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| '''Round-trip gain''' refers to the [[laser physics]], and [[laser cavity|laser cavities]] (or [[laser resonator]]s). | | The writer's title is Christy. Mississippi is exactly where his house is. The favorite hobby for him and his kids is style and he'll be beginning some thing else along with it. Credit authorising is how she makes a living.<br><br>Also visit my webpage :: psychic readings ([http://www.chk.woobi.co.kr/xe/?document_srl=346069 visit the next post]) |
| It is gain, integrated along a ray, which makes a round-trip in the cavity.
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| At the [[continuous-wave operation]], the round-trip gain exactly compensates both the output coupling of the cavity and its background loss.{{Clarify|date=December 2009}}
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| ==Round-trip gain in geometric optics==
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| Generally, the '''Round-trip gain''' may depend on the frequency, on the position and tilt of the ray, and even on the
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| [[polarization of light]]. Usually, we may assume that at some moment of time, at reasonable frequency of operation, the [[gain (lasers)|gain]]
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| <math>~G(x,y,z)~</math> is function of the [[Cartesian coordinates]]
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| <math>~x~</math>,
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| <math>~y~</math>, and
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| <math>~z~</math>. Then, assuming that the [[geometrical optics]] is applicable
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| the round-trip gain <math>~g~</math> can be expressed as follows:
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| <math>~g=\int G(x(a),y(a),z(a))~{\rm d}a~</math>,
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| where <math>~a~</math> is path along the ray, parametrized with functions
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| <math>~x(a)~</math>,
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| <math>~y(a)~</math>,
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| <math>~z(a)~</math>; the integration is performed along the whole ray, which is supposed to
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| form the closed loop.
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| In simple models, the [[flat-top]] distribution of pump and
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| gain <math>~G~</math> is assumed to be constant. In the case of simplest cavity, the round-trip gain
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| <math>~g=2Gh~</math>, where <math>~h~</math> is length of the cavity; the laser light is supposed
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| to go forward and back, this leads to the coefficient 2 in the estimate.
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| In the [[steady-state]] [[continuous wave]] operation of a laser, the round-trip gain is determined by the
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| reflectivity of the mirrors (in the case of [[stable cavity]]) and the [[magnification coefficient]] in the
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| case of [[unstable resonator]] ([[unstable cavity]]).
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| ==Coupling parameter==
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| The '''coupling parameter''' <math>~\theta~</math> of a laser resonator determines, what part of the
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| energy of the [[laser field]] in the cavity goes out at each round-trip. This output can be determined by the
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| transmitivity of the [[output coupler]], or the [[magnification coefficient]] in the case of [[unstable cavity]]
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| .<ref name="siegman">
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| {{cite book
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| |url=http://www.uscibooks.com/siegman.htm
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| |author=A.E.Siegman
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| |title=Lasers
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| |year=1986
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| |publisher=University Science Books
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| |isbn= 0-935702-11-3
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| }}
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| </ref>
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| ==Round-trip loss (background loss)==
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| The '''background loss''', of the '''round-trip loss''' <math>~\beta~</math> determines, what part of the energy of the [[laser field]]
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| becomes unusable at each round-trip; it can be absorbed or scattered.
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| At the [[self-pulsation]], the gain lates to respond the variation of number of photons in the cavity. Within the simple model,
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| the round-trip loss and the output coupling determine the damping parameters of the equivalent [[oscillator Toda]]
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| <ref name="oppo">{{cite journal|url=http://worldcat.org/issn/0722-3277| author=G.L.Oppo|coauthors=A.Politi|title=Toda potential in laser equations|
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| journal=[[Zeitschrift fur Physik]] B|volume=59|pages=111–115| year=1985|doi=10.1007/BF01325388|bibcode = 1985ZPhyB..59..111O }}</ref>
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| .<ref name="kouz">{{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|bibcode = 2007JPhA...40.2107K|issue=9 }}</ref>
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| At the steady-state operation, the round-trip gain <math>~g~</math> exactly compensate both,
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| the output coupling and losses:
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| <math>~\exp(g)~(1-\beta-\theta)=1~</math>.
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| Assuming, that the gain is small (<math>~g~\ll 1~</math>), this relation can be written as follows:
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| <math>~g=\beta+\theta~</math>
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| Such as relation is used in analytic estimates of the performance of lasers
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| .<ref name="uns">{{cite journal
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| | author=D.Kouznetsov
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| | coauthors=J.-F.Bisson, K.Takaichi, K.Ueda
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| | title=Single-mode solid-state laser with short wide unstable cavity
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| |url=http://josab.osa.org/abstract.cfm?id=84730
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| |journal=[[JOSAB]]|volume=22| issue=8| pages=1605–1619
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| | year=2005
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| | doi=10.1364/JOSAB.22.001605
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| | bibcode=2005JOSAB..22.1605K
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| }}</ref> In particular, the
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| round-trip loss <math>~\beta~</math> may be one of important parameters which limit the
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| output power of a [[disk laser]]; at the power scaling, the gain <math>~G~</math> should be decreased
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| (in order to avoid the [[exponential growth]] of the [[amplified spontaneous emission]]), and the round-trip gain
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| <math>~g~</math> should remain larger than the background loss <math>~\beta~</math>;
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| this requires to increase of the thickness of the slab of the [[gain medium]]; at certain thickness, the
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| [[overheating]] prevents the efficient operation
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| .<ref name="kouz06">{{cite 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|bibcode = 2006JOSAB..23.1074K }}; [http://www.ils.uec.ac.jp/~dima/disk.pdf]</ref>
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| For the analysis of processes in active medium, the sum <math>~\beta+\theta~</math> can be also called
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| "loss"
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| .<ref name="siegman"/> This notation leads to confusions as soon as one is interested, which part of the
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| energy is absorbed and scattered, and which part of such a "loss" is actually wanted and useful output of the laser.
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| ==References==
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| <references/>
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| [[Category:Laser science]]
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