thegeometrical optics is applyablethe round-trip gain $~g~$ can be expressed as follows: $~g=int\; G(x(a),y(a),z(a))~\{\; m\; d\}a~$, where $~a~$ is path along the ray, parametrized with functions $~x(a)~$, $~y(a)~$, $~z(a)~$; 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 ofstable cavity ) and themagnification coefficient in thecase ofunstable resonator (unstable cavity ).**Coupling parameter**The

**coupling parameter**$~\; heta~$ of a laser resonator determines, what part of theenergy of thelaser field in the cavity goes out at each round-trip. This output can be deermined by thetransmitivity of theoutput coupler , or themagnification coefficient in the case ofunstable cavity 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] .**Round-trip loss (background loss)**The

**background loss**, of the**round-trip loss**$~eta~$ determines, what part of the energy of thelaser 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 equivalentoscillator Toda cite 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:$~exp(g)~(1-eta-\; heta)=1~$.Assuming, that the gain is small ($~g~ll\; 1~$), this relation can be written as follows:

$~g=eta+\; heta~$

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 $~eta~$ may be one of important parameters which limit theoutput power of adisk laser ; at the power scaling, the gain $~G~$ should be decreased(in order to avoid theexponential growth of theamplified spontaneous emission ), and the round-trip gain$~g~$ should remain larger than the background loss $~eta~$;this requires to increase of the thickness of the slab of thegain medium ; at certain thickness, theoverheating 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 $~eta+\; heta~$ 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**

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