905:
675:
There have been efforts to measure pulse intensity and phase in both the time and the frequency domain by combining the autocorrelation and the spectrum. This technique is called
Temporal Information Via Intensity (TIVI) and it involves an iterative algorithm to find an intensity consistent with the
869:
684:
Spectral
Interferometry has gained momentum in recent years. It is frequently used for measuring the linear response of materials, such as the thickness and refractive index of normal dispersive materials, the amplitude and phase of the electric field in semiconductor nanostructures and the group
648:
detector or a simple camera, the whole interferogram can be recorded simultaneously. Furthermore, the interferogram is not nullified by small fluctuations of the optical path, but reduction in the fringe contrast should be expected in cases of exposure time being bigger than the fluctuation time
927:
Self-Referenced
Spectral Interferometry (SRSI) is a technique where the reference pulse is self created from the unknown pulse being. The self referencing is possible due to pulse shaping optimization and non-linear temporal filtering. It provides all the benefits associated with SI (high
1472:
915:(SPIDER) is a nonlinear self-referencing technique based on spectral shearing interferometry. For this method, the reference pulse should produce a mirror image of itself with a spectral shift, in order to provide the spectral intensity and phase of the probe pulse via a direct
1603:
Geindre, J. P.; Mysyrowicz, A.; Santos, A. Dos; Audebert, P.; Rousse, A.; Hamoniaux, G.; Antonetti, A.; Falliès, F.; Gauthier, J. C. (1994-12-01). "Frequency-domain interferometer for measuring the phase and amplitude of a femtosecond pulse probing a laser-produced plasma".
935:
For SRSI, the generation of a weak mirror image of the unknown pulse is required. That image is perpendicularly polarized and delayed with respect to the input pulse. Then, in order to filter the reference pulse in the time domain, the main portion of the pulse is used for
1125:
940:(XPW) in a nonlinear crystal. The interference between the reference pulse and the mirror image is recorded and analyzed via Fourier transform spectral interferometry (FTSI). Known applications of the SRSI technique include the characterization of pulses below 15 fs.
461:
23:, with the condition that a reference pulse that was previously characterized is available. This technique provides information about the intensity and phase of the pulses. SI was first proposed by Claude Froehly and coworkers in the 1970s.
719:
In cases of relatively long pulses, one can opt for
Spectral Shearing Interferometry. For this method, the reference pulse is obtained by sending its mirror image through a sinusoidal phase modulation. Hence, a spectral shift of magnitude
951:(FROG) is a technique that determines the intensity and phase of a pulse by measuring the spectrum of a particular temporal component of said pulse. This results in an intensity trace, related to the spectrogram of the pulse
748:
2323:
Trabattoni, A.; Oksenhendler, T.; Jousselin, H.; Tempea, G.; De
Silvestri, S.; Sansone, G.; Calegari, F.; Nisoli, M. (November 2015). "Self-referenced spectral interferometry for single-shot measurement of sub-5-fs pulses".
555:
929:
912:
689:
265:
634:
1247:
2531:
Fluegel, B.; Peyghambarian, N.; Olbright, G.; Lindberg, M.; Koch, S. W.; Joffre, M.; Hulin, D.; Migus, A.; Antonetti, A. (1987-11-30). "Femtosecond
Studies of Coherent Transients in Semiconductors".
998:
2385:
Moulet, A.; Grabielle, S.; Cornaggia, C.; Forget, N.; Oksenhendler, T. (2010-11-15). "Single-shot, high-dynamic-range measurement of sub-15 fs pulses by self-referenced spectral interferometry".
1757:
Kumar, V. Nirmal; Rao, D. Narayana (1995-09-01). "Using interference in the frequency domain for precise determination of thickness and refractive indices of normal dispersive materials".
294:
991:
161:
676:
autocorrelation, followed by another iterative algorithm to find the temporal and spectral phases consistent with the intensity and spectrum, but the results are inconclusive.
46:
between them, in order to create spectral fringes. A spectrum is produced by the sum of these two pulses and, by measuring said fringes, one can retrieve the unknown pulse. If
125:
83:
2488:
Becker, P. C.; Fork, R. L.; Brito Cruz, C. H.; Gordon, J. P.; Shank, C. V. (1988-06-13). "Optical Stark Effect in
Organic Dyes Probed with Optical Pulses of 6-fs Duration".
894:
741:
2027:
Tokunaga, E.; Kobayashi, T.; Terasaki, A. (1993-03-01). "Induced phase modulation of chirped continuum pulses studied with a femtosecond frequency-domain interferometer".
1242:
2174:
Kang, Inuk; Dorrer, Christophe; Quochi, Francesco (2003-11-15). "Implementation of electro-optic spectral shearing interferometry for ultrashort pulse characterization".
1162:
1491:
Froehly, Cl; Lacourt, A; Viénot, J Ch (July 1973). "Time impulse response and time frequency response of optical pupils.:Experimental confirmations and applications".
2217:
Oksenhendler, T.; Coudreau, S.; Forget, N.; Crozatier, V.; Grabielle, S.; Herzog, R.; Gobert, O.; Kaplan, D. (April 2010). "Self-referenced spectral interferometry".
1687:
Lepetit, L.; Chériaux, G.; Joffre, M. (1995-12-01). "Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy".
1207:
670:
287:
44:
700:
This technique is not commonly used since it relies on a number of factors in order to obtain strong fringes during experimental processes. Some of them include:
2131:
Dorrer, Christophe; Kang, Inuk (2003-03-15). "Highly sensitive direct characterization of femtosecond pulses by electro-optic spectral shearing interferometry".
1827:
Kovács, A. P.; Szipöcs, R.; Osvay, K.; Bor, Zs. (1995-04-01). "Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry".
864:{\displaystyle \phi (\omega )=\phi _{ref}(\omega +\delta \omega )+\omega \tau ={\frac {\partial \phi _{ref}}{\partial \omega }}\delta \omega +\omega \tau }
1244:, mainly used for femtosecond pump-probe experiments in materials with long dephasing times. It is based on the inverse Fourier transform of the signal:
1171:
But the same principle can be applied exploiting different physical process, like polarization-gated FROG (PG-FROG) or transient-grating FROG (TG-FROG).
1186:
The acquisition of the two quadratures of the interference signal resolves the issue generated by the phase differences being expressed in multiples of
919:(FFT) filtering routine. However, unlike SI, in order to produce the probe pulse phase, it requires phase integration extracted from the interferogram.
904:
468:
168:
2262:"Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping"
896:. Thus, the spectral derivative of the phase of the signal pulse which corresponds to the frequency-dependent group delay can be obtained.
743:
can be correlated to the produced linear temporal phase modulation and the spectrum of the combined pulses then has a modulation phase of:
563:
1467:{\displaystyle F.T._{SI}^{-1}(t)=E_{ref}^{\ast }(-t)\otimes E_{ref}(t)+E_{un}^{\ast }(-t)\otimes E_{un}(t)+f(t-\tau )+f(-t-\tau )^{\ast }}
1179:
There is a variety of linear techniques that are based on the main principles of spectral interferometry. Some of them are listed below.
649:
scale. However, SI produces phase measurements through its cosine only, meaning that results arise for phase differences in multiples of
1210:
948:
2428:
Kane, D.J.; Trebino, R. (Feb 1993). "Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating".
1792:
Tignon, J.; Marquezini, M.V.; Hasche, T.; Chemla, D.S. (April 1999). "Spectral interferometry of semiconductor nanostructures".
1120:{\displaystyle S_{E}(\omega ,\tau )=\left\vert \int \limits _{-\infty }^{\infty }E(t)g(t-\tau )e^{-i\omega }dt\right\vert ^{2}}
937:
2088:
Wong, Victor; Walmsley, Ian A. (1994-02-15). "Analysis of ultrashort pulse-shape measurement using linear interferometers".
127:
are the electric fields of the unknown and reference pulse respectively, the time delay can be expressed as a phase factor
1647:
Dorrer, Christophe; Joffre, Manuel (December 2001). "Characterization of the spectral phase of ultrashort light pulses".
560:
Furthermore, the spectral fringes width can provide information on the spectral phase difference between the two pulses
1872:"Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells"
1165:
2585:
456:{\displaystyle S_{SI}=S_{ref}(\omega )+S_{un}(\omega )+2{\sqrt {S_{ref}(\omega )}}{\sqrt {S_{un}(\omega )}}cos}
692:
is based, thus it is used for four-wave mixing experiments and various phase-resolved pump-probe experiments.
2580:
2590:
954:
916:
645:
130:
2464:
1870:
Chen, X.; Walecki, Wojciech J.; Buccafusca, O.; Fittinghoff, David N.; Smirl, Arthur L. (1997-10-15).
88:
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2226:
2183:
2140:
2097:
2036:
1985:
1930:
1883:
1836:
1801:
1766:
1731:
1696:
1656:
1613:
1539:
1500:
644:
Compared to time-domain interferometry, SI presents some interesting advantages. Firstly, by using a
49:
876:
723:
26:
A known (acting as the reference) and an unknown pulse arrive at a spectrometer, with a time delay
1582:
1224:
2367:
2305:
2242:
1132:
1973:
1918:
1527:
2556:
2513:
2410:
2359:
2297:
2289:
2199:
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2113:
2052:
2009:
2001:
1974:"Measurement of photon echoes by use of femtosecond Fourier-transform spectral interferometry"
1954:
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1852:
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2548:
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2402:
2349:
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1993:
1938:
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Emde, Michel F.; de Boeij, Wim P.; Pshenichnikov, Maxim S.; Wiersma, Douwe A. (1997-09-01).
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1809:
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1739:
1704:
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1621:
1547:
1508:
20:
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932:
technique, neither shear nor harmonic generation are necessary in order to be implemented.
652:
272:
29:
1722:
Peatross, J.; Rundquist, A. (1998-01-01). "Temporal decorrelation of short laser pulses".
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sensitivity, precision and resolution, dynamic and large temporal range) but, unlike the
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1526:
Piasecki, J.; Colombeau, B.; Vampouille, M.; Froehly, C.; Arnaud, J. A. (1980-11-15).
2574:
2246:
2309:
1871:
1512:
2371:
2552:
2509:
550:{\displaystyle \phi _{SI}=\phi _{un}(\omega )-\phi _{ref}(\omega )+\omega \tau }
269:
The average spacing between fringes is inversely proportional to the time delay
2260:
Verluise, F.; Laude, V.; Cheng, Z.; Spielmann, Ch.; Tournois, P. (2000-04-15).
2238:
19:(SI) or frequency-domain interferometry is a linear technique used to measure
2293:
2005:
1950:
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1895:
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1528:"Nouvelle méthode de mesure de la réponse impulsionnelle des fibres optiques"
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1997:
1942:
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1625:
1551:
260:{\displaystyle E_{SI}=E_{ref}(\omega )+E_{un}(\omega )e^{-i\omega \tau }}
2354:
1919:"Spectral interferometry as an alternative to time-domain heterodyning"
688:
In the realm of femtosecond spectroscopy, SI is the technique on which
636:; narrowly spaced fringes indicate rapid phase changes with frequency.
2345:
913:
Spectral Phase
Interferometry for Direct Electric-field Reconstruction
900:
Spectral Phase
Interferometry for Direct Electric-field Reconstruction
2449:
1813:
629:{\displaystyle \Delta \phi =\phi _{un}(\omega )-\phi _{ref}(\omega )}
672:
which can lead to solutions that degrade the signal-to-noise ratio.
903:
1164:
is a variable-delay gate pulse. FROG is commonly combined with
873:
where the approximate relation is appropriate for small enough
1972:
Likforman, J.-P.; Joffre, M.; Thierry-Mieg, V. (1997-07-15).
1221:
It is a technique created for direct determination of
1213:, with the reference beam under circular polarization.
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for the unknown pulses. Then, the combined field is:
133:
91:
52:
32:
1649:
Comptes Rendus de l'Académie des
Sciences, SĂ©rie IV
1209:. The acquisition should happen simultaneously via
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1759:Journal of the Optical Society of America B
1724:Journal of the Optical Society of America B
1689:Journal of the Optical Society of America B
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1394:
1369:
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1333:
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1226:
1218:Fourier-Transform Spectral Interferometry
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1183:Dual-Quadrature Spectral Interferometry
923:Self-Referenced Spectral Interferometry
7:
1682:
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1678:
1598:
1596:
986:{\displaystyle S_{E}(\omega ,\tau )}
2465:"Frequency-resolved Optical Gating"
2430:IEEE Journal of Quantum Electronics
1794:IEEE Journal of Quantum Electronics
289:. Thus, the SI signal is given by:
1228:
1049:
1044:
837:
816:
567:
156:{\displaystyle e^{-i\omega \tau }}
14:
949:Frequency Resolved Optical Gating
944:Frequency-Resolved Optical Gating
2326:Review of Scientific Instruments
715:Spectral Shearing Interferometry
120:{\displaystyle E_{ref}(\omega )}
1583:"Spectral Phase Interferometry"
938:cross-polarized wave generation
640:Comparison with the Time Domain
78:{\displaystyle E_{un}(\omega )}
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889:{\displaystyle \delta \omega }
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736:{\displaystyle \delta \omega }
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1669:10.1016/S1296-2147(01)01279-3
1237:{\displaystyle \Delta \phi }
2553:10.1103/PhysRevLett.59.2588
2510:10.1103/PhysRevLett.60.2462
2607:
1168:(SHG) process (SHG-FROG).
1166:Second Harmonic Generation
1157:{\displaystyle g(t-\tau )}
704:Precision in mode-matching
557:is the oscillation phase.
2239:10.1007/s00340-010-3916-y
2071:"Spectral Interferometry"
1513:10.1088/0335-7368/4/4/301
1211:polarization multiplexing
710:Perfectly collinear beams
696:Experimental Difficulties
1896:10.1103/PhysRevB.56.9738
1493:Nouvelle Revue d'Optique
685:delay on laser mirrors.
2533:Physical Review Letters
2490:Physical Review Letters
2463:Paschotta, Dr RĂĽdiger.
1779:10.1364/JOSAB.12.001559
1744:10.1364/JOSAB.15.000216
1709:10.1364/JOSAB.12.002467
1581:Paschotta, Dr RĂĽdiger.
1175:Other Linear Techniques
17:Spectral interferometry
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917:Fast Fourier Transform
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1202:{\displaystyle 2\pi }
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665:{\displaystyle 2\pi }
631:
552:
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282:{\displaystyle \tau }
262:
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80:
41:
39:{\displaystyle \tau }
2469:www.rp-photonics.com
2407:10.1364/OL.35.003856
2286:10.1364/OL.25.000575
2196:10.1364/OL.28.002264
2153:10.1364/OL.28.000477
2110:10.1364/OL.19.000287
2049:10.1364/OL.18.000370
1998:10.1364/OL.22.001104
1943:10.1364/OL.22.001338
1849:10.1364/OL.20.000788
1626:10.1364/OL.19.001997
1587:www.rp-photonics.com
1552:10.1364/AO.19.003749
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2545:1987PhRvL..59.2588F
2502:1988PhRvL..60.2462B
2442:1993IJQE...29..571K
2399:2010OptL...35.3856M
2338:2015RScI...86k3106T
2278:2000OptL...25..575V
2231:2010ApPhB..99....7O
2188:2003OptL...28.2264K
2145:2003OptL...28..477D
2102:1994OptL...19..287W
2041:1993OptL...18..370T
1990:1997OptL...22.1104L
1935:1997OptL...22.1338E
1888:1997PhRvB..56.9738C
1841:1995OptL...20..788K
1806:1999IJQE...35..510T
1771:1995JOSAB..12.1559K
1736:1998JOSAB..15..216P
1701:1995JOSAB..12.2467L
1661:2001CRASP...2.1415D
1618:1994OptL...19.1997G
1544:1980ApOpt..19.3749P
1505:1973NROpt...4..183F
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2539:(22): 2588–2591.
2496:(24): 2462–2464.
2393:(22): 3856–3858.
2346:10.1063/1.4936289
2219:Applied Physics B
2182:(22): 2264–2266.
1984:(14): 1104–1106.
1929:(17): 1338–1340.
1882:(15): 9738–9743.
1876:Physical Review B
1655:(10): 1415–1426.
1612:(23): 1997–1999.
1538:(22): 3749–3755.
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1030:
1002:
997:
996:
958:
953:
952:
946:
925:
902:
875:
874:
836:
819:
815:
767:
747:
746:
722:
721:
717:
707:Phase stability
698:
682:
651:
650:
642:
601:
576:
562:
561:
513:
488:
472:
467:
466:
437:
401:
372:
342:
314:
298:
293:
292:
271:
270:
238:
216:
188:
172:
167:
166:
134:
129:
128:
92:
87:
86:
53:
48:
47:
28:
27:
12:
11:
5:
2604:
2602:
2594:
2593:
2588:
2583:
2581:Interferometry
2573:
2572:
2567:
2566:
2523:
2480:
2455:
2436:(2): 571–579.
2420:
2387:Optics Letters
2377:
2332:(11): 113106.
2315:
2272:(8): 575–577.
2266:Optics Letters
2252:
2209:
2176:Optics Letters
2166:
2139:(6): 477–479.
2133:Optics Letters
2123:
2090:Optics Letters
2080:
2062:
2035:(5): 370–372.
2029:Optics Letters
2019:
1978:Optics Letters
1964:
1923:Optics Letters
1909:
1862:
1835:(7): 788–790.
1829:Optics Letters
1819:
1800:(4): 510–522.
1784:
1749:
1714:
1674:
1639:
1606:Optics Letters
1592:
1573:
1532:Applied Optics
1518:
1499:(4): 183–196.
1482:
1481:
1479:
1476:
1475:
1474:
1461:
1457:
1453:
1450:
1447:
1444:
1441:
1438:
1435:
1432:
1429:
1426:
1423:
1420:
1417:
1414:
1411:
1408:
1405:
1400:
1397:
1393:
1389:
1386:
1383:
1380:
1377:
1372:
1367:
1364:
1360:
1356:
1353:
1350:
1347:
1342:
1339:
1336:
1332:
1328:
1325:
1322:
1319:
1316:
1311:
1306:
1303:
1300:
1296:
1292:
1289:
1286:
1283:
1278:
1275:
1270:
1267:
1263:
1259:
1256:
1253:
1233:
1230:
1219:
1215:
1214:
1198:
1195:
1184:
1176:
1173:
1153:
1150:
1147:
1144:
1141:
1138:
1114:
1109:
1105:
1102:
1097:
1094:
1091:
1087:
1083:
1080:
1077:
1074:
1071:
1068:
1065:
1062:
1059:
1056:
1051:
1046:
1043:
1039:
1034:
1029:
1026:
1023:
1020:
1017:
1014:
1009:
1005:
982:
979:
976:
973:
970:
965:
961:
945:
942:
924:
921:
901:
898:
885:
882:
860:
857:
854:
851:
848:
842:
839:
832:
829:
826:
822:
818:
812:
809:
806:
803:
800:
797:
794:
791:
788:
785:
780:
777:
774:
770:
766:
763:
760:
757:
754:
732:
729:
716:
713:
712:
711:
708:
705:
697:
694:
681:
678:
661:
658:
641:
638:
625:
622:
619:
614:
611:
608:
604:
600:
597:
594:
591:
586:
583:
579:
575:
572:
569:
546:
543:
540:
537:
534:
531:
526:
523:
520:
516:
512:
509:
506:
503:
498:
495:
491:
487:
482:
479:
475:
452:
447:
444:
440:
436:
433:
430:
427:
422:
419:
416:
411:
408:
404:
396:
393:
390:
385:
382:
379:
375:
369:
366:
363:
360:
357:
352:
349:
345:
341:
338:
335:
332:
327:
324:
321:
317:
313:
308:
305:
301:
278:
254:
251:
248:
245:
241:
237:
234:
231:
226:
223:
219:
215:
212:
209:
206:
201:
198:
195:
191:
187:
182:
179:
175:
150:
147:
144:
141:
137:
116:
113:
110:
105:
102:
99:
95:
74:
71:
68:
63:
60:
56:
35:
21:optical pulses
13:
10:
9:
6:
4:
3:
2:
2603:
2592:
2591:Laser science
2589:
2587:
2584:
2582:
2579:
2578:
2576:
2562:
2558:
2554:
2550:
2546:
2542:
2538:
2534:
2527:
2524:
2519:
2515:
2511:
2507:
2503:
2499:
2495:
2491:
2484:
2481:
2470:
2466:
2459:
2456:
2451:
2447:
2443:
2439:
2435:
2431:
2424:
2421:
2416:
2412:
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2400:
2396:
2392:
2388:
2381:
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2327:
2319:
2316:
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2303:
2299:
2295:
2291:
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2271:
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2256:
2253:
2248:
2244:
2240:
2236:
2232:
2228:
2225:(1–2): 7–12.
2224:
2220:
2213:
2210:
2205:
2201:
2197:
2193:
2189:
2185:
2181:
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2167:
2162:
2158:
2154:
2150:
2146:
2142:
2138:
2134:
2127:
2124:
2119:
2115:
2111:
2107:
2103:
2099:
2095:
2091:
2084:
2081:
2076:
2072:
2066:
2063:
2058:
2054:
2050:
2046:
2042:
2038:
2034:
2030:
2023:
2020:
2015:
2011:
2007:
2003:
1999:
1995:
1991:
1987:
1983:
1979:
1975:
1968:
1965:
1960:
1956:
1952:
1948:
1944:
1940:
1936:
1932:
1928:
1924:
1920:
1913:
1910:
1905:
1901:
1897:
1893:
1889:
1885:
1881:
1877:
1873:
1866:
1863:
1858:
1854:
1850:
1846:
1842:
1838:
1834:
1830:
1823:
1820:
1815:
1811:
1807:
1803:
1799:
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1788:
1785:
1780:
1776:
1772:
1768:
1764:
1760:
1753:
1750:
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1737:
1733:
1729:
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1718:
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1675:
1670:
1666:
1662:
1658:
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1640:
1635:
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1169:
1167:
1148:
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1142:
1136:
1127:
1112:
1107:
1103:
1100:
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1089:
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1075:
1072:
1066:
1060:
1054:
1041:
1037:
1032:
1027:
1021:
1018:
1015:
1007:
1003:
994:
977:
974:
971:
963:
959:
950:
943:
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933:
931:
922:
920:
918:
914:
908:SPIDER set-up
906:
899:
897:
883:
880:
871:
858:
855:
852:
849:
846:
840:
830:
827:
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752:
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730:
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702:
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693:
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673:
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639:
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620:
612:
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406:
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383:
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358:
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333:
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306:
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290:
276:
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246:
243:
239:
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224:
221:
217:
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207:
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180:
177:
173:
164:
148:
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61:
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2472:. Retrieved
2468:
2458:
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2429:
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2390:
2386:
2380:
2355:11311/970109
2329:
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2089:
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2065:
2032:
2028:
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1981:
1977:
1967:
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2575:Categories
2474:2021-06-18
2096:(4): 287.
1730:(1): 216.
1478:References
2294:0146-9592
2247:124727290
2006:0146-9592
1951:0146-9592
1904:0163-1829
1560:0003-6935
1460:∗
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1045:∞
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838:∂
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2118:19829619
2057:19802139
2014:18185765
1959:18188232
1857:19859330
1634:19855721
1568:20234691
2541:Bibcode
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2438:Bibcode
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2372:1518794
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1931:Bibcode
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2557:PMID
2514:PMID
2411:PMID
2360:PMID
2298:PMID
2290:ISSN
2200:PMID
2157:PMID
2114:PMID
2053:PMID
2010:PMID
2002:ISSN
1955:PMID
1947:ISSN
1900:ISSN
1853:PMID
1630:PMID
1564:PMID
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85:and
2549:doi
2506:doi
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2403:doi
2350:hdl
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1994:doi
1939:doi
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