88:. As the pump is switched on, the gain in the active medium rises and exceeds the steady-state value. The number of photons in the cavity increases, depleting the gain below the steady-state value, and so on. The laser pulsates; the output power at the peaks can be orders of magnitude larger than that between pulses. After several strong peaks, the amplitude of pulsation reduces, and the system behaves as a linear oscillator with damping. Then the pulsation decays; this is the beginning of the
22:
1312:. At weak decay of the self-pulsation (even in the case of strong spiking), the solution of corresponding equation can be approximated through elementary function. The error of such approximation of the solution of the initial equations is small compared to the precision of the model.
300:
1046:
Practically, this rate can be orders of magnitude smaller than the repetition rate of pulses. In this case, the decay of the self-pulsation in a real lasers is determined by other physical processes, not taken into account with the initial equations above.
883:
993:
1303:
1315:
The pulsation of real the output of a real lasers in the transient regime usually show significant deviation from the simple model above, although the model gives good qualitative description of the phenomenon of self-pulsation.
1097:, i.e., the lifetime of excitations in the active medium is large compared to the lifetime of photons inside the cavity. The spiking is possible at low dumping of self-pulsation, in the corresponding both parameters
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The transient regime can be important for the quasi-continuous lasers that needs to operate in the pulsed regime, for example, to avoid the overheating.
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at the optical bench is shown in Fig.4. The colored curves are oscillograms of two shouts of the quasi-continuous diode-pumped
46:
295:{\displaystyle ~{\begin{aligned}{{\rm {d}}X}/{{\rm {d}}t}&=KXY-UX\\{{\rm {d}}Y}/{{\rm {d}}t}&=-KXY-VY+W\end{aligned}}}
37:
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1350:
878:{\displaystyle {\begin{aligned}X_{0}&={\frac {W}{U}}-{\frac {V}{K}}\\Y_{0}&={\frac {U}{K}}\end{aligned}}}
89:
308:
694:
1559:
https://web.archive.org/web/20070514062058/http://www.tcd.ie/Physics/Optoelectronics/research/self_pulse.php
988:{\displaystyle {\begin{aligned}\Gamma &=KW/(2U)\\\Omega &={\sqrt {w^{2}-\Gamma ^{2}}}\end{aligned}}}
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ceramics, described by. The thick black curve represents the approximation within the simple model with
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1298:{\displaystyle {\begin{aligned}X&=X_{0}\exp(x)\\Y&=Y_{0}+X_{0}y\\t&=z/w\end{aligned}}}
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Such equations appear in the similar form (with various notations for variables) in
1433:"Self-pulsing laser as oscillator Toda: Approximation through elementary functions"
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The only numerical solutions were believed to exist for the strong pulsation,
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774:
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1162:
1389:"Single-mode solid-state laser with short wide unstable cavity"
15:
511:{\displaystyle ~W=P_{\rm {p}}/({\hbar \omega _{\rm {p}}})~}
1387:
D.Kouznetsov; J.-F.Bisson; K.Takaichi; K.Ueda (2005).
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The simple model of self-pulsation deals with number
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84:. Self-pulsation takes place at the beginning of
150:. The evolution can be described with equations:
1431:D.Kouznetsov; J.-F.Bisson; J.Li; K.Ueda (2007).
8:
781:, for example, the monography by A.Siegman.
1394:Journal of the Optical Society of America B
444:is rate of relaxation of excitation of the
1169:. Only qualitative agreement takes place.
893:Decay of small pulsation occurs with rate
356:{\displaystyle ~K=\sigma /(st_{\rm {r}})~}
120:of photons in the laser cavity and number
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65:Learn how and when to remove this message
1561:(self-pulsation in semiconductor lasers)
1426:
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399:is rate of relaxation of photons in the
1341:
1063:. The strong spiking is possible, when
558:is the round-trip time of light in the
486:
7:
1492:"Toda potential in laser equations"
770:(which is assumed to be constant).
659:{\displaystyle ~\omega _{\rm {s}}~}
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14:
1548:, 2nd ed. Springer-Verlag (1988).
1150:The intent of realization of the
1036:{\displaystyle w={\sqrt {KW-UV}}}
766:is power of pump absorbed in the
20:
42:formatting, grammar, coherence.
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937:
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347:
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1:
1546:Solid-state laser engineering
551:{\displaystyle ~t_{\rm {r}}~}
80:is a transient phenomenon in
1355:. University Science Books.
392:{\displaystyle ~U=\theta L~}
1490:G.L.Oppo; A.Politi (1985).
759:{\displaystyle P_{\rm {p}}}
437:{\displaystyle ~V=1/\tau ~}
40:. The specific problem is:
1596:
1469:10.1088/1751-8113/40/9/016
36:to meet Knowledge (XXG)'s
1308:lead to the equation for
686:{\displaystyle ~\theta ~}
617:{\displaystyle ~\sigma ~}
90:continuous-wave operation
1497:Zeitschrift für Physik B
1090:{\displaystyle U/V\ll 1}
695:transmission coefficient
1415:10.1364/JOSAB.22.001605
721:{\displaystyle ~\tau ~}
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1140:{\displaystyle ~v^{}~}
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626:emission cross-section
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1438:Journal of Physics A
1349:A.E.Siegman (1986).
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1177:Change of variables
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47:improve this article
1544:Koechner, William.
1510:1985ZPhyB..59..111O
1451:2007JPhA...40.2107K
1407:2005JOSAB..22.1605K
728:is the lifetime of
582:{\displaystyle ~s~}
139:{\displaystyle ~Y~}
1518:10.1007/BF01325388
1326:Solid-state lasers
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1159:solid-state laser
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38:quality standards
29:This article may
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1051:Strong pulsation
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1173:Toda Oscillator
1167:oscillator Toda
1152:oscillator Toda
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1553:External links
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55:September 2012
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1371:. Retrieved
1367:the original
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597:is assumed);
520:pumping rate
401:laser cavity
304:
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86:laser action
77:
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61:
52:
45:Please help
41:
30:
1575:Oscillators
1445:(9): 1–18.
768:gain medium
734:gain medium
446:gain medium
148:gain medium
49:if you can.
1569:Categories
1373:2007-03-30
1337:References
1331:Disk laser
730:excitation
1534:119657810
1526:0722-3277
1455:CiteSeerX
1215:
1156:microchip
1082:≪
1023:−
971:Γ
967:−
945:Ω
908:Γ
828:−
775:textbooks
713:τ
678:θ
643:ω
609:σ
491:ω
487:ℏ
429:τ
381:θ
322:σ
274:−
262:−
213:−
96:Equations
1477:53330023
1320:See also
31:require
1506:Bibcode
1447:Bibcode
1403:Bibcode
1061:spiking
732:of the
697:of the
693:is the
628:at the
624:is the
518:is the
33:cleanup
1532:
1524:
1475:
1457:
1359:
1352:Lasers
1163:Yb:YAG
1135:
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998:where
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593:(good
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305:where
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1530:S2CID
1473:S2CID
1522:ISSN
1357:ISBN
1117:and
1514:doi
1465:doi
1411:doi
1212:exp
1161:on
777:on
1571::
1528:.
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1512:.
1502:59
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1423:^
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1413::
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1376:.
1289:w
1285:/
1281:z
1278:=
1271:t
1264:y
1259:0
1255:X
1251:+
1246:0
1242:Y
1238:=
1231:Y
1224:)
1221:x
1218:(
1207:0
1203:X
1199:=
1192:X
1129:v
1105:u
1085:1
1079:V
1075:/
1071:U
1029:V
1026:U
1020:W
1017:K
1012:=
1009:w
975:2
962:2
958:w
952:=
938:)
935:U
932:2
929:(
925:/
921:W
918:K
915:=
867:K
864:U
859:=
850:0
846:Y
836:K
833:V
823:U
820:W
815:=
806:0
802:X
751:p
746:P
736:.
701:.
666:.
648:s
574:s
562:,
540:r
535:t
522:;
503:)
496:p
483:(
479:/
472:p
467:P
463:=
460:W
448:,
425:/
421:1
418:=
415:V
403:,
384:L
378:=
375:U
348:)
342:r
337:t
333:s
330:(
326:/
319:=
316:K
286:W
283:+
280:Y
277:V
271:Y
268:X
265:K
259:=
251:t
246:d
239:/
234:Y
229:d
219:X
216:U
210:Y
207:X
204:K
201:=
193:t
188:d
181:/
176:X
171:d
131:Y
108:X
68:)
62:(
57:)
53:(
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