772:
1784:
481:
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results in the beams propagating divergence-free. Self-focusing in photopolymerizable media is possible, owing to a photoreaction dependent refractive index, and the fact that refractive index in polymers is proportional to molecular weight and crosslinking degree which increases over the duration of
2467:
Self-focusing can also been observed in a number of soft matter systems, such as solutions of polymers and particles as well as photo-polymers. Self-focusing was observed in photo-polymer systems with microscale laser beams of either UV or visible light. The self-trapping of incoherent light was also
2445:
the plasma frequency. For an electron density of 10 cm and radiation at the wavelength of 800 nm, the critical power is about 3 TW. Such values are realisable with modern lasers, which can exceed PW powers. For example, a laser delivering 50 fs pulses with an energy of 1 J has a peak power of 20
174:
is positive in most materials, the refractive index becomes larger in the areas where the intensity is higher, usually at the centre of a beam, creating a focusing density profile which potentially leads to the collapse of a beam on itself. Self-focusing beams have been found to naturally evolve into
2458:
Self-focusing can be induced by a permanent refractive index change resulting from a multi-pulse exposure. This effect has been observed in glasses which increase the refractive index during an exposure to ultraviolet laser radiation. Accumulated self-focusing develops as a wave guiding, rather than
59:
Self-focusing is often observed when radiation generated by femtosecond lasers propagates through many solids, liquids and gases. Depending on the type of material and on the intensity of the radiation, several mechanisms produce variations in the refractive index which result in self-focusing: the
3294:
Borisov, A. B.; Borovskiy, A. V.; Korobkin, V. V.; Prokhorov, A. M.; Shiryaev, O. B.; Shi, X. M.; Luk, T. S.; McPherson, A.; Solem, J. C.; Boyer, K.; Rhodes, C. K. (1992). "Observation of relativistic and charge-displacement self-channeling of intense subpicosecond ultraviolet (248 nm) radiation in
2416:
2073:
Advances in laser technology have recently enabled the observation of self-focusing in the interaction of intense laser pulses with plasmas. Self-focusing in plasma can occur through thermal, relativistic and ponderomotive effects. Thermal self-focusing is due to collisional heating of a plasma
268:
in vacuum and α is a constant which depends on the initial spatial distribution of the beam. Although there is no general analytical expression for α, its value has been derived numerically for many beam profiles. The lower limit is α ≈ 1.86225, which corresponds to Townes beams, whereas for a
2449:
Self-focusing in a plasma can balance the natural diffraction and channel a laser beam. Such effect is beneficial for many applications, since it helps increasing the length of the interaction between laser and medium. This is crucial, for example, in laser-driven particle acceleration,
767:{\displaystyle {\frac {\partial {{E}({\vec {\mathbf {r} }},t)}}{\partial z}}+{\frac {1}{c}}{\frac {\partial {{E}({\vec {\mathbf {r} }},t)}}{\partial t}}+{\frac {i}{2k}}\nabla _{\bot }^{2}E({\vec {\mathbf {r} }},t)=+ikn_{2}|E({\vec {\mathbf {r} }},t)|^{2}{{E}({\vec {\mathbf {r} }},t)}+}
1779:{\displaystyle {\frac {\partial {{E}({\vec {\mathbf {r} }},t)}}{\partial z}}+{\frac {1}{c}}{\frac {\partial {{E}({\vec {\mathbf {r} }},t)}}{\partial t}}+{\frac {i}{2k}}\nabla _{\bot }^{2}E({\vec {\mathbf {r} }},t)=+ikn_{2}|E({\vec {\mathbf {r} }},t)|^{2}{{E}({\vec {\mathbf {r} }},t)}}
1002:
778:
2459:
a lensing effect. The scale of actively forming beam filaments is a function of the exposure dose. Evolution of each beam filament towards a singularity is limited by the maximum induced refractive index change or by laser damage resistance of the glass.
1492:
is affected by modulational instability. The small perturbations caused by roughnesses and medium defects are amplified in propagation. This effect is referred to as
Bespalov-Talanov instability. In a framework of nonlinear Schrödinger equation :
3338:
Monot, P.; Auguste, T.; Gibbon, P.; Jakober, F.; Mainfray, G.; Dulieu, A.; Louis-Jacquet, M.; Malka, G.; Miquel, J. L. (1995). "Experimental
Demonstration of Relativistic Self-Channeling of a Multiterawatt Laser Pulse in an Underdense Plasma".
1311:
1970:
475:
the refractive index is changed. "Red" detuning leads to an increased index of refraction during saturation of the resonant transition, i.e. to self-focusing, while for "blue" detuning the radiation is defocused during saturation:
17:
2266:
3050:
Kasparian, J.; Rodriguez, M.; Méjean, G.; Yu, J.; Salmon, E.; Wille, H.; Bourayou, R.; Frey, S.; André, Y.-B.; Mysyrowicz, A.; Sauerbrey, R.; Wolf, J.-P.; Wöste, L. (2003). "White-Light
Filaments for Atmospheric Analysis".
307:
was developed to overcome the nonlinearities and damage of optical components that self-focusing would produce in the amplification of femtosecond laser pulses. On the other hand, self-focusing is a major mechanism behind
258:
2248:
3784:
Tabak, M.; Clark, D. S.; Hatchett, S. P.; Key, M. H.; Lasinski, B. F.; Snavely, R. A.; Wilks, S. C.; Town, R. P. J.; Stephens, R.; Campbell, E. M.; Kodama, R.; Mima, K.; Tanaka, K. A.; Atzeni, S.; Freeman, R. (2005).
3006:
Garcia, Hernando; Johnson, Anthony M.; Oguama, Ferdinand A.; Trivedi, Sudhir (2003). "New approach to the measurement of the nonlinear refractive index of short (< 25 m) lengths of silica and erbium-doped fibers".
2164:
51:
beam. The peak intensity of the self-focused region keeps increasing as the wave travels through the medium, until defocusing effects or medium damage interrupt this process. Self-focusing of light was discovered by
4127:
Basker, Dinesh K.; Brook, Michael A.; Saravanamuttu, Kalaichelvi (2015). "Spontaneous
Emergence of Nonlinear Light Waves and Self-Inscribed Waveguide Microstructure during the Cationic Polymerization of Epoxides".
4064:
Biria, Saeid; Malley, Philip P. A.; Kahan, Tara F.; Hosein, Ian D. (2016). "Tunable
Nonlinear Optical Pattern Formation and Microstructure in Cross-Linking Acrylate Systems during Free-Radical Polymerization".
1206:{\displaystyle {\frac {\partial {{N}({\vec {\mathbf {r} }},t)}}{\partial t}}=-{\frac {{N_{0}}({\vec {\mathbf {r} }})}{T_{1}}}-\sigma (\omega )N({\vec {\mathbf {r} }},t)|E({\vec {\mathbf {r} }},t)|^{2},}
991:{\displaystyle {\frac {\sigma N({\vec {\mathbf {r} }},t)}{2}}{{E}({\vec {\mathbf {r} }},t)},\nabla _{\bot }^{2}={\frac {\partial ^{2}}{{\partial x}^{2}}}+{\frac {\partial ^{2}}{{\partial y}^{2}}},}
4190:
Biria, Saeid; Hosein, Ian D. (2017-05-09). "Control of
Morphology in Polymer Blends through Light Self-Trapping: An in Situ Study of Structure Evolution, Reaction Kinetics, and Phase Separation".
4092:
Burgess, Ian B.; Shimmell, Whitney E.; Saravanamuttu, Kalaichelvi (2007). "Spontaneous
Pattern Formation Due to Modulation Instability of Incoherent White Light in a Photopolymerizable Medium".
2021:
4155:
Biria, Saeid; Malley, Phillip P. A.; Kahan, Tara F.; Hosein, Ian D. (2016). "Optical
Autocatalysis Establishes Novel Spatial Dynamics in Phase Separation of Polymer Blends during Photocuring".
2063:
3663:
Faure, J.; Malka, V.; Marquès, J.-R.; David, P.-G.; Amiranoff, F.; Ta Phuoc, K.; Rousse, A. (2002). "Effects of pulse duration on self-focusing of ultra-short lasers in underdense plasmas".
1360:
1490:
423:
2963:
Nibbering, E. T. J.; Grillon, G.; Franco, M. A.; Prade, B. S.; Mysyrowicz, A. (1997). "Determination of the inertial contribution to the nonlinear refractive index of air, N
2260:
The evaluation of the contribution and interplay of these processes is a complex task, but a reference threshold for plasma self-focusing is the relativistic critical power
143:
1837:
2074:
exposed to electromagnetic radiation: the rise in temperature induces a hydrodynamic expansion which leads to an increase of the index of refraction and further heating.
473:
377:
446:
350:
1414:
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Kerr-induced self-focusing is crucial for many applications in laser physics, both as a key ingredient and as a limiting factor. For example, the technique of
94:
2257:, which pushes electrons away from the region where the laser beam is more intense, therefore increasing the refractive index and inducing a focusing effect.
2411:{\displaystyle P_{cr}={\frac {m_{e}^{2}c^{5}\omega ^{2}}{e^{2}\omega _{p}^{2}}}\simeq 17{\bigg (}{\frac {\omega }{\omega _{p}}}{\bigg )}^{2}\ {\textrm {GW}}}
3147:
Stibenz, Gero; Zhavoronkov, Nickolai; Steinmeyer, Günter (2006). "Self-compression of millijoule pulses to 78 fs duration in a white-light filament".
3577:
Pizzo, V Del; Luther-Davies, B (1979). "Evidence of filamentation (self-focusing) of a laser beam propagating in a laser-produced aluminium plasma".
188:
76:, a non-linear process which arises in media exposed to intense electromagnetic radiation, and which produces a variation of the refractive index
2184:
2094:
4281:
3930:
Biria, Saeid (2017). "Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives".
3464:
Max, Claire Ellen; Arons, Jonathan; Langdon, A. Bruce (1974). "Self-Modulation and Self-Focusing of
Electromagnetic Waves in Plasmas".
3620:
Del Pizzo, V.; Luther-Davies, B.; Siegrist, M. R. (1979). "Self-focussing of a laser beam in a multiply ionized, absorbing plasma".
2831:
Rashidian Vaziri, M R (2013). "Describing the propagation of intense laser pulses in nonlinear Kerr media using the ducting model".
4018:
Yamashita, T.; Kagami, M. (2005). "Fabrication of light-induced self-written waveguides with a W-shaped refractive index profile".
3236:
Okulov, A Yu; Oraevskiĭ, A N (1988). "Compensation of self-focusing distortions in quasiresonant amplification of a light pulse".
1972:. Generalization of this link between Bespalov-Talanov increments and filament size in gain medium as a function of linear gain
47:
intensity acts as a focusing lens for an electromagnetic wave characterized by an initial transverse intensity gradient, as in a
2874:
Moll, K. D.; Gaeta, Alexander L.; Fibich, Gadi (2003). "Self-Similar
Optical Wave Collapse: Observation of the Townes Profile".
2743:
Garmire, E.; Chiao, R. Y.; Townes, C. H. (1966). "Dynamics and Characteristics of the Self-Trapping of Intense Light Beams".
178:
Self-focusing beyond a threshold of power can lead to laser collapse and damage to the medium, which occurs if the radiation
2574:
Rashidian Vaziri, M.R. (2015). "Comment on 'Nonlinear refraction measurements of materials using the moiré deflectometry'".
1975:
2026:
68:
Kerr-induced self-focusing was first predicted in the 1960s and experimentally verified by studying the interaction of
304:
2920:
Fibich, Gadi; Gaeta, Alexander L. (2000). "Critical power for self-focusing in bulk media and in hollow waveguides".
3698:
Sun, Guo-Zheng; Ott, Edward; Lee, Y. C.; Guzdar, Parvez (1987). "Self-focusing of short intense pulses in plasmas".
2468:
later observed. Self-focusing can also be observed in wide-area beams, wherein the beam undergoes filamentation, or
1316:
1447:
4306:
4301:
40:
382:
3542:
Kaw, P.; Schmidt, G.; Wilcox, T. (1973). "Filamentation and trapping of electromagnetic radiation in plasmas".
2469:
24:
is focused as in a convex lens. In self-focusing, the refractive index gradient is induced by the light itself.
2708:
Lallemand, P.; Bloembergen, N. (1965). "Self-Focusing of Laser Beams and Stimulated Raman Gain in Liquids".
3733:
Malka, V; Faure, J; Glinec, Y; Lifschitz, A.F (2006). "Laser-plasma accelerator: Status and perspectives".
2077:
Relativistic self-focusing is caused by the mass increase of electrons travelling at speed approaching the
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21:
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Mourou, Gerard A.; Tajima, Toshiki; Bulanov, Sergei V. (2006). "Optics in the relativistic regime".
99:
2254:
164:
73:
4233:
Askadskii, A.A (1990). "Influence of crosslinking density on the properties of polymer networks".
3735:
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
3429:
Perkins, F. W.; Valeo, E. J. (1974). "Thermal Self-Focusing of Electromagnetic Waves in Plasmas".
1812:
288:≈ 2.4 GW, corresponding to an energy of about 0.3 mJ for a pulse duration of 100 fs. For silica, n
4043:
3871:
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Khrapko, Rostislav; Lai, Changyi; Casey, Julie; Wood, William A.; Borrelli, Nicholas F. (2014).
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2179:
1306:{\displaystyle \sigma (\omega )={\frac {\sigma _{0}}{1+T_{2}^{2}(\omega _{0}-\omega )^{2}}}}
317:
36:
32:
3272:
2610:
1965:{\displaystyle h^{2}=\kappa ^{2}(n_{2}|E({\vec {\mathbf {r} }},t)|^{2}-\kappa ^{2}/4k^{2})}
1392:
1365:
2477:
179:
53:
3969:
3198:
Cerullo, Giulio; De Silvestri, Sandro (2003). "Ultrafast optical parametric amplifiers".
2852:
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3649:
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Couairon, A; Mysyrowicz, A (2007). "Femtosecond filamentation in transparent media".
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2430:
270:
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3875:
3770:
3257:
3184:
3098:
2635:
Chiao, R. Y.; Garmire, E.; Townes, C. H. (1964). "Self-Trapping of Optical Beams".
3133:
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is governed in gain medium by the nonlinear Schrödinger-Frantz-Nodvik equation.
320:, parametric generation, and many areas of laser-matter interaction in general.
3485:
2764:
2656:
4273:
3382:
Mori, W. B.; Joshi, C.; Dawson, J. M.; Forslund, D. W.; Kindel, J. M. (1988).
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265:
69:
4219:
4141:
4078:
2522:
2472:, spontaneous dividing into a multitude of microscale self-focused beams, or
4039:
3082:
2992:
2773:
253:{\displaystyle P_{\text{cr}}=\alpha {\frac {\lambda ^{2}}{4\pi n_{0}n_{2}}}}
4176:
4113:
4004:
3970:"Self-focusing and self-trapping of optical beams upon photopolymerization"
3951:
3762:
3754:
3415:
3368:
3324:
3176:
3090:
3036:
2949:
2903:
2817:
2243:{\displaystyle \omega _{p}={\sqrt {\frac {ne^{2}}{\gamma m\epsilon _{0}}}}}
2788:
Gaeta, Alexander L. (2000). "Catastrophic Collapse of Ultrashort Pulses".
2159:{\displaystyle n_{rel}={\sqrt {1-{\frac {\omega _{p}^{2}}{\omega ^{2}}}}}}
3996:
3866:
3499:
Pukhov, Alexander (2003). "Strong field interaction of laser radiation".
3168:
3028:
2941:
2611:"Cerenkov Radiation and Transition Radiation from Electromagnetic Waves"
3641:
3384:"Evolution of self-focusing of intense electromagnetic waves in plasma"
4105:
3943:
3915:
3890:
3822:
3813:
3684:
3563:
3219:
159:
are the linear and non-linear components of the refractive index, and
16:
3719:
3383:
60:
main cases are Kerr-induced self-focusing and plasma self-focusing.
1416:
are longitudinal and transverse lifetimes of two-level medium and
332:
two-level atoms may focus or defocus light when carrier frequency
48:
3891:"Accumulated self-focusing of ultraviolet light in silica glass"
1789:
The rate of the perturbation growth or instability increment
2971:
by use of unfocused high-intensity femtosecond laser pulses".
2509:
Cumberbatch, E. (1970). "Self-focusing in Non-linear Optics".
3273:"Filamentary Structure of Light Beams in Nonlinear Liquids"
284:≈ 4×10 m/W for λ = 800 nm, and the critical power is P
1362:
is the population inversion density before pulse arrival,
2673:
Kelley, P. L. (1965). "Self-Focusing of Optical Beams".
2437:
the speed of light, ω the radiation angular frequency,
379:. Laser pulse propagation with slowly varying envelope
4264:
Carrigan, Richard A.; Ellison, James A., eds. (1987).
352:
is detuned downward or upward the center of gain line
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43:. A medium whose refractive index increases with the
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a Townes profile regardless of their initial shape.
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2450:laser-fusion schemes and high harmonic generation.
2016:{\displaystyle {\sigma N({\vec {\mathbf {r} }},t)}}
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2058:{\displaystyle \delta \omega =\omega _{0}-\omega }
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2015:
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72:with glasses and liquids. Its origin lies in the
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2463:Self-focusing in soft matter and polymer systems
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2615:Journal of Experimental and Theoretical Physics
1355:{\displaystyle {N_{0}}({\vec {\mathbf {r} }})}
4059:
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2253:Ponderomotive self-focusing is caused by the
2081:, which modifies the plasma refractive index
1444:The laser beam with a smooth spatial profile
8:
2534:
2532:
1485:{\displaystyle {E}({\vec {\mathbf {r} }},t)}
3968:Kewitsch, Anthony S.; Yariv, Amnon (1996).
2973:Journal of the Optical Society of America B
2630:
2628:
2476:. The balance of self-focusing and natural
324:Self-focusing and defocusing in gain medium
1313:is the stimulated emission cross section,
418:{\displaystyle E({\vec {\mathbf {r} }},t)}
316:in transparent media, self-compression of
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241:
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81:
4094:Journal of the American Chemical Society
3839:"Relativistic laser plasma interactions"
15:
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3846:Journal of Physics D: Applied Physics
3787:"Review of progress in Fast Ignition"
3579:Journal of Physics D: Applied Physics
3238:Soviet Journal of Quantum Electronics
7:
4130:The Journal of Physical Chemistry C
4067:The Journal of Physical Chemistry C
448:is detuned downward or upward from
182:is greater than the critical power
4268:. NATO ASI Series. Vol. 165.
3271:Bespalov, VI; Talanov, VI (1966).
2511:IMA Journal of Applied Mathematics
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35:process induced by the change in
3200:Review of Scientific Instruments
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39:of materials exposed to intense
4020:Journal of Lightwave Technology
3258:10.1070/QE1988v018n02ABEH011482
2178:the relativistically corrected
3501:Reports on Progress in Physics
2853:10.1088/1054-660X/23/10/105401
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854:
835:
823:
814:
802:
791:
757:
745:
734:
718:
713:
701:
690:
683:
657:
645:
634:
583:
571:
560:
520:
508:
497:
412:
400:
389:
138:{\displaystyle n=n_{0}+n_{2}I}
1:
3134:10.1016/j.physrep.2006.12.005
2896:10.1103/PhysRevLett.90.203902
1809:is linked with filament size
4247:10.1016/0032-3950(90)90361-9
4212:10.1021/acs.macromol.7b00484
4169:10.1021/acsmacrolett.6b00659
2596:10.1016/j.optcom.2014.09.017
1832:{\displaystyle \kappa ^{-1}}
96:as described by the formula
3451:10.1103/PhysRevLett.32.1234
3408:10.1103/PhysRevLett.60.1298
3361:10.1103/PhysRevLett.74.2953
3317:10.1103/PhysRevLett.68.2309
2810:10.1103/PhysRevLett.84.3582
2730:10.1103/PhysRevLett.15.1010
2695:10.1103/PhysRevLett.15.1005
468:{\displaystyle \omega _{0}}
372:{\displaystyle \omega _{0}}
305:chirped pulse amplification
4328:
3858:10.1088/0022-3727/36/8/202
3837:Umstadter, Donald (2003).
3599:10.1088/0022-3727/12/8/005
3521:10.1088/0034-4885/66/1/202
3486:10.1103/PhysRevLett.33.209
2765:10.1103/PhysRevLett.16.347
2657:10.1103/PhysRevLett.13.479
2088:according to the equation
64:Kerr-induced self-focusing
4274:10.1007/978-1-4757-6394-2
2609:Askar'yan, G. A. (1962).
2561:10.1103/RevModPhys.78.309
2541:Reviews of Modern Physics
2454:Accumulated self-focusing
2441:the electron charge and ω
2170:where ω is the radiation
1436:is the propagation axis.
264:where λ is the radiation
41:electromagnetic radiation
4142:10.1021/acs.jpcc.5b07117
4079:10.1021/acs.jpcc.5b11377
2065:had been realized in .
167:of the radiation. Since
20:Light passing through a
4266:Relativistic Channeling
4235:Polymer Science U.S.S.R
4040:10.1109/JLT.2005.850783
3895:Applied Physics Letters
3466:Physical Review Letters
3431:Physical Review Letters
3388:Physical Review Letters
3341:Physical Review Letters
3297:Physical Review Letters
3083:10.1126/science.1085020
2993:10.1364/JOSAB.14.000650
2876:Physical Review Letters
2790:Physical Review Letters
2745:Physical Review Letters
2710:Physical Review Letters
2675:Physical Review Letters
2637:Physical Review Letters
441:{\displaystyle \omega }
345:{\displaystyle \omega }
330:homogeneously broadened
318:ultrashort laser pulses
3755:10.1098/rsta.2005.1725
2523:10.1093/imamat/6.3.250
2481:photo-polymerization.
2470:Modulation Instability
2412:
2244:
2160:
2059:
2017:
1966:
1833:
1803:
1780:
1486:
1430:
1410:
1383:
1356:
1307:
1207:
992:
768:
469:
442:
419:
373:
346:
328:Kelley predicted that
254:
139:
90:
25:
2576:Optics Communications
2413:
2245:
2161:
2060:
2018:
1967:
1839:via simple equation:
1834:
1804:
1781:
1487:
1431:
1411:
1409:{\displaystyle T_{2}}
1384:
1382:{\displaystyle T_{1}}
1357:
1308:
1208:
993:
769:
470:
443:
420:
374:
347:
310:Kerr-lens modelocking
255:
140:
91:
19:
3997:10.1364/ol.21.000024
3169:10.1364/OL.31.000274
3029:10.1364/OL.28.001796
2942:10.1364/OL.25.000335
2491:Filament propagation
2267:
2185:
2095:
2069:Plasma self-focusing
2027:
1976:
1843:
1813:
1793:
1497:
1448:
1420:
1393:
1366:
1317:
1219:
1003:
779:
482:
452:
432:
383:
356:
336:
189:
100:
80:
4204:2017MaMol..50.3617B
4032:2005JLwT...23.2542Y
3989:1996OptL...21...24K
3907:2014ApPhL.105x4110K
3806:2005PhPl...12e7305T
3747:2006RSPTA.364..601M
3712:1987PhFl...30..526S
3677:2002PhPl....9..756F
3634:1979ApPhy..18..199D
3591:1979JPhD...12.1261D
3556:1973PhFl...16.1522K
3513:2003RPPh...66...47P
3478:1974PhRvL..33..209M
3443:1974PhRvL..32.1234P
3400:1988PhRvL..60.1298M
3353:1995PhRvL..74.2953M
3309:1992PhRvL..68.2309B
3250:1988QuEle..18..233O
3212:2003RScI...74....1C
3161:2006OptL...31..274S
3126:2007PhR...441...47C
3065:2003Sci...301...61K
3021:2003OptL...28.1796G
2985:1997JOSAB..14..650N
2934:2000OptL...25..335F
2888:2003PhRvL..90t3902M
2845:2013LaPhy..23j5401R
2802:2000PhRvL..84.3582G
2757:1966PhRvL..16..347G
2722:1965PhRvL..15.1010L
2687:1965PhRvL..15.1005K
2649:1964PhRvL..13..479C
2588:2015OptCo.357..200R
2553:2006RvMP...78..309M
2350:
2303:
2255:ponderomotive force
2141:
1645:
1270:
920:
630:
314:laser filamentation
74:optical Kerr effect
22:gradient-index lens
3794:Physics of Plasmas
3665:Physics of Plasmas
3642:10.1007/BF00934416
2408:
2336:
2289:
2240:
2156:
2127:
2055:
2013:
1962:
1829:
1799:
1776:
1631:
1482:
1426:
1406:
1379:
1352:
1303:
1256:
1203:
988:
906:
764:
616:
465:
438:
415:
369:
342:
250:
135:
86:
33:non-linear optical
26:
4283:978-1-4419-3207-5
4157:ACS Macro Letters
4106:10.1021/ja068967b
3944:10.1063/1.5001821
3916:10.1063/1.4904098
3814:10.1063/1.1871246
3700:Physics of Fluids
3685:10.1063/1.1447556
3564:10.1063/1.1694552
3544:Physics of Fluids
3394:(13): 1298–1301.
3347:(15): 2953–2956.
3303:(15): 2309–2312.
3220:10.1063/1.1523642
2681:(26): 1005–1008.
2405:
2400:
2382:
2352:
2238:
2237:
2172:angular frequency
2154:
2152:
2000:
1904:
1802:{\displaystyle h}
1763:
1719:
1663:
1629:
1611:
1589:
1561:
1548:
1526:
1470:
1429:{\displaystyle z}
1346:
1301:
1176:
1142:
1108:
1091:
1054:
1032:
983:
951:
890:
821:
805:
748:
704:
648:
614:
596:
574:
546:
533:
511:
403:
248:
199:
89:{\displaystyle n}
4319:
4307:Plasma phenomena
4302:Nonlinear optics
4287:
4251:
4250:
4230:
4224:
4223:
4198:(9): 3617–3626.
4187:
4181:
4180:
4152:
4146:
4145:
4124:
4118:
4117:
4089:
4083:
4082:
4061:
4052:
4051:
4015:
4009:
4008:
3974:
3965:
3956:
3955:
3927:
3921:
3920:
3918:
3886:
3880:
3879:
3869:
3843:
3834:
3828:
3827:
3825:
3791:
3781:
3775:
3774:
3741:(1840): 601–10.
3730:
3724:
3723:
3720:10.1063/1.866349
3695:
3689:
3688:
3660:
3654:
3653:
3617:
3611:
3610:
3574:
3568:
3567:
3539:
3533:
3532:
3496:
3490:
3489:
3461:
3455:
3454:
3426:
3420:
3419:
3379:
3373:
3372:
3335:
3329:
3328:
3291:
3285:
3284:
3268:
3262:
3261:
3233:
3224:
3223:
3195:
3189:
3188:
3144:
3138:
3137:
3109:
3103:
3102:
3076:
3074:10.1.1.1028.4581
3047:
3041:
3040:
3003:
2997:
2996:
2960:
2954:
2953:
2917:
2908:
2907:
2871:
2865:
2864:
2828:
2822:
2821:
2785:
2779:
2778:
2776:
2774:2060/19660014476
2740:
2734:
2733:
2705:
2699:
2698:
2670:
2661:
2660:
2632:
2623:
2622:
2606:
2600:
2599:
2571:
2565:
2564:
2536:
2527:
2526:
2506:
2417:
2415:
2414:
2409:
2407:
2406:
2403:
2398:
2397:
2396:
2391:
2390:
2383:
2381:
2380:
2368:
2366:
2365:
2353:
2351:
2349:
2344:
2335:
2334:
2324:
2323:
2322:
2313:
2312:
2302:
2297:
2287:
2282:
2281:
2249:
2247:
2246:
2241:
2239:
2236:
2235:
2234:
2218:
2217:
2216:
2203:
2202:
2197:
2196:
2180:plasma frequency
2165:
2163:
2162:
2157:
2155:
2153:
2151:
2150:
2140:
2135:
2126:
2118:
2113:
2112:
2064:
2062:
2061:
2056:
2048:
2047:
2022:
2020:
2019:
2014:
2012:
2002:
2001:
1996:
1991:
1971:
1969:
1968:
1963:
1958:
1957:
1945:
1940:
1939:
1927:
1926:
1921:
1906:
1905:
1900:
1895:
1886:
1881:
1880:
1868:
1867:
1855:
1854:
1838:
1836:
1835:
1830:
1828:
1827:
1808:
1806:
1805:
1800:
1785:
1783:
1782:
1777:
1775:
1765:
1764:
1759:
1754:
1748:
1742:
1741:
1736:
1721:
1720:
1715:
1710:
1701:
1696:
1695:
1665:
1664:
1659:
1654:
1644:
1639:
1630:
1628:
1617:
1612:
1610:
1602:
1601:
1591:
1590:
1585:
1580:
1574:
1564:
1562:
1554:
1549:
1547:
1539:
1538:
1528:
1527:
1522:
1517:
1511:
1501:
1491:
1489:
1488:
1483:
1472:
1471:
1466:
1461:
1455:
1435:
1433:
1432:
1427:
1415:
1413:
1412:
1407:
1405:
1404:
1388:
1386:
1385:
1380:
1378:
1377:
1361:
1359:
1358:
1353:
1348:
1347:
1342:
1337:
1331:
1330:
1329:
1312:
1310:
1309:
1304:
1302:
1300:
1299:
1298:
1283:
1282:
1269:
1264:
1248:
1247:
1238:
1212:
1210:
1209:
1204:
1199:
1198:
1193:
1178:
1177:
1172:
1167:
1158:
1144:
1143:
1138:
1133:
1109:
1107:
1106:
1097:
1093:
1092:
1087:
1082:
1076:
1075:
1074:
1063:
1055:
1053:
1045:
1044:
1034:
1033:
1028:
1023:
1017:
1007:
997:
995:
994:
989:
984:
982:
981:
976:
967:
966:
957:
952:
950:
949:
944:
935:
934:
925:
919:
914:
902:
892:
891:
886:
881:
875:
866:
865:
847:
846:
822:
817:
807:
806:
801:
796:
783:
773:
771:
770:
765:
760:
750:
749:
744:
739:
733:
727:
726:
721:
706:
705:
700:
695:
686:
681:
680:
650:
649:
644:
639:
629:
624:
615:
613:
602:
597:
595:
587:
586:
576:
575:
570:
565:
559:
549:
547:
539:
534:
532:
524:
523:
513:
512:
507:
502:
496:
486:
474:
472:
471:
466:
464:
463:
447:
445:
444:
439:
424:
422:
421:
416:
405:
404:
399:
394:
378:
376:
375:
370:
368:
367:
351:
349:
348:
343:
259:
257:
256:
251:
249:
247:
246:
245:
236:
235:
219:
218:
209:
201:
200:
197:
144:
142:
141:
136:
131:
130:
118:
117:
95:
93:
92:
87:
37:refractive index
4327:
4326:
4322:
4321:
4320:
4318:
4317:
4316:
4292:
4291:
4290:
4284:
4263:
4259:
4254:
4232:
4231:
4227:
4189:
4188:
4184:
4163:(11): 1237–41.
4154:
4153:
4149:
4126:
4125:
4121:
4100:(15): 4738–46.
4091:
4090:
4086:
4063:
4062:
4055:
4017:
4016:
4012:
3972:
3967:
3966:
3959:
3929:
3928:
3924:
3888:
3887:
3883:
3841:
3836:
3835:
3831:
3789:
3783:
3782:
3778:
3732:
3731:
3727:
3697:
3696:
3692:
3662:
3661:
3657:
3622:Applied Physics
3619:
3618:
3614:
3576:
3575:
3571:
3541:
3540:
3536:
3498:
3497:
3493:
3463:
3462:
3458:
3428:
3427:
3423:
3381:
3380:
3376:
3337:
3336:
3332:
3293:
3292:
3288:
3270:
3269:
3265:
3235:
3234:
3227:
3197:
3196:
3192:
3146:
3145:
3141:
3120:(2–4): 47–189.
3114:Physics Reports
3111:
3110:
3106:
3049:
3048:
3044:
3005:
3004:
3000:
2970:
2966:
2962:
2961:
2957:
2919:
2918:
2911:
2873:
2872:
2868:
2830:
2829:
2825:
2787:
2786:
2782:
2742:
2741:
2737:
2707:
2706:
2702:
2672:
2671:
2664:
2634:
2633:
2626:
2608:
2607:
2603:
2573:
2572:
2568:
2538:
2537:
2530:
2508:
2507:
2503:
2499:
2487:
2478:beam divergence
2465:
2456:
2444:
2427:
2384:
2372:
2326:
2325:
2314:
2304:
2288:
2270:
2265:
2264:
2226:
2219:
2208:
2204:
2188:
2183:
2182:
2177:
2142:
2098:
2093:
2092:
2086:
2071:
2039:
2025:
2024:
1974:
1973:
1949:
1931:
1916:
1872:
1859:
1846:
1841:
1840:
1816:
1811:
1810:
1791:
1790:
1731:
1687:
1621:
1603:
1565:
1540:
1502:
1495:
1494:
1446:
1445:
1442:
1418:
1417:
1396:
1391:
1390:
1369:
1364:
1363:
1321:
1315:
1314:
1290:
1274:
1249:
1239:
1217:
1216:
1188:
1098:
1066:
1064:
1046:
1008:
1001:
1000:
968:
958:
936:
926:
857:
838:
784:
777:
776:
716:
672:
606:
588:
550:
525:
487:
480:
479:
455:
450:
449:
430:
429:
381:
380:
359:
354:
353:
334:
333:
326:
299:
295:
291:
287:
283:
279:
237:
227:
220:
210:
192:
187:
186:
173:
158:
151:
122:
109:
98:
97:
78:
77:
66:
54:Gurgen Askaryan
12:
11:
5:
4325:
4323:
4315:
4314:
4309:
4304:
4294:
4293:
4289:
4288:
4282:
4260:
4258:
4255:
4253:
4252:
4241:(10): 2061–9.
4225:
4192:Macromolecules
4182:
4147:
4119:
4084:
4073:(8): 4517–28.
4053:
4010:
3977:Optics Letters
3957:
3938:(10): 104611.
3922:
3901:(24): 244110.
3881:
3852:(8): R151–65.
3829:
3776:
3725:
3690:
3655:
3628:(2): 199–204.
3612:
3585:(8): 1261–73.
3569:
3534:
3491:
3456:
3421:
3374:
3330:
3286:
3283:(12): 307–310.
3263:
3225:
3190:
3149:Optics Letters
3139:
3104:
3059:(5629): 61–4.
3042:
3015:(19): 1796–8.
3009:Optics Letters
2998:
2968:
2964:
2955:
2922:Optics Letters
2909:
2882:(20): 203902.
2866:
2839:(10): 105401.
2823:
2796:(16): 3582–5.
2780:
2735:
2700:
2662:
2624:
2601:
2566:
2528:
2500:
2498:
2495:
2494:
2493:
2486:
2483:
2464:
2461:
2455:
2452:
2442:
2425:
2420:
2419:
2395:
2389:
2379:
2375:
2371:
2364:
2359:
2356:
2348:
2343:
2339:
2333:
2329:
2321:
2317:
2311:
2307:
2301:
2296:
2292:
2285:
2280:
2277:
2273:
2233:
2229:
2225:
2222:
2215:
2211:
2207:
2200:
2195:
2191:
2175:
2168:
2167:
2149:
2145:
2139:
2134:
2130:
2124:
2121:
2116:
2111:
2108:
2105:
2101:
2084:
2079:speed of light
2070:
2067:
2054:
2051:
2046:
2042:
2038:
2035:
2032:
2011:
2008:
2005:
1999:
1995:
1988:
1985:
1982:
1961:
1956:
1952:
1948:
1944:
1938:
1934:
1930:
1925:
1920:
1915:
1912:
1909:
1903:
1899:
1892:
1889:
1885:
1879:
1875:
1871:
1866:
1862:
1858:
1853:
1849:
1826:
1823:
1819:
1798:
1774:
1771:
1768:
1762:
1758:
1751:
1747:
1740:
1735:
1730:
1727:
1724:
1718:
1714:
1707:
1704:
1700:
1694:
1690:
1686:
1683:
1680:
1677:
1674:
1671:
1668:
1662:
1658:
1651:
1648:
1643:
1638:
1634:
1627:
1624:
1620:
1615:
1609:
1606:
1600:
1597:
1594:
1588:
1584:
1577:
1573:
1568:
1560:
1557:
1552:
1546:
1543:
1537:
1534:
1531:
1525:
1521:
1514:
1510:
1505:
1481:
1478:
1475:
1469:
1465:
1458:
1454:
1441:
1438:
1425:
1403:
1399:
1376:
1372:
1351:
1345:
1341:
1334:
1328:
1324:
1297:
1293:
1289:
1286:
1281:
1277:
1273:
1268:
1263:
1259:
1255:
1252:
1246:
1242:
1236:
1233:
1230:
1227:
1224:
1202:
1197:
1192:
1187:
1184:
1181:
1175:
1171:
1164:
1161:
1157:
1153:
1150:
1147:
1141:
1137:
1130:
1127:
1124:
1121:
1118:
1115:
1112:
1105:
1101:
1096:
1090:
1086:
1079:
1073:
1069:
1061:
1058:
1052:
1049:
1043:
1040:
1037:
1031:
1027:
1020:
1016:
1011:
987:
980:
975:
972:
965:
961:
955:
948:
943:
940:
933:
929:
923:
918:
913:
909:
905:
901:
898:
895:
889:
885:
878:
874:
869:
864:
860:
856:
853:
850:
845:
841:
837:
834:
831:
828:
825:
820:
816:
813:
810:
804:
800:
793:
790:
787:
763:
759:
756:
753:
747:
743:
736:
732:
725:
720:
715:
712:
709:
703:
699:
692:
689:
685:
679:
675:
671:
668:
665:
662:
659:
656:
653:
647:
643:
636:
633:
628:
623:
619:
612:
609:
605:
600:
594:
591:
585:
582:
579:
573:
569:
562:
558:
553:
545:
542:
537:
531:
528:
522:
519:
516:
510:
506:
499:
495:
490:
462:
458:
437:
414:
411:
408:
402:
398:
391:
388:
366:
362:
341:
325:
322:
297:
293:
289:
285:
281:
277:
262:
261:
244:
240:
234:
230:
226:
223:
217:
213:
207:
204:
195:
171:
156:
149:
134:
129:
125:
121:
116:
112:
108:
105:
85:
65:
62:
45:electric field
13:
10:
9:
6:
4:
3:
2:
4324:
4313:
4312:Laser science
4310:
4308:
4305:
4303:
4300:
4299:
4297:
4285:
4279:
4275:
4271:
4267:
4262:
4261:
4256:
4248:
4244:
4240:
4236:
4229:
4226:
4221:
4217:
4213:
4209:
4205:
4201:
4197:
4193:
4186:
4183:
4178:
4174:
4170:
4166:
4162:
4158:
4151:
4148:
4143:
4139:
4136:(35): 20606.
4135:
4131:
4123:
4120:
4115:
4111:
4107:
4103:
4099:
4095:
4088:
4085:
4080:
4076:
4072:
4068:
4060:
4058:
4054:
4049:
4045:
4041:
4037:
4033:
4029:
4026:(8): 2542–8.
4025:
4021:
4014:
4011:
4006:
4002:
3998:
3994:
3990:
3986:
3982:
3978:
3971:
3964:
3962:
3958:
3953:
3949:
3945:
3941:
3937:
3933:
3926:
3923:
3917:
3912:
3908:
3904:
3900:
3896:
3892:
3885:
3882:
3877:
3873:
3868:
3867:2027.42/48918
3863:
3859:
3855:
3851:
3847:
3840:
3833:
3830:
3824:
3819:
3815:
3811:
3807:
3803:
3800:(5): 057305.
3799:
3795:
3788:
3780:
3777:
3772:
3768:
3764:
3760:
3756:
3752:
3748:
3744:
3740:
3736:
3729:
3726:
3721:
3717:
3713:
3709:
3705:
3701:
3694:
3691:
3686:
3682:
3678:
3674:
3670:
3666:
3659:
3656:
3651:
3647:
3643:
3639:
3635:
3631:
3627:
3623:
3616:
3613:
3608:
3604:
3600:
3596:
3592:
3588:
3584:
3580:
3573:
3570:
3565:
3561:
3557:
3553:
3549:
3545:
3538:
3535:
3530:
3526:
3522:
3518:
3514:
3510:
3507:(1): 47–101.
3506:
3502:
3495:
3492:
3487:
3483:
3479:
3475:
3471:
3467:
3460:
3457:
3452:
3448:
3444:
3440:
3436:
3432:
3425:
3422:
3417:
3413:
3409:
3405:
3401:
3397:
3393:
3389:
3385:
3378:
3375:
3370:
3366:
3362:
3358:
3354:
3350:
3346:
3342:
3334:
3331:
3326:
3322:
3318:
3314:
3310:
3306:
3302:
3298:
3290:
3287:
3282:
3278:
3274:
3267:
3264:
3259:
3255:
3251:
3247:
3243:
3239:
3232:
3230:
3226:
3221:
3217:
3213:
3209:
3205:
3201:
3194:
3191:
3186:
3182:
3178:
3174:
3170:
3166:
3162:
3158:
3154:
3150:
3143:
3140:
3135:
3131:
3127:
3123:
3119:
3115:
3108:
3105:
3100:
3096:
3092:
3088:
3084:
3080:
3075:
3070:
3066:
3062:
3058:
3054:
3046:
3043:
3038:
3034:
3030:
3026:
3022:
3018:
3014:
3010:
3002:
2999:
2994:
2990:
2986:
2982:
2979:(3): 650–60.
2978:
2974:
2959:
2956:
2951:
2947:
2943:
2939:
2935:
2931:
2927:
2923:
2916:
2914:
2910:
2905:
2901:
2897:
2893:
2889:
2885:
2881:
2877:
2870:
2867:
2862:
2858:
2854:
2850:
2846:
2842:
2838:
2834:
2833:Laser Physics
2827:
2824:
2819:
2815:
2811:
2807:
2803:
2799:
2795:
2791:
2784:
2781:
2775:
2770:
2766:
2762:
2758:
2754:
2750:
2746:
2739:
2736:
2731:
2727:
2723:
2719:
2715:
2711:
2704:
2701:
2696:
2692:
2688:
2684:
2680:
2676:
2669:
2667:
2663:
2658:
2654:
2650:
2646:
2642:
2638:
2631:
2629:
2625:
2620:
2616:
2612:
2605:
2602:
2597:
2593:
2589:
2585:
2581:
2577:
2570:
2567:
2562:
2558:
2554:
2550:
2546:
2542:
2535:
2533:
2529:
2524:
2520:
2517:(3): 250–62.
2516:
2512:
2505:
2502:
2496:
2492:
2489:
2488:
2484:
2482:
2479:
2475:
2471:
2462:
2460:
2453:
2451:
2447:
2440:
2436:
2432:
2431:electron mass
2428:
2393:
2377:
2373:
2369:
2357:
2354:
2346:
2341:
2337:
2331:
2327:
2319:
2315:
2309:
2305:
2299:
2294:
2290:
2283:
2278:
2275:
2271:
2263:
2262:
2261:
2258:
2256:
2251:
2231:
2227:
2223:
2220:
2213:
2209:
2205:
2198:
2193:
2189:
2181:
2173:
2147:
2143:
2137:
2132:
2128:
2122:
2119:
2114:
2109:
2106:
2103:
2099:
2091:
2090:
2089:
2087:
2080:
2075:
2068:
2066:
2052:
2049:
2044:
2040:
2036:
2033:
2030:
2023:and detuning
2006:
2003:
1983:
1980:
1954:
1950:
1946:
1942:
1936:
1932:
1928:
1923:
1910:
1907:
1887:
1877:
1873:
1864:
1860:
1856:
1851:
1847:
1824:
1821:
1817:
1796:
1787:
1769:
1766:
1745:
1738:
1725:
1722:
1702:
1692:
1688:
1684:
1681:
1678:
1675:
1669:
1666:
1646:
1641:
1625:
1622:
1618:
1613:
1607:
1595:
1592:
1571:
1558:
1555:
1550:
1544:
1532:
1529:
1508:
1476:
1473:
1452:
1440:Filamentation
1439:
1437:
1423:
1401:
1397:
1374:
1370:
1326:
1322:
1295:
1287:
1284:
1279:
1275:
1266:
1261:
1257:
1253:
1250:
1244:
1240:
1234:
1228:
1222:
1213:
1200:
1195:
1182:
1179:
1159:
1148:
1145:
1125:
1119:
1113:
1110:
1103:
1099:
1071:
1067:
1059:
1056:
1050:
1038:
1035:
1014:
998:
985:
978:
973:
963:
953:
946:
941:
931:
921:
916:
903:
896:
893:
872:
862:
858:
851:
848:
843:
839:
832:
829:
826:
818:
811:
808:
788:
785:
774:
761:
754:
751:
730:
723:
710:
707:
687:
677:
673:
669:
666:
663:
660:
654:
651:
631:
626:
610:
607:
603:
598:
592:
580:
577:
556:
543:
540:
535:
529:
517:
514:
493:
477:
460:
456:
435:
426:
409:
406:
386:
364:
360:
339:
331:
323:
321:
319:
315:
311:
306:
301:
274:
272:
271:Gaussian beam
267:
242:
238:
232:
228:
224:
221:
215:
211:
205:
202:
193:
185:
184:
183:
181:
176:
170:
166:
162:
155:
148:
132:
127:
123:
119:
114:
110:
106:
103:
83:
75:
71:
63:
61:
57:
55:
50:
46:
42:
38:
34:
30:
29:Self-focusing
23:
18:
4265:
4257:Bibliography
4238:
4234:
4228:
4195:
4191:
4185:
4160:
4156:
4150:
4133:
4129:
4122:
4097:
4093:
4087:
4070:
4066:
4023:
4019:
4013:
3980:
3976:
3935:
3931:
3925:
3898:
3894:
3884:
3849:
3845:
3832:
3797:
3793:
3779:
3738:
3734:
3728:
3703:
3699:
3693:
3668:
3664:
3658:
3625:
3621:
3615:
3582:
3578:
3572:
3547:
3543:
3537:
3504:
3500:
3494:
3469:
3465:
3459:
3437:(22): 1234.
3434:
3430:
3424:
3391:
3387:
3377:
3344:
3340:
3333:
3300:
3296:
3289:
3280:
3277:JETP Letters
3276:
3266:
3244:(2): 233–7.
3241:
3237:
3203:
3199:
3193:
3155:(2): 274–6.
3152:
3148:
3142:
3117:
3113:
3107:
3056:
3052:
3045:
3012:
3008:
3001:
2976:
2972:
2958:
2928:(5): 335–7.
2925:
2921:
2879:
2875:
2869:
2836:
2832:
2826:
2793:
2789:
2783:
2748:
2744:
2738:
2716:(26): 1010.
2713:
2709:
2703:
2678:
2674:
2640:
2636:
2618:
2614:
2604:
2579:
2575:
2569:
2544:
2540:
2514:
2510:
2504:
2466:
2457:
2448:
2438:
2434:
2423:
2421:
2259:
2252:
2169:
2082:
2076:
2072:
1788:
1443:
1214:
999:
775:
478:
427:
327:
302:
275:
273:α ≈ 1.8962.
263:
177:
168:
160:
153:
146:
67:
58:
28:
27:
3983:(1): 24–6.
3550:(9): 1522.
2643:(15): 479.
2621:(5): 943–6.
70:ruby lasers
4296:Categories
3823:11094/3277
3706:(2): 526.
3671:(3): 756.
3472:(4): 209.
3295:plasmas".
2751:(9): 347.
2547:(2): 309.
2497:References
300:≈ 2.8 MW.
292:≈ 1.453, n
276:For air, n
266:wavelength
4220:0024-9297
3650:122912958
3607:250749005
3529:250909633
3069:CiteSeerX
2861:250912159
2582:: 200–1.
2474:filaments
2374:ω
2370:ω
2355:≃
2338:ω
2316:ω
2228:ϵ
2221:γ
2190:ω
2144:ω
2129:ω
2123:−
2053:ω
2050:−
2041:ω
2034:ω
2031:δ
1998:→
1981:σ
1933:κ
1929:−
1902:→
1861:κ
1822:−
1818:κ
1761:→
1717:→
1661:→
1637:⊥
1633:∇
1605:∂
1587:→
1567:∂
1542:∂
1524:→
1504:∂
1468:→
1344:→
1288:ω
1285:−
1276:ω
1241:σ
1229:ω
1223:σ
1174:→
1140:→
1120:ω
1114:σ
1111:−
1089:→
1060:−
1048:∂
1030:→
1010:∂
971:∂
960:∂
939:∂
928:∂
912:⊥
908:∇
888:→
852:ω
849:−
840:ω
803:→
786:σ
746:→
702:→
646:→
622:⊥
618:∇
590:∂
572:→
552:∂
527:∂
509:→
489:∂
457:ω
436:ω
401:→
361:ω
340:ω
225:π
212:λ
206:α
165:intensity
4177:35614732
4114:17378567
4048:36961681
4005:19865292
3952:29092420
3876:10185064
3771:12223379
3763:16483951
3416:10037999
3369:10058066
3325:10045362
3206:(1): 1.
3185:12957688
3177:16441054
3099:37270331
3091:12843384
3037:14514104
2950:18059872
2904:12785895
2818:11019151
2485:See also
145:, where
4200:Bibcode
4028:Bibcode
3985:Bibcode
3903:Bibcode
3802:Bibcode
3743:Bibcode
3708:Bibcode
3673:Bibcode
3630:Bibcode
3587:Bibcode
3552:Bibcode
3509:Bibcode
3474:Bibcode
3439:Bibcode
3396:Bibcode
3349:Bibcode
3305:Bibcode
3246:Bibcode
3208:Bibcode
3157:Bibcode
3122:Bibcode
3061:Bibcode
3053:Science
3017:Bibcode
2981:Bibcode
2967:, and O
2930:Bibcode
2884:Bibcode
2841:Bibcode
2798:Bibcode
2753:Bibcode
2718:Bibcode
2683:Bibcode
2645:Bibcode
2584:Bibcode
2549:Bibcode
2429:is the
163:is the
4280:
4218:
4175:
4112:
4046:
4003:
3950:
3874:
3769:
3761:
3648:
3605:
3527:
3414:
3367:
3323:
3183:
3175:
3097:
3089:
3071:
3035:
2948:
2902:
2859:
2816:
2422:where
2399:
1215:where
280:≈ 1, n
4044:S2CID
3973:(PDF)
3932:Chaos
3872:S2CID
3842:(PDF)
3790:(PDF)
3767:S2CID
3646:S2CID
3603:S2CID
3525:S2CID
3181:S2CID
3095:S2CID
2857:S2CID
2174:and ω
428:When
180:power
49:laser
31:is a
4278:ISBN
4216:ISSN
4173:PMID
4110:PMID
4001:PMID
3948:PMID
3759:PMID
3412:PMID
3365:PMID
3321:PMID
3173:PMID
3087:PMID
3033:PMID
2946:PMID
2900:PMID
2814:PMID
2446:TW.
1389:and
152:and
4270:doi
4243:doi
4208:doi
4165:doi
4138:doi
4134:119
4102:doi
4098:129
4075:doi
4071:120
4036:doi
3993:doi
3940:doi
3911:doi
3899:105
3862:hdl
3854:doi
3818:hdl
3810:doi
3751:doi
3739:364
3716:doi
3681:doi
3638:doi
3595:doi
3560:doi
3517:doi
3482:doi
3447:doi
3404:doi
3357:doi
3313:doi
3254:doi
3216:doi
3165:doi
3130:doi
3118:441
3079:doi
3057:301
3025:doi
2989:doi
2938:doi
2892:doi
2849:doi
2806:doi
2769:hdl
2761:doi
2726:doi
2691:doi
2653:doi
2592:doi
2580:357
2557:doi
2519:doi
2085:rel
4298::
4276:.
4239:32
4237:.
4214:.
4206:.
4196:50
4194:.
4171:.
4159:.
4132:.
4108:.
4096:.
4069:.
4056:^
4042:.
4034:.
4024:23
4022:.
3999:.
3991:.
3981:21
3979:.
3975:.
3960:^
3946:.
3936:27
3934:.
3909:.
3897:.
3893:.
3870:.
3860:.
3850:36
3848:.
3844:.
3816:.
3808:.
3798:12
3796:.
3792:.
3765:.
3757:.
3749:.
3737:.
3714:.
3704:30
3702:.
3679:.
3667:.
3644:.
3636:.
3626:18
3624:.
3601:.
3593:.
3583:12
3581:.
3558:.
3548:16
3546:.
3523:.
3515:.
3505:66
3503:.
3480:.
3470:33
3468:.
3445:.
3435:32
3433:.
3410:.
3402:.
3392:60
3390:.
3386:.
3363:.
3355:.
3345:74
3343:.
3319:.
3311:.
3301:68
3299:.
3279:.
3275:.
3252:.
3242:18
3240:.
3228:^
3214:.
3204:74
3202:.
3179:.
3171:.
3163:.
3153:31
3151:.
3128:.
3116:.
3093:.
3085:.
3077:.
3067:.
3055:.
3031:.
3023:.
3013:28
3011:.
2987:.
2977:14
2975:.
2944:.
2936:.
2926:25
2924:.
2912:^
2898:.
2890:.
2880:90
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