1763:
716:
175:
520:
1327:, which is actually not a coefficient at all; one has to multiply it to the length of propagation (thickness), change the signum, take inverse of the exponential, and only then get the coefficient of attenuation of the sample.
303:
902:
612:
987:
means gain multiplied by the length of propagation of the laser emission during a single round-trip. In the case of gain varying along the length, the round-trip gain can be expressed with integral
1258:
1193:
1283:
There is no established terminology about gain and absorption. Everyone is free to use own notations, and it is not possible to cover all the systems of notations in this article.
975:
940:
1024:
405:
1091:
1126:
749:
555:
1264:
607:
823:
790:
333:
1317:
1053:
581:
361:
204:
76:
84:
210:
410:
1268:
1026:. This definition assumes either flat-top profile of the laser beam inside the laser, or some effective gain, averaged across the beam cross-section.
222:
1431:
The transformation of the transverse structure of monochromatic light in the non-linear media. In book: -- Optics and Lasers. ed: G.G.Petrash
78:
as it passes through the medium. The factor by which an input beam is amplified by a medium is called the gain and is represented by G.
831:
711:{\displaystyle ~\Delta _{\rm {\perp }}=\left({\frac {\partial ^{2}}{\partial x^{2}}}+{\frac {\partial ^{2}}{\partial y^{2}}}\right)~}
1723:
206:
is the coordinate in the direction of propagation. This equation neglects the effects of the transversal profile of the beam.
1202:
1346:, exploiting the analogy between paraxial propagation of quasi-monochromatic waves and time evolution of a dynamic system.
1402:
1462:
1134:
1392:
1632:
1267:. The magnification characterizes the scale of enlarging of an image; such enlargement can be realized with
1688:
945:
910:
990:
1492:
366:
29:
1058:
1366:
1096:
721:
525:
1787:
1662:
1482:
1358:, gain multiplied by the length of propagation of the laser emission during a single round-trip
1339:
586:
213:
1550:
795:
762:
312:
1657:
1540:
1528:
1455:
8:
1708:
1627:
1567:
1487:
1296:
1032:
759:
In the simple quasi two-level system, the gain can be expressed in terms of populations
560:
340:
183:
55:
170:{\displaystyle G={\frac {\rm {d}}{{\rm {d}}z}}\ln(P)={\frac {{\rm {d}}P/{\rm {d}}z}{P}}}
515:{\displaystyle ~E_{\rm {phys}}={\rm {Re}}\left({\vec {e}}E\exp(ikz-i\omega t)\right)~}
1728:
1602:
1577:
1398:
1371:
1738:
1703:
1683:
1652:
1293:
In many articles on laser physics, which do not use the amplification coefficient
1766:
1647:
1637:
1448:
1355:
984:
298:{\displaystyle 2ik{\frac {\partial E}{\partial z}}=\Delta _{\perp }E+2\nu E+iGE}
32:, resulting in an increase in optical power. This is the basic principle of all
1743:
1733:
1693:
1642:
1560:
1513:
1497:
1781:
1698:
1678:
1619:
1545:
978:
17:
1718:
1587:
1582:
1523:
1287:
1263:
The gain and the amplification coefficient should not be confused with the
41:
28:
is a process where the medium transfers part of its energy to the emitted
1748:
1609:
1592:
1572:
1272:
1597:
1408:
1361:
1713:
1555:
1535:
1518:
1343:
977:
are effective emission and absorption cross-sections. In the case of
335:
is variation of index of refraction (Which is supposed to be small),
44:
to increase optical power. However, overall a laser consumes energy.
897:{\displaystyle ~G=\sigma _{\rm {e}}N_{2}-\sigma _{\rm {a}}N_{1}~}
216:, the gain can be taken into account with the following equation
52:
The gain can be defined as the derivative of logarithm of power
33:
1471:
1290:, gain may mean logarithm of the amplification coefficient.
1440:
363:
is complex field, related to the physical electric field
1278:
1253:{\displaystyle ~K=\exp \left(\int G{\rm {d}}z\right)~}
1299:
1205:
1137:
1099:
1061:
1035:
993:
948:
913:
834:
798:
765:
724:
615:
589:
563:
528:
413:
369:
343:
315:
225:
186:
87:
58:
1311:
1252:
1187:
1120:
1085:
1047:
1018:
969:
934:
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817:
784:
743:
710:
601:
575:
549:
514:
399:
355:
327:
297:
198:
169:
70:
754:
1779:
1428:
1456:
1188:{\displaystyle ~K=P_{\rm {out}}/P_{\rm {in}}}
1055:can be defined as ratio of the output power
1390:
1463:
1449:
1724:Multiple-prism grating laser oscillator
1780:
1384:
1444:
1279:Alternative terminology and notations
1422:
970:{\displaystyle ~\sigma _{\rm {a}}~}
935:{\displaystyle ~\sigma _{\rm {e}}~}
13:
1319:defined above, the gain is called
1234:
1179:
1176:
1159:
1156:
1153:
1112:
1109:
1077:
1074:
1071:
1019:{\displaystyle g=\int G{\rm {d}}z}
1008:
958:
923:
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850:
733:
730:
684:
674:
652:
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620:
446:
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388:
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379:
259:
246:
238:
153:
138:
104:
97:
14:
1799:
40:is a measure of the ability of a
1762:
1761:
400:{\displaystyle ~E_{\rm {phys}}~}
1633:Amplified spontaneous emission
1086:{\displaystyle ~P_{\rm {out}}}
1029:The amplification coefficient
981:medium, the gain is negative.
755:Gain in quasi two-level system
538:
501:
477:
462:
127:
121:
1:
1377:
1121:{\displaystyle ~P_{\rm {in}}}
825:of lower and excited states:
47:
1397:. University Science Books.
744:{\displaystyle ~{\rm {Re~}}}
550:{\displaystyle ~{\vec {e}}~}
7:
1689:Chirped pulse amplification
1349:
1330:Some publications use term
557:is vector of polarization,
10:
1804:
1493:List of laser applications
1470:
718:is transversal Laplacian;
1757:
1671:
1618:
1506:
1478:
1321:Amplification coefficient
1265:magnification coefficient
1199:It is related with gain;
602:{\displaystyle ~\omega ~}
30:electromagnetic radiation
1367:Effective cross-sections
1429:D.Yu.Kuznetsov (1995).
818:{\displaystyle ~N_{2}~}
785:{\displaystyle ~N_{1}~}
1483:List of laser articles
1340:absorption coefficient
1325:Absorption coefficient
1313:
1254:
1189:
1122:
1087:
1049:
1020:
971:
936:
898:
819:
786:
745:
712:
603:
577:
551:
516:
401:
357:
329:
328:{\displaystyle ~\nu ~}
299:
214:paraxial approximation
200:
171:
72:
1314:
1255:
1190:
1123:
1088:
1050:
1021:
972:
937:
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820:
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604:
578:
552:
517:
402:
358:
330:
300:
201:
172:
73:
1658:Population inversion
1391:A.E.Siegman (1986).
1334:instead of gain and
1297:
1203:
1135:
1097:
1059:
1033:
991:
946:
911:
832:
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763:
722:
613:
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367:
341:
313:
223:
184:
85:
56:
1709:Laser beam profiler
1628:Active laser medium
1568:Free-electron laser
1488:List of laser types
1312:{\displaystyle ~K~}
1093:to the input power
1048:{\displaystyle ~K~}
576:{\displaystyle ~k~}
356:{\displaystyle ~E~}
211:quasi-monochromatic
199:{\displaystyle ~z~}
71:{\displaystyle ~P~}
1323:, in analogy with
1309:
1250:
1185:
1118:
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1045:
1016:
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932:
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782:
741:
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512:
397:
353:
325:
295:
196:
167:
68:
36:. Quantitatively,
1775:
1774:
1729:Optical amplifier
1578:Solid-state laser
1372:McCumber relation
1308:
1302:
1249:
1208:
1140:
1102:
1064:
1044:
1038:
966:
951:
931:
916:
893:
837:
814:
801:
781:
768:
751:means real part.
738:
727:
707:
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666:
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346:
324:
318:
253:
195:
189:
165:
113:
67:
61:
1795:
1765:
1764:
1739:Optical isolator
1704:Injection seeder
1684:Beam homogenizer
1663:Ultrashort pulse
1653:Lasing threshold
1465:
1458:
1451:
1442:
1441:
1435:
1434:
1426:
1420:
1419:
1417:
1416:
1407:. Archived from
1388:
1318:
1316:
1315:
1310:
1306:
1300:
1269:passive elements
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370:
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1798:
1797:
1796:
1794:
1793:
1792:
1778:
1777:
1776:
1771:
1753:
1667:
1648:Laser linewidth
1638:Continuous wave
1614:
1507:Types of lasers
1502:
1474:
1469:
1439:
1438:
1427:
1423:
1414:
1412:
1405:
1389:
1385:
1380:
1356:Round-trip gain
1352:
1298:
1295:
1294:
1281:
1233:
1232:
1225:
1221:
1204:
1201:
1200:
1175:
1174:
1170:
1165:
1152:
1151:
1147:
1136:
1133:
1132:
1108:
1107:
1103:
1098:
1095:
1094:
1070:
1069:
1065:
1060:
1057:
1056:
1034:
1031:
1030:
1007:
1006:
992:
989:
988:
985:Round-trip gain
957:
956:
952:
947:
944:
943:
922:
921:
917:
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908:
885:
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719:
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641:
639:
638:
634:
624:
623:
619:
614:
611:
610:
588:
585:
584:
583:is wavenumber,
562:
559:
558:
533:
532:
527:
524:
523:
457:
456:
455:
451:
442:
441:
422:
421:
417:
412:
409:
408:
407:with relation
378:
377:
373:
368:
365:
364:
342:
339:
338:
314:
311:
310:
262:
258:
245:
237:
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146:
137:
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135:
133:
103:
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101:
96:
94:
86:
83:
82:
57:
54:
53:
50:
12:
11:
5:
1801:
1791:
1790:
1773:
1772:
1770:
1769:
1758:
1755:
1754:
1752:
1751:
1746:
1744:Output coupler
1741:
1736:
1734:Optical cavity
1731:
1726:
1721:
1716:
1711:
1706:
1701:
1696:
1694:Gain-switching
1691:
1686:
1681:
1675:
1673:
1669:
1668:
1666:
1665:
1660:
1655:
1650:
1645:
1643:Laser ablation
1640:
1635:
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1616:
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1607:
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1600:
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1590:
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1558:
1553:
1548:
1543:
1541:Carbon dioxide
1533:
1532:
1531:
1529:Liquid-crystal
1526:
1516:
1514:Chemical laser
1510:
1508:
1504:
1503:
1501:
1500:
1498:Laser acronyms
1495:
1490:
1485:
1479:
1476:
1475:
1468:
1467:
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609:is frequency,
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1788:Laser science
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1700:
1699:Gaussian beam
1697:
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1682:
1680:
1679:Beam expander
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1623:
1621:
1620:Laser physics
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1411:on 2016-12-06
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1404:0-935702-11-3
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1342:to avoid the
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62:
45:
43:
39:
35:
31:
27:
26:amplification
23:
19:
18:laser physics
1719:Mode locking
1672:Laser optics
1430:
1424:
1413:. Retrieved
1409:the original
1393:
1386:
1335:
1331:
1329:
1324:
1320:
1292:
1288:radiophysics
1285:
1282:
1262:
1198:
1028:
983:
906:
758:
337:
308:
208:
179:
51:
42:laser medium
37:
25:
21:
15:
1749:Q-switching
1610:X-ray laser
1603:Ti-sapphire
1573:Laser diode
1551:Helium–neon
1338:instead of
1273:gain medium
1415:2007-04-09
1378:References
1362:Disk laser
1271:, without
979:non-pumped
48:Definition
1714:M squared
1536:Gas laser
1519:Dye laser
1344:ambiguity
1336:decrement
1332:increment
1227:∫
1219:
1001:∫
954:σ
919:σ
871:σ
867:−
846:σ
685:∂
675:∂
653:∂
643:∂
626:⊥
621:Δ
594:ω
539:→
496:ω
490:−
475:
463:→
320:ν
278:ν
264:⊥
260:Δ
247:∂
239:∂
119:
1782:Category
1767:Category
1561:Nitrogen
1350:See also
907:where
522:, where
1546:Excimer
309:where
209:In the
1588:Nd:YAG
1583:Er:YAG
1524:Bubble
1472:Lasers
1401:
1394:Lasers
1307:
1301:
1248:
1207:
1139:
1101:
1063:
1043:
1037:
965:
950:
930:
915:
892:
836:
813:
800:
780:
767:
737:
726:
706:
617:
597:
591:
571:
565:
545:
530:
510:
415:
395:
371:
351:
345:
323:
317:
194:
188:
180:where
66:
60:
34:lasers
1593:Raman
792:and
1598:Ruby
1399:ISBN
942:and
38:gain
22:gain
1556:Ion
1286:In
1275:.
1216:exp
472:exp
24:or
16:In
1784::
1260:.
1128::
116:ln
20:,
1464:e
1457:t
1450:v
1433:.
1418:.
1304:K
1244:)
1240:z
1235:d
1230:G
1223:(
1213:=
1210:K
1195:.
1180:n
1177:i
1172:P
1167:/
1160:t
1157:u
1154:o
1149:P
1145:=
1142:K
1113:n
1110:i
1105:P
1078:t
1075:u
1072:o
1067:P
1040:K
1014:z
1009:d
1004:G
998:=
995:g
959:a
924:e
887:1
883:N
876:a
862:2
858:N
851:e
842:=
839:G
808:2
804:N
775:1
771:N
734:e
731:R
702:)
693:2
689:y
679:2
669:+
661:2
657:x
647:2
636:(
632:=
568:k
536:e
506:)
502:)
499:t
493:i
487:z
484:k
481:i
478:(
469:E
460:e
453:(
447:e
444:R
439:=
433:s
430:y
427:h
424:p
419:E
389:s
386:y
383:h
380:p
375:E
348:E
305:,
293:E
290:G
287:i
284:+
281:E
275:2
272:+
269:E
256:=
250:z
242:E
233:k
230:i
227:2
191:z
163:P
159:z
154:d
148:/
144:P
139:d
131:=
128:)
125:P
122:(
110:z
105:d
98:d
92:=
89:G
63:P
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