427:
etc.). Additionally, during the high harmonic generation process, electrons are accelerated, and some of them return to their parent ion, resulting in X-ray bursts. However, the majority of these electrons do not return and instead contribute to dispersion for the co-propagating waves. The returning electrons carry phase due to processes like ionization, recombination, and propagation. Furthermore, the ionized atoms can influence the refractive index of the medium, providing another source of dispersion.
775:
315:
295:
112:
436:
33:) is a non-linear process during which a target (gas, plasma, solid or liquid sample) is illuminated by an intense laser pulse. Under such conditions, the sample will emit the high harmonics of the generation beam (above the fifth harmonic). Due to the coherent nature of the process, high-harmonics generation is a prerequisite of
770:{\displaystyle \Delta k=k_{q}-qk_{L}=\underbrace {\Delta k_{\mathrm {neutrals} }} _{<0}+\underbrace {\Delta k_{\mathrm {ions} }} _{<0}+\underbrace {\Delta k_{\mathrm {electrons} }} _{>0}+\underbrace {\Delta k_{\mathrm {geometry} }} _{>0}+\underbrace {\Delta k_{\mathrm {intrinsic} }} _{>\;\!0}+\cdots }
1446:
geometries, spectra extending to 1.6 keV, have been generated. For UV-VIS driven high harmonics, the waveguide term is small, and the phase-matching picture resembles the plane-wave geometry. In such geometries, narrow bandwidth harmonics extending to the carbon edge (300 eV) have been generated.
1445:
term is small. The generation of High-order harmonics in waveguide allows propagation with characteristics close to those of plane wave propagation. Such geometries benefit, especially X-ray spectra generated by IR beams, where long interaction volumes are needed for optimal power extraction. In such
359:
is due to wavefront phase jump close to the focus, and varies along it. Finally the dipole phase arises from the atomic response in the HHG process. When using a gas jet geometry, the optimal conditions for generating high harmonics emitted from short trajectories are obtained when the generating gas
1400:
is small. To phase-match the process, low pressures are needed. Moreover, in the UV, very high ionization levels can be tolerated (much larger than 100%). This gives HHG photon energy scalability with the intensity of the driving UV laser. Plain-wave geometry or loose focusing geometry allows highly
426:
In order to achieve intensity levels that can distort an atom's binding potential, it is necessary to focus the driving laser beam. This introduces dispersion terms affecting the phase mismatch, depending on the specific geometry (such as plane wave propagation, free focusing, hollow core waveguide,
158:
High harmonic generation strongly depends on the driving laser field and as a result the harmonics have similar temporal and spatial coherence properties. High harmonics are often generated with pulse durations shorter than that of the driving laser. This is due to the nonlinearity of the generation
130:
generated from solid targets. HHG in gases, far more widespread in application today, was first observed by McPherson and colleagues in 1987, and later by Ferray et al. in 1988, with surprising results: the high harmonics were found to decrease in intensity at low orders, as expected, but then were
2441:
Popmintchev, T.; Chen, M.-C.; Popmintchev, D.; Arpin, P.; Brown, S.; Alisauskas, S.; Andriukaitis, G.; Balciunas, T.; MĂĽcke, O. D.; Pugzlys, A.; Baltuska, A.; Shim, B.; Schrauth, S. E.; Gaeta, A.; Hernández-GarcĂa, C.; Plaja, L.; Becker, A.; Jaron-Becker, A.; Murnane, M. M.; et al. (2012).
334:
causes the returning electron to miss the parent nucleus. Quantum mechanically, the overlap of the returning electron wavepacket with the nuclear wavepacket is reduced. This has been observed experimentally, where the intensity of harmonics decreases rapidly with increasing ellipticity. Another
2374:
Popmintchev, D.; Hernández-GarcĂa, C.; Dollar, F.; Mancuso, C. A.; Peng, P.-C.; Barwick, B.; Gorman, T. T.; Alonso-Mori, R.; Ališauskas, S.; Andriukaitis, G.; Baltuška, A.; Bostedt, C.; Chen, M.-C.; Dakovski, G. L.; Durfee, C. G.; Eckert, S.; Fan, T.-M.; Ferguson, W. R.; Frischkorn, C. G.;
363:
Furthermore, the implementation of loose focusing geometry for the driving field enables a higher number of emitters and photons to contribute to the generation process and thus, enhance the harmonic yield. When using a gas jet geometry, focusing the laser into the
84:). In 1967 New et al. observed the first third harmonic generation in a gas. In monatomic gases it is only possible to produce odd numbered harmonics for reasons of symmetry. Harmonic generation in the perturbative (weak field) regime is characterised by
339:. At intensities above 10 W·cm the magnetic component of the laser pulse, which is ignored in weak field optics, can become strong enough to deflect the returning electron. This will cause it to "miss" the parent nucleus and hence prevent HHG.
351:
process, phase matching plays an important role in high harmonic generation in the gas phase. In free-focusing geometry, the four causes of wavevector mismatch are: neutral dispersion, plasma dispersion, Gouy phase, and dipole phase.
163:. Often harmonics are only produced in a very small temporal window when the phase matching condition is met. Depletion of the generating media due to ionization also means that harmonic generation is mainly confined to the
302:
Half an optical cycle after ionization, the electron will reverse direction as the electric field changes sign, and will accelerate back towards the parent nucleus. Upon return to the parent nucleus it can then emit
1289:
is quite small and close to one. To phase-match the process of HHG, very high pressures and low ionization levels are required, thus giving a large number of emitters. In the opposite UV spectral range, the term
322:
Since the frequency of the emitted radiation depends on both the kinetic energy and on the ionization potential, the different frequencies are emitted at different recombination times (i.e. the emitted pulse is
1112:
170:
High harmonics are emitted co-linearly with the driving laser and can have a very tight angular confinement, sometimes with less divergence than that of the fundamental field and near
Gaussian beam profiles.
1177:
1398:
1243:
147:/soft X-rays, synchronised with the driving laser and produced with the same repetition rate. The harmonic cut-off varies linearly with increasing laser intensity up until the saturation intensity I
131:
observed to form a plateau, with the intensity of the harmonics remaining approximately constant over many orders. Plateau harmonics spanning hundreds of eV have been measured which extend into the
327:). Furthermore, for every frequency, there are two corresponding recombination times. We refer to these two trajectories as the short trajectory (which are emitted first), and the long trajectory.
255:
1039:
is the phase accumulated by the electron during the time it spends away from the atom, etc. Each term has a specific sign which allows balancing the mismatch at a particular time and frequency.
1037:
928:
981:
831:
1443:
1332:
1287:
872:
1470:
421:
2048:
Dietrich, P.; Burnett, N. H.; Ivanov, M.; Corkum, P. B. (1994). "High-harmonic generation and correlated two-electron multiphoton ionization with elliptically polarized light".
2239:
Balcou, Philippe; Salieres, Pascal; L'Huillier, Anne; Lewenstein, Maciej (1997). "Generalized phase-matching conditions for high harmonics: The role of field-gradient forces".
1807:
423:, we need to find such parameters in the high dimensional space that will effectively make the combined refractive index at the driving laser wavelength nearly 1.
360:
is located after the focus, while generation of high harmonics from long trajectory can be obtained off-axis when the generating gas is located before the focus.
279:
This cut-off energy is derived from a semi-classical calculation, often called the three-step model. The electron is initially treated quantum mechanically as it
2515:
Rundquist, A.; Durfee, C. G.; Chang, Z.; Herne, C.; Backus, S.; Murnane, M. M.; Kapteyn, H. C. (1998). "Phase-matched generation of coherent soft X-rays".
1490:
1664:
Li, X. F.; L'Huillier, A.; Ferray, M.; Lompre, L. A.; Mainfray, G. (1989). "Multiple-harmonic generation in rare gases at high laser intensity".
2274:
Takahashi, E.; Nabekawa, Y.; Midorikawa, K. (2002). "Generation of 10-uj coherent extreme-ultraviolet light by use of high-order harmonics".
179:
The maximum photon energy producible with high harmonic generation is given by the cut-off of the harmonic plateau. This can be calculated
371:
More generally, in the X-ray spectral region, materials have a refractive index that is very close to 1. To balance the phase mismatch,
1045:
1117:
355:
The neutral dispersion is caused by the atoms while the plasma dispersion is due to the ions, and the two have opposite signs. The
1337:
1182:
1994:
1586:
McPherson, A.; et al. (1987). "Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases".
193:
155:
but these have a lower conversion efficiency so there is a balance to be found depending on the photon energies required.
2375:
et al. (2015). "Ultraviolet surprise: Efficient soft x-ray high-harmonic generation in multiply ionized plasmas".
330:
In the semiclassical picture, HHG will only occur if the driving laser field is linearly polarised. Ellipticity on the
283:
from the parent atom, but its subsequent dynamics are treated classically. The electron is assumed to be born into the
430:
The phase mismatch (> 0 phase velocity of the laser is faster than that of the X-rays) can be represented as:
986:
877:
151:
where harmonic generation stops. The saturation intensity can be increased by changing the atomic species to lighter
933:
783:
1404:
1293:
1248:
318:
Electron return energy (full blue curve) and excursion time (blue dashed curve), as a function of the return time
874:
is the contribution from ions (when neutrals are ionized, this term can be still sufficiently large in the UV),
836:
88:
efficiency with increasing harmonic order. This behaviour can be understood by considering an atom absorbing
374:
2317:
Grant-Jacob, James; Mills, Ben; Butcher, Tom; Chapman, Richard; Brocklesby, William; Frey, Jeremy (2011).
57:
of the original light's frequency. This process was first discovered in 1961 by
Franken et al., using a
53:
can be used to generate new frequencies of light. The newly generated frequencies are integer multiples
81:
2581:
1766:
2442:"Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers".
1903:
Tisch, J. W. G.; et al. (1994). "Angularly resolved high-order harmonic generation in helium".
1621:
Ferray, M.; et al. (1988). "Multiple-harmonic conversion of 1064 nm radiation in rare gases".
1868:
1764:
Brabec, T.; Krausz, F. (2000). "Intense few-cycle laser fields: Frontiers of nonlinear optics".
2576:
1849:
Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared,
143:
High harmonics have a number of interesting properties. They are a tunable table-top source of
2091:
Altucci, C.; Starczewski, T.; Mevel, E.; Wahlström, C.-G.; Carré, B.; L'Huillier, A. (1996).
2135:
311:. This description has become known as the recollisional model of high harmonic generation.
2536:
2463:
2386:
2333:
2283:
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2150:
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2006:
1959:
1912:
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1816:
1775:
1720:
1673:
1630:
1595:
1560:
1551:
Burnett, N. H.; et al. (1977). "Harmonic generation in CO2 laser target interaction".
1512:
273:
265:
1401:
collinear phase matching and maximum flux extraction at the driving wavelengths where the
8:
2318:
180:
144:
20:
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2010:
1963:
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1975:
1928:
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1738:
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1650:
1642:
280:
116:
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2034:
122:
The first high harmonic generation was observed in 1977 in interaction of intense CO
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2479:
2471:
2424:
2402:
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2341:
2291:
2256:
2213:
2193:
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2014:
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1638:
1603:
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1520:
1460:
308:
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with zero initial velocity, and to be subsequently accelerated by the laser beam's
135:
regime. This plateau ends abruptly at a position called the high harmonic cut-off.
127:
66:
2548:
307:-like radiation during a recombination process with the atom as it returns to its
1948:"High-order harmonic generation from atoms and ions in the high intensity regime"
1538:
1503:
New, G. H. C.; Ward, J. F. (1967). "Optical Third-Harmonic
Generation in Gases".
1465:
1334:
is large because of the closely located UV resonances, and in addition, the term
2162:
2018:
1971:
1889:
1524:
304:
288:
184:
45:
Perturbative harmonic generation is a process whereby laser light of frequency
2069:
1787:
1042:
The contribution from the electrons scales quadratically with the wavelength:
103:
increases, explaining the rapid decrease in the initial harmonic intensities.
2570:
2260:
2217:
1685:
365:
336:
77:
2475:
2398:
2116:
1924:
2493:
2416:
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2303:
2170:
2026:
1979:
1742:
1607:
2556:
2225:
2077:
1932:
1693:
2346:
2295:
164:
2484:
2407:
2373:
95:
then emitting a single high energy photon. The probability of absorbing
1850:
356:
160:
132:
73:
58:
2238:
1946:
Krause, Jeffrey L.; Schafer, Kenneth J.; Kulander, Kenneth C. (1992).
1114:, while the contribution from atoms scales inversely with wavelength:
348:
183:
by examining the maximum energy the ionized electron can gain in the
152:
2194:"Phase of the atomic polarization in high-order harmonic generation"
1947:
1863:
1802:
1733:
1708:
1572:
2531:
2458:
983:
is the free focusing geometry, plane-wave of waveguiding geometry,
1471:
Resonant high harmonic generation from laser ablated plasma plumes
314:
1107:{\displaystyle \Delta n_{\mathrm {electrons} }\sim -\lambda ^{2}}
2191:
2090:
111:
2440:
2192:
Lewenstein, Maciej; Salieres, Pascal; L'huillier, Anne (1995).
2093:"Influence of atomic density in high-order harmonic generation"
284:
92:
62:
2316:
2129:
1709:"Laser technology: Source of coherent kiloelectronvolt X-rays"
1172:{\displaystyle \Delta n_{\mathrm {atoms} }\sim 1/\lambda ^{2}}
335:
effect which limits the intensity of the driving laser is the
1800:
331:
324:
1663:
1393:{\displaystyle \left|\Delta n_{\mathrm {electrons} }\right|}
1238:{\displaystyle \left|\Delta n_{\mathrm {electrons} }\right|}
294:
2273:
2047:
1995:"Plasma perspective on strong field multiphoton ionization"
1808:
Journal of
Physics B: Atomic, Molecular and Optical Physics
1623:
Journal of
Physics B: Atomic, Molecular and Optical Physics
1803:"Theoretical aspects of intense field harmonic generation"
2514:
2319:"Gas jet structure influence on high harmonic generation"
76:
solids is well understood and extensively used in modern
1801:
L'Huillier, A.; Schafer, K. J.; Kulander, K. C. (1991).
19:
For generation of the fourth and lower harmonics, see
1945:
1864:"High Harmonic Generation from Ultrafast Pump Lasers"
1407:
1340:
1296:
1251:
1185:
1120:
1048:
989:
936:
880:
839:
786:
439:
377:
196:
368:
can increase the efficiency of harmonic generation.
250:{\displaystyle E_{\mathrm {max} }=I_{p}+3.17\ U_{p}}
40:
2436:
2434:
2369:
2367:
2365:
1437:
1392:
1326:
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1237:
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975:
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866:
825:
769:
415:
249:
755:
2568:
2431:
2362:
1861:
1032:{\displaystyle \Delta k_{\mathrm {intrinsic} }}
923:{\displaystyle \Delta k_{\mathrm {electrons} }}
976:{\displaystyle \Delta k_{\mathrm {geometry} }}
826:{\displaystyle \Delta k_{\mathrm {neutrals} }}
187:of the laser. The cut-off energy is given by:
2508:
1489:P. A. Franken, A. E. Hill, C. W. Peters, and
1763:
1245:is quite large per electron, while the term
2136:"Coherence control of high-order harmonics"
1438:{\displaystyle {\vec {v}}\times {\vec {B}}}
1327:{\displaystyle \Delta n_{\mathrm {atoms} }}
1282:{\displaystyle \Delta n_{\mathrm {atoms} }}
867:{\displaystyle \Delta k_{\mathrm {ions} }}
754:
174:
115:Spectrum of a neon HHG source driven by a
2530:
2483:
2457:
2406:
2345:
1732:
1585:
1179:. Thus at long IR wavelengths, the term
1862:Schafer, K. J.; Kulander, K. C. (1997).
313:
293:
110:
1550:
1502:
2569:
1992:
1620:
1902:
1706:
416:{\displaystyle \Delta k=k_{q}-qk_{L}}
2130:Pascal, Salieres; L'Huillier, Anne;
1851:https://doi.org/10.1364/OE.25.027506
833:is the neutral atoms contribution,
13:
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482:
440:
378:
209:
206:
203:
14:
2593:
1493:, Phys. Rev. Lett. 7, 118 (1961).
342:
41:Perturbative harmonic generation
2310:
2267:
2232:
2185:
2123:
2084:
2041:
1986:
1939:
1896:
1855:
1843:
1794:
1707:Seres, J.; et al. (2005).
1757:
1700:
1657:
1614:
1579:
1544:
1531:
1496:
1483:
1429:
1414:
106:
1:
2549:10.1126/science.280.5368.1412
1476:
138:
930:is the plasma contribution,
159:process, phase matching and
7:
2163:10.1103/physrevlett.74.3776
2019:10.1103/physrevlett.71.1994
1972:10.1103/PhysRevLett.68.3535
1829:10.1088/0953-4075/24/15/004
1449:
10:
2598:
1890:10.1103/physrevlett.78.638
1643:10.1088/0953-4075/21/3/001
1537:J. Wildenauer, Journal of
1525:10.1103/physrevlett.19.556
268:from the laser field and I
82:second-harmonic generation
18:
2070:10.1103/physreva.50.r3585
1788:10.1103/revmodphys.72.545
1767:Reviews of Modern Physics
2261:10.1103/PhysRevA.55.3204
2218:10.1103/physreva.52.4747
1686:10.1103/physreva.39.5751
27:High-harmonic generation
2476:10.1126/science.1218497
2399:10.1126/science.aac9755
2143:Physical Review Letters
2117:10.1364/JOSAB.13.000148
1999:Physical Review Letters
1952:Physical Review Letters
1925:10.1103/physreva.49.r28
1869:Physical Review Letters
175:Semi-classical approach
72:Harmonic generation in
1993:Corkum, P. B. (1993).
1608:10.1364/JOSAB.4.000595
1439:
1394:
1328:
1283:
1239:
1173:
1108:
1033:
977:
924:
868:
827:
771:
417:
319:
299:
251:
167:of the driving pulse.
119:
1440:
1395:
1329:
1284:
1240:
1174:
1109:
1034:
978:
925:
869:
828:
772:
418:
317:
297:
252:
114:
99:photons decreases as
16:Laser science process
2347:10.1364/OE.19.009801
2296:10.1364/OL.27.001920
1405:
1338:
1294:
1249:
1183:
1118:
1046:
987:
934:
878:
837:
784:
437:
375:
298:The three-step model
274:ionization potential
266:ponderomotive energy
194:
2541:1998Sci...280.1412R
2525:(5368): 1412–1415.
2468:2012Sci...336.1287P
2452:(6086): 1287–1291.
2391:2015Sci...350.1225P
2385:(6265): 1225–1231.
2338:2011OExpr..19.9801G
2288:2002OptL...27.1920T
2253:1997PhRvA..55.3204B
2210:1995PhRvA..52.4747L
2155:1995PhRvL..74.3776S
2109:1996JOSAB..13..148A
2062:1994PhRvA..50.3585D
2011:1993PhRvL..71.1994C
1964:1992PhRvL..68.3535K
1917:1994PhRvA..49...28T
1882:1997PhRvL..78..638S
1821:1991JPhB...24.3315L
1780:2000RvMP...72..545B
1725:2005Natur.433..596S
1678:1989PhRvA..39.5751L
1635:1988JPhB...21L..31F
1600:1987JOSAB...4..595M
1565:1977ApPhL..31..172B
1517:1967PhRvL..19..556N
61:, with crystalline
21:harmonic generation
2132:Lewenstein, Maciej
2097:J. Opt. Soc. Am. B
2056:(5): R3585–R3588.
1456:Attosecond physics
1435:
1390:
1324:
1279:
1235:
1169:
1104:
1029:
973:
920:
864:
823:
767:
760:
748:
697:
687:
639:
629:
578:
568:
532:
522:
413:
320:
300:
247:
126:laser pulses with
120:
86:rapidly decreasing
49:and photon energy
35:attosecond physics
2332:(10): 9801–9806.
2282:(21): 1920–1922.
2241:Physical Review A
2198:Physical Review A
2149:(19): 3776–3779.
2050:Physical Review A
2005:(13): 1994–1997.
1958:(24): 3535–3538.
1905:Physical Review A
1815:(15): 3315–3341.
1672:(11): 5751–5761.
1666:Physical Review A
1432:
1417:
703:
701:
645:
643:
584:
582:
538:
536:
480:
478:
236:
117:Ti-sapphire laser
2589:
2582:Nonlinear optics
2561:
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2512:
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2505:
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2349:
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2314:
2308:
2307:
2271:
2265:
2264:
2247:(4): 3204–3210.
2236:
2230:
2229:
2204:(6): 4747–4754.
2189:
2183:
2182:
2140:
2127:
2121:
2120:
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1553:Appl. Phys. Lett
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1542:
1535:
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1528:
1500:
1494:
1487:
1461:Nonlinear optics
1444:
1442:
1441:
1436:
1434:
1433:
1425:
1419:
1418:
1410:
1399:
1397:
1396:
1391:
1389:
1385:
1384:
1383:
1382:
1333:
1331:
1330:
1325:
1323:
1322:
1321:
1288:
1286:
1285:
1280:
1278:
1277:
1276:
1244:
1242:
1241:
1236:
1234:
1230:
1229:
1228:
1227:
1178:
1176:
1175:
1170:
1168:
1167:
1158:
1147:
1146:
1145:
1113:
1111:
1110:
1105:
1103:
1102:
1087:
1086:
1085:
1038:
1036:
1035:
1030:
1028:
1027:
1026:
982:
980:
979:
974:
972:
971:
970:
929:
927:
926:
921:
919:
918:
917:
873:
871:
870:
865:
863:
862:
861:
832:
830:
829:
824:
822:
821:
820:
776:
774:
773:
768:
759:
749:
744:
743:
742:
741:
696:
688:
683:
682:
681:
680:
638:
630:
625:
624:
623:
622:
577:
569:
564:
563:
562:
561:
531:
523:
518:
517:
516:
515:
474:
473:
458:
457:
422:
420:
419:
414:
412:
411:
396:
395:
256:
254:
253:
248:
246:
245:
234:
227:
226:
214:
213:
212:
67:nonlinear medium
2597:
2596:
2592:
2591:
2590:
2588:
2587:
2586:
2567:
2566:
2565:
2564:
2513:
2509:
2439:
2432:
2372:
2363:
2321:
2315:
2311:
2272:
2268:
2237:
2233:
2190:
2186:
2138:
2128:
2124:
2089:
2085:
2046:
2042:
1991:
1987:
1944:
1940:
1901:
1897:
1860:
1856:
1848:
1844:
1799:
1795:
1762:
1758:
1734:10.1038/433596a
1705:
1701:
1662:
1658:
1619:
1615:
1584:
1580:
1573:10.1063/1.89628
1549:
1545:
1539:Applied Physics
1536:
1532:
1511:(10): 556–559.
1505:Phys. Rev. Lett
1501:
1497:
1488:
1484:
1479:
1466:Photoionization
1452:
1424:
1423:
1409:
1408:
1406:
1403:
1402:
1354:
1353:
1349:
1345:
1341:
1339:
1336:
1335:
1305:
1304:
1300:
1295:
1292:
1291:
1260:
1259:
1255:
1250:
1247:
1246:
1199:
1198:
1194:
1190:
1186:
1184:
1181:
1180:
1163:
1159:
1154:
1129:
1128:
1124:
1119:
1116:
1115:
1098:
1094:
1057:
1056:
1052:
1047:
1044:
1043:
998:
997:
993:
988:
985:
984:
945:
944:
940:
935:
932:
931:
889:
888:
884:
879:
876:
875:
848:
847:
843:
838:
835:
834:
795:
794:
790:
785:
782:
781:
750:
713:
712:
708:
704:
702:
689:
655:
654:
650:
646:
644:
631:
594:
593:
589:
585:
583:
570:
548:
547:
543:
539:
537:
524:
490:
489:
485:
481:
479:
469:
465:
453:
449:
438:
435:
434:
407:
403:
391:
387:
376:
373:
372:
345:
271:
263:
241:
237:
222:
218:
202:
201:
197:
195:
192:
191:
177:
150:
141:
125:
109:
43:
24:
17:
12:
11:
5:
2595:
2585:
2584:
2579:
2563:
2562:
2507:
2430:
2361:
2326:Optics Express
2309:
2276:Optics Letters
2266:
2231:
2184:
2122:
2103:(1): 148–156.
2083:
2040:
1985:
1938:
1911:(1): R28–R31.
1895:
1876:(4): 638–641.
1854:
1842:
1793:
1774:(2): 545–591.
1756:
1699:
1656:
1613:
1578:
1559:(3): 172–174.
1543:
1541:62, 41 (1987).
1530:
1495:
1481:
1480:
1478:
1475:
1474:
1473:
1468:
1463:
1458:
1451:
1448:
1431:
1428:
1422:
1416:
1413:
1388:
1381:
1378:
1375:
1372:
1369:
1366:
1363:
1360:
1357:
1352:
1348:
1344:
1320:
1317:
1314:
1311:
1308:
1303:
1299:
1275:
1272:
1269:
1266:
1263:
1258:
1254:
1233:
1226:
1223:
1220:
1217:
1214:
1211:
1208:
1205:
1202:
1197:
1193:
1189:
1166:
1162:
1157:
1153:
1150:
1144:
1141:
1138:
1135:
1132:
1127:
1123:
1101:
1097:
1093:
1090:
1084:
1081:
1078:
1075:
1072:
1069:
1066:
1063:
1060:
1055:
1051:
1025:
1022:
1019:
1016:
1013:
1010:
1007:
1004:
1001:
996:
992:
969:
966:
963:
960:
957:
954:
951:
948:
943:
939:
916:
913:
910:
907:
904:
901:
898:
895:
892:
887:
883:
860:
857:
854:
851:
846:
842:
819:
816:
813:
810:
807:
804:
801:
798:
793:
789:
778:
777:
766:
763:
758:
753:
747:
740:
737:
734:
731:
728:
725:
722:
719:
716:
711:
707:
700:
695:
692:
686:
679:
676:
673:
670:
667:
664:
661:
658:
653:
649:
642:
637:
634:
628:
621:
618:
615:
612:
609:
606:
603:
600:
597:
592:
588:
581:
576:
573:
567:
560:
557:
554:
551:
546:
542:
535:
530:
527:
521:
514:
511:
508:
505:
502:
499:
496:
493:
488:
484:
477:
472:
468:
464:
461:
456:
452:
448:
445:
442:
410:
406:
402:
399:
394:
390:
386:
383:
380:
344:
343:Phase matching
341:
305:bremsstrahlung
289:electric field
281:tunnel ionizes
269:
261:
258:
257:
244:
240:
233:
230:
225:
221:
217:
211:
208:
205:
200:
185:electric field
176:
173:
148:
140:
137:
123:
108:
105:
42:
39:
15:
9:
6:
4:
3:
2:
2594:
2583:
2580:
2578:
2577:Laser science
2575:
2574:
2572:
2558:
2554:
2550:
2546:
2542:
2538:
2533:
2528:
2524:
2520:
2519:
2511:
2503:
2499:
2495:
2491:
2486:
2481:
2477:
2473:
2469:
2465:
2460:
2455:
2451:
2447:
2446:
2437:
2435:
2426:
2422:
2418:
2414:
2409:
2404:
2400:
2396:
2392:
2388:
2384:
2380:
2379:
2370:
2368:
2366:
2357:
2353:
2348:
2343:
2339:
2335:
2331:
2327:
2320:
2313:
2305:
2301:
2297:
2293:
2289:
2285:
2281:
2277:
2270:
2262:
2258:
2254:
2250:
2246:
2242:
2235:
2227:
2223:
2219:
2215:
2211:
2207:
2203:
2199:
2195:
2188:
2180:
2176:
2172:
2168:
2164:
2160:
2156:
2152:
2148:
2144:
2137:
2133:
2126:
2118:
2114:
2110:
2106:
2102:
2098:
2094:
2087:
2079:
2075:
2071:
2067:
2063:
2059:
2055:
2051:
2044:
2036:
2032:
2028:
2024:
2020:
2016:
2012:
2008:
2004:
2000:
1996:
1989:
1981:
1977:
1973:
1969:
1965:
1961:
1957:
1953:
1949:
1942:
1934:
1930:
1926:
1922:
1918:
1914:
1910:
1906:
1899:
1891:
1887:
1883:
1879:
1875:
1871:
1870:
1865:
1858:
1852:
1846:
1838:
1834:
1830:
1826:
1822:
1818:
1814:
1810:
1809:
1804:
1797:
1789:
1785:
1781:
1777:
1773:
1769:
1768:
1760:
1752:
1748:
1744:
1740:
1735:
1730:
1726:
1722:
1719:(7026): 596.
1718:
1714:
1710:
1703:
1695:
1691:
1687:
1683:
1679:
1675:
1671:
1667:
1660:
1652:
1648:
1644:
1640:
1636:
1632:
1628:
1624:
1617:
1609:
1605:
1601:
1597:
1593:
1589:
1582:
1574:
1570:
1566:
1562:
1558:
1554:
1547:
1540:
1534:
1526:
1522:
1518:
1514:
1510:
1506:
1499:
1492:
1486:
1482:
1472:
1469:
1467:
1464:
1462:
1459:
1457:
1454:
1453:
1447:
1426:
1420:
1411:
1386:
1350:
1342:
1301:
1256:
1231:
1195:
1187:
1164:
1160:
1155:
1151:
1148:
1125:
1099:
1095:
1091:
1088:
1053:
1040:
994:
941:
885:
844:
791:
764:
761:
756:
751:
745:
709:
698:
693:
690:
684:
651:
640:
635:
632:
626:
590:
579:
574:
571:
565:
544:
533:
528:
525:
519:
486:
475:
470:
466:
462:
459:
454:
450:
446:
443:
433:
432:
431:
428:
424:
408:
404:
400:
397:
392:
388:
384:
381:
369:
367:
361:
358:
353:
350:
340:
338:
337:Lorentz force
333:
328:
326:
316:
312:
310:
306:
296:
292:
290:
286:
282:
277:
275:
267:
242:
238:
231:
228:
223:
219:
215:
198:
190:
189:
188:
186:
182:
172:
168:
166:
162:
156:
154:
146:
136:
134:
129:
118:
113:
104:
102:
98:
94:
91:
87:
83:
79:
78:laser physics
75:
70:
68:
64:
60:
56:
52:
48:
38:
36:
32:
28:
22:
2522:
2516:
2510:
2485:10366/147089
2449:
2443:
2408:10366/147088
2382:
2376:
2329:
2325:
2312:
2279:
2275:
2269:
2244:
2240:
2234:
2201:
2197:
2187:
2146:
2142:
2125:
2100:
2096:
2086:
2053:
2049:
2043:
2002:
1998:
1988:
1955:
1951:
1941:
1908:
1904:
1898:
1873:
1867:
1857:
1845:
1812:
1806:
1796:
1771:
1765:
1759:
1716:
1712:
1702:
1669:
1665:
1659:
1626:
1622:
1616:
1591:
1587:
1581:
1556:
1552:
1546:
1533:
1508:
1504:
1498:
1491:G. Weinreich
1485:
1041:
779:
429:
425:
370:
362:
354:
347:As in every
346:
329:
321:
309:ground state
301:
278:
259:
178:
169:
165:leading edge
157:
142:
121:
100:
96:
89:
71:
54:
50:
46:
44:
30:
26:
25:
181:classically
153:noble gases
107:Development
2571:Categories
2532:2403.19636
2459:2403.19535
1629:(3): L31.
1594:(4): 595.
1477:References
357:Gouy phase
332:laser beam
161:ionization
139:Properties
133:soft X-ray
74:dielectric
59:ruby laser
1837:250751106
1651:250827054
1430:→
1421:×
1415:→
1347:Δ
1298:Δ
1253:Δ
1192:Δ
1161:λ
1149:∼
1122:Δ
1096:λ
1092:−
1089:∼
1050:Δ
991:Δ
938:Δ
882:Δ
841:Δ
788:Δ
765:⋯
746:⏟
706:Δ
685:⏟
648:Δ
627:⏟
587:Δ
566:⏟
541:Δ
520:⏟
483:Δ
460:−
441:Δ
398:−
379:Δ
366:Mach disk
349:nonlinear
2502:24628513
2494:22679093
2417:26785483
2356:21643236
2304:18033402
2179:35091499
2171:10058294
2134:(1995).
2035:29947935
2027:10054556
1980:10045729
1743:15703738
1450:See also
2557:9603725
2537:Bibcode
2518:Science
2464:Bibcode
2445:Science
2425:2342988
2387:Bibcode
2378:Science
2334:Bibcode
2284:Bibcode
2249:Bibcode
2226:9912816
2206:Bibcode
2151:Bibcode
2105:Bibcode
2078:9911439
2058:Bibcode
2007:Bibcode
1960:Bibcode
1933:9910285
1913:Bibcode
1878:Bibcode
1817:Bibcode
1776:Bibcode
1751:4425428
1721:Bibcode
1694:9901157
1674:Bibcode
1631:Bibcode
1596:Bibcode
1561:Bibcode
1513:Bibcode
325:chirped
272:is the
264:is the
260:where U
93:photons
65:as the
2555:
2500:
2492:
2423:
2415:
2354:
2302:
2224:
2177:
2169:
2076:
2033:
2025:
1978:
1931:
1835:
1749:
1741:
1713:Nature
1692:
1649:
1588:JOSA B
780:where
285:vacuum
235:
128:plasma
63:quartz
2527:arXiv
2498:S2CID
2454:arXiv
2421:S2CID
2322:(PDF)
2175:S2CID
2139:(PDF)
2031:S2CID
1833:S2CID
1747:S2CID
1647:S2CID
80:(see
2553:PMID
2490:PMID
2413:PMID
2352:PMID
2300:PMID
2222:PMID
2167:PMID
2074:PMID
2023:PMID
1976:PMID
1929:PMID
1739:PMID
1690:PMID
752:>
691:>
633:>
572:<
526:<
232:3.17
2545:doi
2523:280
2480:hdl
2472:doi
2450:336
2403:hdl
2395:doi
2383:350
2342:doi
2292:doi
2257:doi
2214:doi
2159:doi
2113:doi
2066:doi
2015:doi
1968:doi
1921:doi
1886:doi
1825:doi
1784:doi
1729:doi
1717:433
1682:doi
1639:doi
1604:doi
1569:doi
1521:doi
149:sat
145:XUV
31:HHG
2573::
2551:.
2543:.
2535:.
2521:.
2496:.
2488:.
2478:.
2470:.
2462:.
2448:.
2433:^
2419:.
2411:.
2401:.
2393:.
2381:.
2364:^
2350:.
2340:.
2330:19
2328:.
2324:.
2298:.
2290:.
2280:27
2278:.
2255:.
2245:55
2243:.
2220:.
2212:.
2202:52
2200:.
2196:.
2173:.
2165:.
2157:.
2147:74
2145:.
2141:.
2111:.
2101:13
2099:.
2095:.
2072:.
2064:.
2054:50
2052:.
2029:.
2021:.
2013:.
2003:71
2001:.
1997:.
1974:.
1966:.
1956:68
1954:.
1950:.
1927:.
1919:.
1909:49
1907:.
1884:.
1874:78
1872:.
1866:.
1831:.
1823:.
1813:24
1811:.
1805:.
1782:.
1772:72
1770:.
1745:.
1737:.
1727:.
1715:.
1711:.
1688:.
1680:.
1670:39
1668:.
1645:.
1637:.
1627:21
1625:.
1602:.
1590:.
1567:.
1557:31
1555:.
1519:.
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1507:.
291:.
276:.
69:.
55:nω
51:ħω
37:.
2559:.
2547::
2539::
2529::
2504:.
2482::
2474::
2466::
2456::
2427:.
2405::
2397::
2389::
2358:.
2344::
2336::
2306:.
2294::
2286::
2263:.
2259::
2251::
2228:.
2216::
2208::
2181:.
2161::
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2119:.
2115::
2107::
2080:.
2068::
2060::
2037:.
2017::
2009::
1982:.
1970::
1962::
1935:.
1923::
1915::
1892:.
1888::
1880::
1839:.
1827::
1819::
1790:.
1786::
1778::
1753:.
1731::
1723::
1696:.
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1676::
1653:.
1641::
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1527:.
1523::
1515::
1427:B
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792:k
762:+
757:0
739:c
736:i
733:s
730:n
727:i
724:r
721:t
718:n
715:i
710:k
699:+
694:0
678:y
675:r
672:t
669:e
666:m
663:o
660:e
657:g
652:k
641:+
636:0
620:s
617:n
614:o
611:r
608:t
605:c
602:e
599:l
596:e
591:k
580:+
575:0
559:s
556:n
553:o
550:i
545:k
534:+
529:0
513:s
510:l
507:a
504:r
501:t
498:u
495:e
492:n
487:k
476:=
471:L
467:k
463:q
455:q
451:k
447:=
444:k
409:L
405:k
401:q
393:q
389:k
385:=
382:k
270:p
262:p
243:p
239:U
229:+
224:p
220:I
216:=
210:x
207:a
204:m
199:E
124:2
101:n
97:n
90:n
47:ω
29:(
23:.
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