- 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.
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
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 is function of the Cartesian coordinates,, and . Then, assuming that the geometrical opticsis applyablethe round-trip gain can be expressed as follows: , where is path along the ray, parametrized with functions , , ; the integration is performed along the whole ray, which is supposed toform the closed loop.
In simple models, the
flat-topdistribution of pump andgain is assumed to be constant. In the case of simlest cavity, the round-trip gain, where is length of the cavity; the laser light is supposedto go forward and back, this leads to the coefficient 2 in the estimate.
steady-state continuous waveoperation of a laser, the round-trip gain is determined by thereflectivity of the mirrors (in the case of stable cavity) and the magnification coefficientin thecase of unstable resonator( unstable cavity).
The coupling parameter of a laser resonator determines, what part of theenergy of the
laser fieldin the cavity goes out at each round-trip. This output can be deermined by thetransmitivity of the output coupler, or the magnification coefficientin 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 determines, what part of the energy of the
laser fieldbecomes unusable at each round-trip; it can be absorbed or scattered.
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
Zeitschrift fur PhysikB|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 exactly compensate both,the output coupling and losses:.Assuming, that the gain is small (), this relation can be written as follows:
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
JOSAB|volume=22| issue=8| pages=1605–1619
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 should be decreased(in order to avoid the exponential growthof the amplified spontaneous emission), and the round-trip gain 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 overheatingprevents 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
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.
Wikimedia Foundation. 2010.