1471:
20:
632:(5HG) or more is theoretically possible, but the interaction requires a very high number of photons to interact and has therefore a low probability to happen: the signal at higher harmonics will be very low, and requires very intense lasers to be generated. To generate high harmonics (like
1077:
Kojima, Tetsuo; Konno, Susumu; Fujikawa, Shuichi; Yasui, Koji; Yoshizawa, Kenji; Mori, Yusuke; Sasaki, Takatomo; Tanaka, Mitsuhiro; Okada, Yukikatsu (2000). "20-W ultraviolet-beam generation by fourth-harmonic generation of an all-solid-state laser".
186:
Because the process requires that many photons are present at the same time and at the same place, the generation process has a low probability to occur, and this probability decreases with the order
181:
551:
457:
306:
279:
420:
366:
601:
656:
630:
518:
400:
346:
252:
204:
131:
103:
83:
60:
1051:
520:. Reported around the year 2000, powerful lasers now enable efficient FHG. This process involves the 4th order nonlinear susceptibility
1431:
1061:
744:
723:
875:
848:
815:
704:
683:
694:
1170:
734:
1340:
1007:
Cheng, Ji-Xin; Xie, X. Sunney (2002). "Green's function formulation for third-harmonic generation microscopy".
462:
Unlike SHG, it is a volumetric process and has been shown in liquids. However, it is enhanced at interfaces.
775:
65:
with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with
1396:
865:
673:
1200:
765:
317:
210:, for instance), and the light source must be intense and well-controlled spatially (with a collimated
1495:
206:. To generate efficiently, the symmetry of the medium must allow the signal to be amplified (through
891:
Moreaux, Laurent; Sandre, Olivier; Charpak, Serge; Blanchard-Desce, Mireille; Mertz, Jerome (2001).
770:
659:
223:
142:
348:. Also a special case of sum-frequency generation in which both photons are at the same frequency
148:
523:
429:
284:
257:
1370:
1190:
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1365:
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8:
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68:
45:
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1446:
1411:
1391:
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973:
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803:
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423:
39:
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1355:
1345:
1156:
1451:
1441:
1401:
1350:
1268:
1221:
1205:
207:
486:
can convert THG, otherwise THG can be generated from membranes in microscopy.
1489:
1406:
1386:
1327:
1253:
1107:
1036:
985:
977:
924:
562:
471:
1028:
1426:
1295:
1290:
1231:
1115:
942:
426:
is preferred. This process involves the 3rd order nonlinear susceptibility
19:
993:
1456:
1317:
1300:
1280:
1099:
956:
Kajzar, F.; Messier, J. (1985). "Third-harmonic generation in liquids".
1305:
183:), the medium must have no center of symmetry (non-centrosymmetrical).
110:
1421:
1263:
1243:
1226:
106:
1129:
376:
A special case in which the number of photons in the interaction is
322:
A special case in which the number of photons in the interaction is
228:
A special case in which the number of photons in the interaction is
890:
494:
A special case in which the number of photons in interaction is
62:
214:) and temporally (more signal if the laser has short pulses).
145:, harmonic generation is possible. Note that for even orders (
1179:
211:
489:
1148:
794:
Boyd, R. (2007). "The
Nonlinear Optical Susceptibility".
1076:
893:"Coherent Scattering in Multi-Harmonic Light Microscopy"
422:. If they have different frequency, the general term of
85:
times the energy of the initial photons (equivalently,
638:
612:
583:
526:
500:
432:
408:
382:
354:
328:
287:
260:
234:
192:
151:
119:
91:
71:
48:
658:and so on), the substantially different process of
311:
1050:Pavone, Francesco S.; Campagnola, Paul J. (2016).
650:
624:
595:
545:
512:
451:
414:
394:
371:
360:
340:
300:
273:
246:
198:
175:
125:
97:
77:
54:
217:
1487:
1049:
949:
884:
732:
254:, but with two different photons at frequencies
1053:Second Harmonic Generation Imaging, 2nd edition
1070:
1164:
955:
402:, if all the photons have the same frequency
1009:Journal of the Optical Society of America B
1000:
733:Zernike, Frits; Midwinter, John E. (2006).
1171:
1157:
838:
692:
932:
832:
556:
465:
1006:
18:
1432:Multiple-prism grating laser oscillator
787:
490:Fourth-harmonic generation (FHG or 4HG)
1488:
1152:
713:
863:
793:
671:
857:
13:
808:10.1016/B978-0-12-369470-6.00001-0
136:
14:
1507:
802:(third ed.). pp. 1–67.
141:In a medium having a substantial
1470:
1469:
718:(4th ed.). Addison-Wesley.
312:Second-harmonic generation (SHG)
839:Sutherland, Richard L. (2003).
693:Sutherland, Richard L. (2003).
372:Third-harmonic generation (THG)
1341:Amplified spontaneous emission
1122:
1043:
538:
532:
444:
438:
218:Sum-frequency generation (SFG)
1:
917:10.1016/S0006-3495(01)76129-2
781:
870:(third ed.). Elsevier.
841:Handbook of Nonlinear Optics
776:Optical frequency multiplier
696:Handbook of Nonlinear Optics
678:(third ed.). Elsevier.
176:{\displaystyle n=2,4,\dots }
36:multiple harmonic generation
7:
1397:Chirped pulse amplification
843:(2nd ed.). CRC Press.
754:
699:(2nd ed.). CRC Press.
546:{\displaystyle \chi ^{(4)}}
470:Nonlinear crystals such as
452:{\displaystyle \chi ^{(3)}}
301:{\displaystyle \omega _{2}}
274:{\displaystyle \omega _{1}}
10:
1512:
1201:List of laser applications
1178:
1056:. CRC Taylor&Francis.
766:Second-harmonic generation
665:
318:Second-harmonic generation
315:
221:
1465:
1379:
1326:
1214:
1186:
16:Nonlinear optical process
978:10.1103/PhysRevA.32.2352
771:High harmonic generation
736:Applied Nonlinear Optics
660:high harmonic generation
606:Harmonic generation for
577:Harmonic generation for
224:Sum-frequency generation
143:nonlinear susceptibility
23:N-th harmonic generation
1029:10.1364/JOSAB.19.001604
415:{\displaystyle \omega }
361:{\displaystyle \omega }
1191:List of laser articles
739:. Dover Publications.
714:Hecht, Eugene (2002).
652:
626:
597:
596:{\displaystyle n>4}
557:Materials used for FHG
547:
514:
466:Materials used for THG
453:
416:
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342:
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248:
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127:
99:
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24:
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100:
80:
57:
22:
1366:Population inversion
1100:10.1364/OL.25.000058
651:{\displaystyle n=30}
636:
610:
581:
573:) are used for FHG.
524:
498:
430:
406:
380:
352:
326:
285:
258:
232:
190:
149:
117:
89:
69:
46:
1417:Laser beam profiler
1336:Active laser medium
1276:Free-electron laser
1196:List of laser types
1092:2000OptL...25...58K
1021:2002JOSAB..19.1604C
970:1985PhRvA..32.2352K
909:2001BpJ....80.1568M
897:Biophysical Journal
864:Boyd, R.W. (2007).
672:Boyd, R.W. (2007).
625:{\displaystyle n=5}
513:{\displaystyle n=4}
395:{\displaystyle n=3}
341:{\displaystyle n=2}
247:{\displaystyle n=2}
28:Harmonic generation
648:
622:
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25:
1483:
1482:
1437:Optical amplifier
1286:Solid-state laser
1063:978-1-4398-4914-9
958:Physical Review A
199:{\displaystyle n}
126:{\displaystyle n}
98:{\displaystyle n}
78:{\displaystyle n}
55:{\displaystyle n}
42:process in which
40:nonlinear optical
1503:
1496:Nonlinear optics
1473:
1472:
1447:Optical isolator
1412:Injection seeder
1392:Beam homogenizer
1371:Ultrashort pulse
1361:Lasing threshold
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1166:
1159:
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1120:
1119:
1074:
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1004:
998:
997:
964:(4): 2352–2363.
953:
947:
946:
936:
903:(3): 1568–1574.
888:
882:
881:
867:Nonlinear optics
861:
855:
854:
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798:Nonlinear optics
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761:Nonlinear optics
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1500:
1486:
1485:
1484:
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1461:
1375:
1356:Laser linewidth
1346:Continuous wave
1322:
1215:Types of lasers
1210:
1182:
1177:
1147:
1138:
1136:
1128:
1127:
1123:
1075:
1071:
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747:
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707:
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137:General process
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115:
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70:
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66:
47:
44:
43:
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12:
11:
5:
1509:
1499:
1498:
1481:
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1478:
1477:
1466:
1463:
1462:
1460:
1459:
1454:
1452:Output coupler
1449:
1444:
1442:Optical cavity
1439:
1434:
1429:
1424:
1419:
1414:
1409:
1404:
1402:Gain-switching
1399:
1394:
1389:
1383:
1381:
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1376:
1374:
1373:
1368:
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1358:
1353:
1351:Laser ablation
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1343:
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1324:
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1251:
1249:Carbon dioxide
1241:
1240:
1239:
1237:Liquid-crystal
1234:
1224:
1222:Chemical laser
1218:
1216:
1212:
1211:
1209:
1208:
1206:Laser acronyms
1203:
1198:
1193:
1187:
1184:
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1146:
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1121:
1080:Optics Letters
1069:
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773:
768:
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756:
753:
752:
751:
746:978-0486453606
745:
730:
725:978-0805385663
724:
711:
705:
690:
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664:
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316:Main article:
313:
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243:
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222:Main article:
219:
216:
208:phase matching
195:
172:
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138:
135:
122:
94:
74:
51:
34:, also called
15:
9:
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4:
3:
2:
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1433:
1430:
1428:
1425:
1423:
1420:
1418:
1415:
1413:
1410:
1408:
1407:Gaussian beam
1405:
1403:
1400:
1398:
1395:
1393:
1390:
1388:
1387:Beam expander
1385:
1384:
1382:
1378:
1372:
1369:
1367:
1364:
1362:
1359:
1357:
1354:
1352:
1349:
1347:
1344:
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1339:
1337:
1334:
1333:
1331:
1329:
1328:Laser physics
1325:
1319:
1316:
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1307:
1304:
1302:
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1223:
1220:
1219:
1217:
1213:
1207:
1204:
1202:
1199:
1197:
1194:
1192:
1189:
1188:
1185:
1181:
1174:
1169:
1167:
1162:
1160:
1155:
1154:
1151:
1135:
1131:
1130:"BBO for FHG"
1125:
1117:
1113:
1109:
1105:
1101:
1097:
1093:
1089:
1085:
1081:
1073:
1065:
1059:
1055:
1054:
1046:
1038:
1034:
1030:
1026:
1022:
1018:
1014:
1010:
1003:
995:
991:
987:
983:
979:
975:
971:
967:
963:
959:
952:
944:
940:
935:
930:
926:
922:
918:
914:
910:
906:
902:
898:
894:
887:
879:
877:9780123694706
873:
869:
868:
860:
852:
850:9780824742430
846:
842:
835:
827:
823:
819:
817:9780123694706
813:
809:
805:
800:
799:
790:
786:
777:
774:
772:
769:
767:
764:
762:
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758:
748:
742:
738:
737:
731:
727:
721:
717:
712:
708:
706:9780824742430
702:
698:
697:
691:
687:
685:9780123694706
681:
677:
676:
670:
669:
663:
662:can be used.
661:
645:
642:
639:
619:
616:
613:
590:
587:
584:
574:
564:
554:
535:
528:
507:
504:
501:
487:
485:
473:
463:
460:
441:
434:
425:
409:
389:
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383:
369:
355:
335:
332:
329:
319:
309:
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289:
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241:
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193:
184:
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167:
164:
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155:
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144:
134:
120:
112:
108:
92:
72:
64:
49:
41:
37:
33:
29:
21:
1427:Mode locking
1380:Laser optics
1137:. Retrieved
1133:
1124:
1086:(1): 58–60.
1083:
1079:
1072:
1052:
1045:
1012:
1008:
1002:
961:
957:
951:
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866:
859:
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834:
797:
789:
735:
715:
695:
674:
605:
560:
493:
469:
461:
375:
321:
227:
185:
140:
35:
31:
27:
26:
1457:Q-switching
1318:X-ray laser
1311:Ti-sapphire
1281:Laser diode
1259:Helium–neon
1015:(7): 1604.
113:divided by
1139:2019-12-01
1134:raicol.com
782:References
111:wavelength
105:times the
1422:M squared
1244:Gas laser
1227:Dye laser
1108:0146-9592
1037:0740-3224
986:0556-2791
925:0006-3495
529:χ
435:χ
410:ω
356:ω
290:ω
263:ω
171:…
107:frequency
1490:Category
1475:Category
1269:Nitrogen
1116:18059781
943:11222317
826:15660817
755:See also
109:and the
1254:Excimer
1088:Bibcode
1017:Bibcode
994:9896350
966:Bibcode
934:1301348
905:Bibcode
666:Sources
63:photons
38:) is a
1296:Nd:YAG
1291:Er:YAG
1232:Bubble
1180:Lasers
1114:
1106:
1060:
1035:
992:
984:
941:
931:
923:
874:
847:
824:
814:
743:
722:
716:Optics
703:
682:
565:(β-BaB
474:(β-BaB
1301:Raman
822:S2CID
561:Some
482:) or
212:laser
1306:Ruby
1112:PMID
1104:ISSN
1058:ISBN
1033:ISSN
990:PMID
982:ISSN
939:PMID
921:ISSN
872:ISBN
845:ISBN
812:ISBN
741:ISBN
720:ISBN
701:ISBN
680:ISBN
588:>
281:and
1264:Ion
1096:doi
1025:doi
974:doi
929:PMC
913:doi
804:doi
563:BBO
553:.
484:LBO
472:BBO
133:).
1492::
1132:.
1110:.
1102:.
1094:.
1084:25
1082:.
1031:.
1023:.
1013:19
1011:.
988:.
980:.
972:.
962:32
960:.
937:.
927:.
919:.
911:.
901:80
899:.
895:.
820:.
810:.
646:30
459:.
368:.
308:.
32:HG
1172:e
1165:t
1158:v
1142:.
1118:.
1098::
1090::
1066:.
1039:.
1027::
1019::
996:.
976::
968::
945:.
915::
907::
880:.
853:.
828:.
806::
749:.
728:.
709:.
688:.
643:=
640:n
620:5
617:=
614:n
591:4
585:n
571:4
569:O
567:2
539:)
536:4
533:(
508:4
505:=
502:n
480:4
478:O
476:2
445:)
442:3
439:(
390:3
387:=
384:n
336:2
333:=
330:n
294:2
267:1
242:2
239:=
236:n
194:n
168:,
165:4
162:,
159:2
156:=
153:n
121:n
93:n
73:n
50:n
30:(
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