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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 10 — May. 9, 2011
  • pp: 9118–9126
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Filamentation in air with ultrashort mid-infrared pulses

Bonggu Shim, Samuel E. Schrauth, and Alexander L. Gaeta  »View Author Affiliations


Optics Express, Vol. 19, Issue 10, pp. 9118-9126 (2011)
http://dx.doi.org/10.1364/OE.19.009118


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Abstract

We theoretically investigate filamentation of ultrashort laser pulses in air in the mid-infrared regime under conditions in which the group-velocity dispersion (GVD) is anomalous. When a high-power, ultra-short mid-infrared laser beam centered at 3.1-μm forms a filament, a spatial solitary wave is stabilized by the plasma formation and propagates several times its diffraction length. Compared with temporal self-compression in gases due to plasma formation and pulse splitting in the normal-GVD regime, the minimum achievable pulse duration (∼ 70 fs) is limited by the bandwidth of the anomalous-GVD region in air. For the relatively high powers, multiple pulse splitting due to the plasma effect and shock formation is observed, which is similar to that which occurs in solids. Our simulations show that the energy reservoir also plays a critical role for longer propagation of the air filament in the anomalous-GVD regime.

© 2011 OSA

1. Introduction

Self-channeling beams (i.e. filaments) in air with high-power, ultrashort pulses have been shown to propagate several diffraction lengths with little apparent change in the beam shape due to the balance between self-focusing and diffraction/plasma formation [1

1. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou,“Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett.20, 73–75 (1995), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-20-1-73. [CrossRef] [PubMed]

10

10. V. P. Kandidov, S. A. Shlenov, and O. G. Kosareva, “Filamentation of high-power femtosecond laser radiation,” Quantum Electron. 39, 205 (2009). [CrossRef]

]. These filaments have received significant attention due to applications to remote sensing [11

11. L. Wöste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, “Femtosecond atmospheric lamp,” Laser Optoelektron. 29, 51 (1997).

, 12

12. P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000). [CrossRef]

], lightning guiding [13

13. J.-C. Diels, R. Bernstein, K. Stahlkopf, and X. M. Zhao, “Lightning control with lasers,” Sci. Am. 277, 50–55 (1997). [CrossRef]

15

15. A. Houard, C. D’Amico, Y. Liu, Y. B. Andre, M. Franco, B. Prade, A. Mysyrowicz, E. Salmon, P. Pierlot, and L.-M. Cleon, “High current permanent discharges in air induced by femtosecond laser filamentation,” Appl. Phys. Lett. 90, 171501 (2007). [CrossRef]

], supercontinuum generation (SCG) [16

16. See, for example, The Supercontinuum Laser Source, ed. by R. R. Alfano (Springer-Verlag, 1989).

], pulse compression [17

17. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004). [CrossRef]

], and THz generation [18

18. C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007). [CrossRef] [PubMed]

]. Although several experimental [19

19. K. D. Moll and A. L. Gaeta, “Role of dispersion in multiple-collapse dynamics,” Opt. Lett.29, 995–997 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-9-995. [CrossRef] [PubMed]

21

21. M. A. Porras, A. Dubietis, A. Matijošius, R. Piskarskas, F. Bragheri, A. Averchi, and P. Di Trapani, “Characterization of conical emission of light filaments in media with anomalous dispersion,” J. Opt. Soc. Am. B24, 581–584 (2007), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-3-581. [CrossRef]

] and theoretical studies in solids [22

22. M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791 (1998). [CrossRef]

25

25. L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008). [CrossRef] [PubMed]

] for filamentation and soliton generation in the anomalous group-velocity dispersion (GVD) regime have been reported recently [26

26. Although 3-D optical bullets are predicted to be unstable and have not been experimentally observed, several approaches have been theoretically proposed recently. For example, see [27–30].

30

30. S. Chen and J. M. Dudley, “Spatiotemporal nonlinear optical self-similarity in three dimensions,” Phys. Rev. Lett. 102, 233903 (2009). [CrossRef] [PubMed]

], studies of air (or gas) filaments have been limited to the normal-GVD regime [25

25. L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008). [CrossRef] [PubMed]

, 31

31. I. G. Koprinkov, A. Suda, P. Wang, and K. Midorikawa, “Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847–3850 (2000). [CrossRef] [PubMed]

35

35. L. M. Kovachev, “Collapse arrest and self-guiding of femtosecond pulses,” Opt. Express15, 10318–10323 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-16-10318. [CrossRef] [PubMed]

]. Only recently has the ability of laser technology with difference-frequency generation (DFG) [36

36. P. Agostini and L. F. DiMauro, “Atoms in high intensity mid-infrared pulses,” Contemp. Phys. 49, 179 (2008). [CrossRef]

] and optical parametric chirped-pulse amplification (OPCPA) [37

37. O. Chalus, A. Thai, P. K. Bates, and J. Biegert, “Six-cycle mid-infrared source with 3.8 μJ at 100 kHz,” Opt. Lett.35, 3204–3206 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-19-3204. [CrossRef] [PubMed]

, 38

38. T. Popmintchev, M. Chen, P. Arpin, M. Gerrity, M. Seaberg, B. Zhang, D. Popmintchev, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuška, M. Murnane, and H. Kapteyn, “Bright coherent ultrafast X-rays from mid-IR lasers,” in High Intensity Lasers and High Field Phenomena, OSA Technical Digest (CD) (Optical Society of America, 2011), paper HThB5, http://www.opticsinfobase.org/abstract.cfm?URI=HILAS-2011-HThB5.

] been developed to produce > 100-GW pulses in the mid-infrared region where the GVD is anomalous, and investigations of self-focusing in air in the anomalous-GVD regime are now a possibility.

In this Letter, we present the first simulation results for air filamentation and spatial solitary-wave formation in the anomalous-GVD regime of air. When a high-power (> 100-GW), ultrashort pulse undergoes self-focusing due to the Kerr nonlinearity, multi-photon absorption (MPA) and plasma formation halt beam collapse. As a result, a spatial solitary wave is formed and stabilized during the filamentation process, and its shape can be maintained for several diffraction lengths. Although spectral broadening induced by phase modulation occurs, the relatively narrow bandwidth of the anomalous-GVD regime (approximately 200-nm) near 3-μm inhibits formation of a temporal solitary wave, which contrasts to the generation of few-cycle optical pulses predicted for solids in the broadband anomalous-GVD region [23

23. L. Bergé and S. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71, 065601 (2005). [CrossRef]

, 24

24. J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited with filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006). [CrossRef]

] and to pulse self-compression down to few-cycles which occurs via plasma formation and/or pulse splitting in gases for the normal-GVD regime [31

31. I. G. Koprinkov, A. Suda, P. Wang, and K. Midorikawa, “Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847–3850 (2000). [CrossRef] [PubMed]

, 32

32. A. L. Gaeta and F. W. Wise, Comment on “Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 87, 229401 (2001). [CrossRef] [PubMed]

, 39

33. L. Bergé and A. Couairon, “Gas-induced solitons,” Phys. Rev. Lett. 86, 1003–1006 (2001). [CrossRef] [PubMed]

44

44. F. Reiter, U. Graf, E. E. Serebryannikov, W. Schweinberger, M. Fiess, M. Schultze, A. M. Azzeer, R. Kienberger, F. Krausz, A. M. Zheltikov, and E. Goulielmakis, “Route to attosecond nonlinear spectroscopy,” Phys. Rev. Lett. 105, 243902 (2010). [CrossRef]

].

2. Simulation and refractive index of air

In our simulations, we use the radially-symmetric nonlinear envelope equation (NEE) in normalized units including diffraction, dispersion, self-focusing with the delayed Raman response, MPA, and plasma de-focusing and absorption, which is given as [23

23. L. Bergé and S. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71, 065601 (2005). [CrossRef]

, 43

43. L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, “Spectral reshaping and pulse compression via sequential filamentation in gases,” Opt. Express16, 390–401 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-390. [CrossRef] [PubMed]

, 45

45. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997). [CrossRef]

47

47. M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002). [CrossRef]

],
ψζ=i4(1+iωτpτ)12ψ+iLdfn=2n=6βnn!(iτpτ)nψ+i(1+iωτpτ)LdfLnl(|ψ|22+τp2τkτeτpτk(ττ)|ψ(τ)|2dτ)ψLdf2Lmpψ|ψ|2ητLdfLpl(i+1ωτc)η(ψ+τcψτpτ1iωτc),
(1)
where ψ is the field normalized by the peak input field amplitude A 0, ζ = z/Ldf is the propagation distance normalized by the diffraction length Ldf=n0πw02/λ0, n 0 is the refractive index of air, w 0 is the 1/e 2 spot size radius, λ 0 is the central wavelength, 2 is the transverse Laplacian, τ is the retarded time normalized by the 1/e 2 input pulse duration τp, βn is the nth-order dispersion parameter [48

48. We calculate the dispersion parameters up to sixth-order order since the formula for the refractive index of air (n0) is a function of the fifth-order Tayolor expansion in Ref. [49] and thus the wavelumber (k = ωn0/c) is a sixth-order function of the laser angular frequency.

], Lnl = c/(ωn 2 I 0) is the nonlinear length, n 2 is the nonlinear refractive index, I 0 = cn 0 |A 0 | 2 /2π is the peak input intensity, τk = 70 fs is the Raman relaxation time, Lmp=1/(β(m)I0(m1)) is the m-photon absorption length, β ( m =31) =3×10−384 cm59/W30 is the 31-photon absorption coefficient [7

7. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007). [CrossRef]

], Lpl = 2/(σρ 0 ωτc) is the plasma length, σ is the inverse bremsstrahlung cross section, ρ0=β(m)I0(m1)τp/(mh¯ω) is the total electron density that would be produced by the input laser pulse via multi-photon ionization, τc is the electron-ion collision time, η = ρe/ρ 0 is the normalized electron density. The operator (1 + i∂/ωτp∂τ) accounts for space-time focusing in the diffraction term and self-steepening in the self-focusing term. The plasma is generated by multi-photon ionization and avalanche ionization, and the electron density satisfies the equation,
ητ=|ψ|2m+αη|ψ|2,
(2)
where α=σI0τp/(n02Eg) is the avalanche ionization coefficient, and Eg = 12.1 eV the band-gap energy for oxygen.

Fig. 1 Calculated group-velocity dispersion (GVD) for different values of the humidity using the Taylor expansion formula based on Ref. [49] at T = 17.5°C, p = 101325 Pa (standard atmospheric pressure).

3. Results and discussion

Figure 2(a) shows a plot of the peak intensity as a function of normalized distance for different input powers. Here we assume the collimated, initial spot size (1/e 2 radius) is 12-mm and the initial pulse duration (FWHM) is 150 fs such that Ldf = 146-m approximately matches with Lds=τp2/β2=306-m. As the peak intensity increases due to self-focusing and anomalous GVD, a low-density plasma is created as shown in Fig. 2(b). At that point, plasma absorption and de-focusing combined with MPA arrest beam collapse so that an air filament with I = 5 × 1012 W/cm2 forms and propagates stably about 0.03, 0.05 and 0.06 times the diffraction length of the input beam for P/Pcr = 2, 3 and 4. For increasing powers, collapse occurs at shorter distances, and the filament length is extended. According to the calculated beam diameter (FWHM) [Figs. 2(c)], the filament maintains its diameter (1.4-mm FWHM), which is 1/10 that of the initial beam and thus a spatial solitary wave is generated during filamentation, propagating for at least 3 times of the diffraction length based on its minimum spot size. As is shown in Fig. 2(d), although the pulse duration initially decreases due to anomalous GVD, it suddenly increases near the peak intensity due to spectral broadening into the normal GVD regime via self-phase modulation and slowly decreases again since the field components at wavelengths in the anomalous GVD regime undergo compression as the pulse propagates. Therefore, compared with calculated few-cycle spatio-temporal solitary waves in the anomalous-GVD regime for solids [23

23. L. Bergé and S. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71, 065601 (2005). [CrossRef]

, 24

24. J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited with filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006). [CrossRef]

], a solitary wave is not generated near 3.1-μm due to the relatively narrow bandwidth of the anomalous-GVD region.

Fig. 2 Calculated (a) peak intensity, (b) peak plasma density, (c) beam diameter (FWHM) of the fluence Fr =∫I(r,t)dt and (d) pulse duration (FWHM) of the fluence Ft =∫I(r,t)rdr as functions of normalized propagation distance for various input powers.

Figure 3(a) shows examples of the spatio-temporal intensity distributions for various propagation distances with P/Pcr = 2. As the beam self-focuses, self-steepening and space-time focusing combined with third-order dispersion generate a relatively steep edge at the rear of the pulse (i.e., an optical shock) and push the pulse toward positive times [23

23. L. Bergé and S. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71, 065601 (2005). [CrossRef]

, 24

24. J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited with filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006). [CrossRef]

, 46

46. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000). [CrossRef] [PubMed]

, 54

54. A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998). [CrossRef]

, 55

55. G. P. AgrawalNolinear Fiber Optics, (Academic Press, 2007).

] [see Fig. 3(a) at ζ = 0.6]. Subsequently, the pulse collapses at ζ = 0.9, and SCG occurs as shown in the on-axis spectra [Fig. 3(b)]. Blue-shifted wavelength components in the normal-GVD regime (i.e., below 3-μm in Fig. 1) that are generated by the optical shock form a long trailing edge [24

24. J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited with filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006). [CrossRef]

], and it diffracts as the beam loses its energy by MPA and plasma generation. Similar spatio-temporal behavior during beam collapse and filament generation is observed for P/Pcr = 3 and 4 [Figs. 3(c) and 3(d)].

Fig. 3 (a) Spatio-temporal intensity profiles at various propagation distances ζ = z/Ldf for P/Pcr = 2. (b) On-axis spectra at various propagation distances for P/Pcr = 2. (c) Spatiotemporal intensity profiles of collapsing pulses at ζ = 0.54 for P/Pcr = 3, and (d) at ζ = 0.42 for P/Pcr =4

Multiple collapse is observed for higher powers (P/Pcr = 6 and 8), as experimentally demonstrated in solids [19

19. K. D. Moll and A. L. Gaeta, “Role of dispersion in multiple-collapse dynamics,” Opt. Lett.29, 995–997 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-9-995. [CrossRef] [PubMed]

] [Fig. 4(a)]. Although similar spatio-temporal shapes are generated in the first collapse region, as in the case at low powers, plasma defocusing and refocusing in the temporal domain combined with strong shock terms produce pulse-splitting accompanied by complicated temporal dynamics such as further splitting and energy transfer between split pulses in the secondary collapse regions [Fig. 4(c)] [23

23. L. Bergé and S. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71, 065601 (2005). [CrossRef]

].

Fig. 4 Calculated (a) peak intensity, (b) beam diameter (FWHM) as functions of normalized propagation distance for P/Pcr = 6 and 8. (c) Examples of spatio-temporal intensity profiles at various distances for P/Pcr =6.

The role of the background energy reservoir supplying the energy into the filament core which contains approximately one critical power when it loses energy due to mechanisms such as MPA has been studied by many groups [56

56. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999). [CrossRef]

63

63. Z. Hao, J. Zhang, X. Lu, T. Xi, Z. Zhang, and Z. Wang, “Energy interchange between large-scale free propagating filaments and its background reservoir,” J. Opt. Soc. Am. B26, 499–502 (2009), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-26-3-499. [CrossRef]

]. We also compare air-filament propagation for P/Pcr = 6 by simulating the placement of apertures with different diameters that block a fraction of the reservoir energy [Fig. 5]. Simulation results show that the filament length and the number of multiple collapse regions decrease with apertures, which confirms that the background energy is important for longer propagation of the filamen, as is the case in the normal-GVD regime.

Fig. 5 Air filament formation and propagation with apertures of which sizes are 4 and 6 times of the minimum spot size (∼ 1.2-mm) at ζ = 0.3 for P/Pcr =6.

4. Conclusion

This work was supported by NSF under Grant No. PHY-0703870 and the Army Research Office under Grant No. 186695-PH. The authors gratefully acknowledge useful discussions with Y. Okawachi, M. Foster, and A. Chong.

References and links

1.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou,“Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett.20, 73–75 (1995), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-20-1-73. [CrossRef] [PubMed]

2.

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett.21, 62–65 (1996), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-21-1-62. [CrossRef] [PubMed]

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A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett.22, 304–306 (1997), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-22-5-304. [CrossRef] [PubMed]

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J. R. Peñano, P. Sprangle, B. Hafizi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, “Propagation of ultra-short, intense laser pulses in air,” Phys. Plasmas 11, 2865 (2004). [CrossRef]

5.

A. Ting, I. Alexeev, D. Gordon, R. Fischer, D. Kaganovich, T. Jones, E. Briscoe, J. Peñano, R. Hubbard, and P. Sprangle, “Measurements of intense femtosecond laser pulse propagation in air,” Phys. Plasmas 12, 056705 (2005). [CrossRef]

6.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in opticalmedia: physics, applications, and new challenges,” Can. J. Phys. 83, 863–905 (2005). [CrossRef]

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A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007). [CrossRef]

8.

L. Bergé, S Skupin, R Nuter, J Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633 (2007). [CrossRef]

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10.

V. P. Kandidov, S. A. Shlenov, and O. G. Kosareva, “Filamentation of high-power femtosecond laser radiation,” Quantum Electron. 39, 205 (2009). [CrossRef]

11.

L. Wöste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, “Femtosecond atmospheric lamp,” Laser Optoelektron. 29, 51 (1997).

12.

P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000). [CrossRef]

13.

J.-C. Diels, R. Bernstein, K. Stahlkopf, and X. M. Zhao, “Lightning control with lasers,” Sci. Am. 277, 50–55 (1997). [CrossRef]

14.

R. P. Fischer, A. C. Ting, D. F. Gordon, R. F. Fernsler, D. P. DiComo, and P. Sprangle, “Conductivity measurements of femtosecond laserplasma filaments,” IEEE Trans. Plasma Sci. 35, 1430 (2007). [CrossRef]

15.

A. Houard, C. D’Amico, Y. Liu, Y. B. Andre, M. Franco, B. Prade, A. Mysyrowicz, E. Salmon, P. Pierlot, and L.-M. Cleon, “High current permanent discharges in air induced by femtosecond laser filamentation,” Appl. Phys. Lett. 90, 171501 (2007). [CrossRef]

16.

See, for example, The Supercontinuum Laser Source, ed. by R. R. Alfano (Springer-Verlag, 1989).

17.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004). [CrossRef]

18.

C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007). [CrossRef] [PubMed]

19.

K. D. Moll and A. L. Gaeta, “Role of dispersion in multiple-collapse dynamics,” Opt. Lett.29, 995–997 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-9-995. [CrossRef] [PubMed]

20.

A. Saliminia, S. L. Chin, and R. Vallée, “Ultra-broad and coherent white light generation in silica glass by focused femtosecond pulses at 1.5 um,” Opt. Express13, 5731–5738 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-15-5731. [CrossRef] [PubMed]

21.

M. A. Porras, A. Dubietis, A. Matijošius, R. Piskarskas, F. Bragheri, A. Averchi, and P. Di Trapani, “Characterization of conical emission of light filaments in media with anomalous dispersion,” J. Opt. Soc. Am. B24, 581–584 (2007), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-3-581. [CrossRef]

22.

M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791 (1998). [CrossRef]

23.

L. Bergé and S. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71, 065601 (2005). [CrossRef]

24.

J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited with filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006). [CrossRef]

25.

L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008). [CrossRef] [PubMed]

26.

Although 3-D optical bullets are predicted to be unstable and have not been experimentally observed, several approaches have been theoretically proposed recently. For example, see [27–30].

27.

M. Belić, N. Petrović, W.-P. Zhong, R.-H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008). [CrossRef] [PubMed]

28.

L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett.34, 1129–1131 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-7-1129. [CrossRef] [PubMed]

29.

I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009). [CrossRef] [PubMed]

30.

S. Chen and J. M. Dudley, “Spatiotemporal nonlinear optical self-similarity in three dimensions,” Phys. Rev. Lett. 102, 233903 (2009). [CrossRef] [PubMed]

31.

I. G. Koprinkov, A. Suda, P. Wang, and K. Midorikawa, “Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847–3850 (2000). [CrossRef] [PubMed]

32.

A. L. Gaeta and F. W. Wise, Comment on “Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 87, 229401 (2001). [CrossRef] [PubMed]

33.

L. Bergé and A. Couairon, “Gas-induced solitons,” Phys. Rev. Lett. 86, 1003–1006 (2001). [CrossRef] [PubMed]

34.

T.-T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006). [CrossRef] [PubMed]

35.

L. M. Kovachev, “Collapse arrest and self-guiding of femtosecond pulses,” Opt. Express15, 10318–10323 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-16-10318. [CrossRef] [PubMed]

36.

P. Agostini and L. F. DiMauro, “Atoms in high intensity mid-infrared pulses,” Contemp. Phys. 49, 179 (2008). [CrossRef]

37.

O. Chalus, A. Thai, P. K. Bates, and J. Biegert, “Six-cycle mid-infrared source with 3.8 μJ at 100 kHz,” Opt. Lett.35, 3204–3206 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-19-3204. [CrossRef] [PubMed]

38.

T. Popmintchev, M. Chen, P. Arpin, M. Gerrity, M. Seaberg, B. Zhang, D. Popmintchev, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuška, M. Murnane, and H. Kapteyn, “Bright coherent ultrafast X-rays from mid-IR lasers,” in High Intensity Lasers and High Field Phenomena, OSA Technical Digest (CD) (Optical Society of America, 2011), paper HThB5, http://www.opticsinfobase.org/abstract.cfm?URI=HILAS-2011-HThB5.

39.

N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Self-compression of ultrashort pulses through ionization-induced spatiotemporal reshaping,” Phys. Rev. Lett. 93, 173902 (2004). [CrossRef] [PubMed]

40.

A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006). [CrossRef]

41.

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett.31, 274–276 (2006), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-2-274. . [CrossRef] [PubMed]

42.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnürer, N. Zhavoronkov, and G. Steinmeyer, “Self-compression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006). [CrossRef]

43.

L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, “Spectral reshaping and pulse compression via sequential filamentation in gases,” Opt. Express16, 390–401 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-390. [CrossRef] [PubMed]

44.

F. Reiter, U. Graf, E. E. Serebryannikov, W. Schweinberger, M. Fiess, M. Schultze, A. M. Azzeer, R. Kienberger, F. Krausz, A. M. Zheltikov, and E. Goulielmakis, “Route to attosecond nonlinear spectroscopy,” Phys. Rev. Lett. 105, 243902 (2010). [CrossRef]

45.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997). [CrossRef]

46.

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000). [CrossRef] [PubMed]

47.

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002). [CrossRef]

48.

We calculate the dispersion parameters up to sixth-order order since the formula for the refractive index of air (n0) is a function of the fifth-order Tayolor expansion in Ref. [49] and thus the wavelumber (k = ωn0/c) is a sixth-order function of the laser angular frequency.

49.

R. J. Mathar, “Refractive index of humid air in the infrared: model fits,” J. Opt. A, Pure Appl. Opt. 9, 470 (2007). [CrossRef]

50.

R. J. Mathar, “Calculated refractivity of water vapor and moist air in the atmospheric window at 10 μm,” Appl. Opt. 43, 928 (2004). [CrossRef] [PubMed]

51.

See, for example, http://irina.eas.gatech.edu/irina/eas8803_fall2009/Lec6.pdf.

52.

G. Fibich and A. L. Gaeta, “On the critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett.25, 335–337 (2000), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-25-5-335. [CrossRef]

53.

J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985). [CrossRef]

54.

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998). [CrossRef]

55.

G. P. AgrawalNolinear Fiber Optics, (Academic Press, 2007).

56.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999). [CrossRef]

57.

M. Kolesik and J. V. Moloney, “Self-healing femtosecond light filaments,” Opt. Lett.29, 590–592 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-6-590. [CrossRef] [PubMed]

58.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Rev. Lett. 83, 213 (2003). [CrossRef]

59.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light filaments without self-channeling,” Phys. Rev. Lett. 92, 253903 (2004). [CrossRef] [PubMed]

60.

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. (Vern) Schlie, A. Mysyrowicz, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Propagation of fs TW laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005). [CrossRef]

61.

W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett.30, 2602–2604 (2005), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-30-19-2602. [CrossRef] [PubMed]

62.

S. Eisenmann, J. Peñano, P. Sprangle, and A. Zigler, “Effect of an energy reservoir on the atmospheric propagation of laser-plasma filaments,” Phys. Rev. Lett. 100, 155003 (2008). [CrossRef] [PubMed]

63.

Z. Hao, J. Zhang, X. Lu, T. Xi, Z. Zhang, and Z. Wang, “Energy interchange between large-scale free propagating filaments and its background reservoir,” J. Opt. Soc. Am. B26, 499–502 (2009), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-26-3-499. [CrossRef]

OCIS Codes
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Ultrafast Optics

History
Original Manuscript: January 12, 2011
Revised Manuscript: April 4, 2011
Manuscript Accepted: April 16, 2011
Published: April 26, 2011

Citation
Bonggu Shim, Samuel E. Schrauth, and Alexander L. Gaeta, "Filamentation in air with ultrashort mid-infrared pulses," Opt. Express 19, 9118-9126 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9118


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References

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  12. P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000). [CrossRef]
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  15. A. Houard, C. D’Amico, Y. Liu, Y. B. Andre, M. Franco, B. Prade, A. Mysyrowicz, E. Salmon, P. Pierlot, and L.-M. Cleon, “High current permanent discharges in air induced by femtosecond laser filamentation,” Appl. Phys. Lett. 90, 171501 (2007). [CrossRef]
  16. See, for example, The Supercontinuum Laser Source , ed. by R. R. Alfano (Springer-Verlag, 1989).
  17. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004). [CrossRef]
  18. C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007). [CrossRef] [PubMed]
  19. K. D. Moll and A. L. Gaeta, “Role of dispersion in multiple-collapse dynamics,” Opt. Lett. 29, 995–997 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-9-995 . [CrossRef] [PubMed]
  20. A. Saliminia, S. L. Chin, and R. Vallée, “Ultra-broad and coherent white light generation in silica glass by focused femtosecond pulses at 1.5 um,” Opt. Express 13, 5731–5738 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-15-5731 . [CrossRef] [PubMed]
  21. M. A. Porras, A. Dubietis, A. Matijošius, R. Piskarskas, F. Bragheri, A. Averchi, and P. Di Trapani, “Characterization of conical emission of light filaments in media with anomalous dispersion,” J. Opt. Soc. Am. B 24, 581–584 (2007), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-3-581 . [CrossRef]
  22. M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791 (1998). [CrossRef]
  23. L. Bergé and S. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71, 065601 (2005). [CrossRef]
  24. J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited with filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74, 043801 (2006). [CrossRef]
  25. L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100, 113902 (2008). [CrossRef] [PubMed]
  26. Although 3-D optical bullets are predicted to be unstable and have not been experimentally observed, several approaches have been theoretically proposed recently. For example, see [27–30].
  27. M. Belić, N. Petrović, W.-P. Zhong, R.-H. Xie, and G. Chen, “Analytical light bullet solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation,” Phys. Rev. Lett. 101, 123904 (2008). [CrossRef] [PubMed]
  28. L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1131 (2009), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-34-7-1129 . [CrossRef] [PubMed]
  29. I. B. Burgess, M. Peccianti, G. Assanto, and R. Morandotti, “Accessible light bullets via synergetic nonlinearities,” Phys. Rev. Lett. 102, 203903 (2009). [CrossRef] [PubMed]
  30. S. Chen and J. M. Dudley, “Spatiotemporal nonlinear optical self-similarity in three dimensions,” Phys. Rev. Lett. 102, 233903 (2009). [CrossRef] [PubMed]
  31. I. G. Koprinkov, A. Suda, P. Wang, and K. Midorikawa, “Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 84, 3847–3850 (2000). [CrossRef] [PubMed]
  32. A. L. Gaeta and F. W. Wise, Comment on “Self-compression of high-intensity femtosecond optical pulses and spatiotemporal soliton generation,” Phys. Rev. Lett. 87, 229401 (2001). [CrossRef] [PubMed]
  33. L. Bergé and A. Couairon, “Gas-induced solitons,” Phys. Rev. Lett. 86, 1003–1006 (2001). [CrossRef] [PubMed]
  34. T.-T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006). [CrossRef] [PubMed]
  35. L. M. Kovachev, “Collapse arrest and self-guiding of femtosecond pulses,” Opt. Express 15, 10318–10323 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-16-10318 . [CrossRef] [PubMed]
  36. P. Agostini and L. F. DiMauro, “Atoms in high intensity mid-infrared pulses,” Contemp. Phys. 49, 179 (2008). [CrossRef]
  37. O. Chalus, A. Thai, P. K. Bates, and J. Biegert, “Six-cycle mid-infrared source with 3.8 μJ at 100 kHz,” Opt. Lett. 35, 3204–3206 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-19-3204 . [CrossRef] [PubMed]
  38. T. Popmintchev, M. Chen, P. Arpin, M. Gerrity, M. Seaberg, B. Zhang, D. Popmintchev, G. Andriukaitis, T. Balciunas, O. D. Mücke, A. Pugzlys, A. Baltuška, M. Murnane, and H. Kapteyn, “Bright coherent ultrafast X-rays from mid-IR lasers,” in High Intensity Lasers and High Field Phenomena, OSA Technical Digest (CD) (Optical Society of America, 2011), paper HThB5, http://www.opticsinfobase.org/abstract.cfm?URI=HILAS-2011-HThB5 .
  39. N. L. Wagner, E. A. Gibson, T. Popmintchev, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Self-compression of ultrashort pulses through ionization-induced spatiotemporal reshaping,” Phys. Rev. Lett. 93, 173902 (2004). [CrossRef] [PubMed]
  40. A. Couairon, J. Biegert, C. P. Hauri, W. Kornelis, F. W. Helbing, U. Keller, and A. Mysyrowicz, “Self-compression of ultra-short laser pulses down to one optical cycle by filamentation,” J. Mod. Opt. 53, 75–85 (2006). [CrossRef]
  41. G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31, 274–276 (2006), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-2-274 . . [CrossRef] [PubMed]
  42. S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnürer, N. Zhavoronkov, and G. Steinmeyer, “Self-compression by femtosecond pulse filamentation: Experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006). [CrossRef]
  43. L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, “Spectral reshaping and pulse compression via sequential filamentation in gases,” Opt. Express 16, 390–401 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-390 . [CrossRef] [PubMed]
  44. F. Reiter, U. Graf, E. E. Serebryannikov, W. Schweinberger, M. Fiess, M. Schultze, A. M. Azzeer, R. Kienberger, F. Krausz, A. M. Zheltikov, and E. Goulielmakis, “Route to attosecond nonlinear spectroscopy,” Phys. Rev. Lett. 105, 243902 (2010). [CrossRef]
  45. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997). [CrossRef]
  46. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000). [CrossRef] [PubMed]
  47. M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002). [CrossRef]
  48. We calculate the dispersion parameters up to sixth-order order since the formula for the refractive index of air (n0) is a function of the fifth-order Tayolor expansion in Ref. [49] and thus the wavelumber (k = ωn0/c) is a sixth-order function of the laser angular frequency.
  49. R. J. Mathar, “Refractive index of humid air in the infrared: model fits,” J. Opt. A, Pure Appl. Opt. 9, 470 (2007). [CrossRef]
  50. R. J. Mathar, “Calculated refractivity of water vapor and moist air in the atmospheric window at 10 μm,” Appl. Opt. 43, 928 (2004). [CrossRef] [PubMed]
  51. See, for example, http://irina.eas.gatech.edu/irina/eas8803_fall2009/Lec6.pdf .
  52. G. Fibich and A. L. Gaeta, “On the critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-25-5-335 . [CrossRef]
  53. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985). [CrossRef]
  54. A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998). [CrossRef]
  55. G. P. AgrawalNolinear Fiber Optics , (Academic Press, 2007).
  56. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999). [CrossRef]
  57. M. Kolesik and J. V. Moloney, “Self-healing femtosecond light filaments,” Opt. Lett. 29, 590–592 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-6-590 . [CrossRef] [PubMed]
  58. F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Rev. Lett. 83, 213 (2003). [CrossRef]
  59. A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light filaments without self-channeling,” Phys. Rev. Lett. 92, 253903 (2004). [CrossRef] [PubMed]
  60. G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. (Vern) Schlie, A. Mysyrowicz, R. Sauerbrey, L. Wöste, and J.-P. Wolf, “Propagation of fs TW laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005). [CrossRef]
  61. W. Liu, F. Théberge, E. Arévalo, J.-F. Gravel, A. Becker, and S. L. Chin, “Experiment and simulations on the energy reservoir effect in femtosecond light filaments,” Opt. Lett. 30, 2602–2604 (2005), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-30-19-2602 . [CrossRef] [PubMed]
  62. S. Eisenmann, J. Peñano, P. Sprangle, and A. Zigler, “Effect of an energy reservoir on the atmospheric propagation of laser-plasma filaments,” Phys. Rev. Lett. 100, 155003 (2008). [CrossRef] [PubMed]
  63. Z. Hao, J. Zhang, X. Lu, T. Xi, Z. Zhang, and Z. Wang, “Energy interchange between large-scale free propagating filaments and its background reservoir,” J. Opt. Soc. Am. B 26, 499–502 (2009), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-26-3-499 . [CrossRef]

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