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(x,y,z)~ 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(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 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
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 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=| 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=| 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
coauthors=J.-F.Bisson, K.Takaichi, K.Ueda
title=Single-mode solid-state laser with short wide unstable cavity
journal=JOSAB|volume=22| issue=8| pages=1605–1619
] . In particular, the round-trip loss ~eta~ 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 ~eta~;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=| accessdate=2007-01-26| doi=10.1364/JOSAB.23.001074; [] ] .

For the analysis of processes in active medium, the sum ~eta+ heta~ can be also called"loss"cite book
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.


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