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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 9 — Apr. 23, 2012
  • pp: 9558–9563
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Dynamics of femtosecond laser filamentation in argon with non-uniform density distribution

Zhanxin Wang, Chaojin Zhang, Jiansheng Liu, and Zhizhan Xu  »View Author Affiliations


Optics Express, Vol. 20, Issue 9, pp. 9558-9563 (2012)
http://dx.doi.org/10.1364/OE.20.009558


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Abstract

We numerically investigated the femtosecond laser filamentation in a cell filled with argon of non-uniform density distribution. By comparison with the case of uniform density distribution, we demonstrated the crucial differences in the dynamics between the two cases. We found that the pulse-splitting appeared earlier due to the sensitivity of rear-part refocusing to the plasma density and a double Λ shape appeared in the spatio-temporal intensity profile in the non-uniform density case.

© 2012 OSA

1. Introduction

The researches on femtosecond laser filaments can be traced back to the 1990s [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(1), 73–75 (1995). [CrossRef] [PubMed]

,2

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(1), 62–65 (1996). [CrossRef] [PubMed]

]. Since then, lots of works have been done because of its physical interest and its potential applications [3

3. J. Kasparian and J.-P. Wolf, “Physics and applications of atmospheric nonlinear optics and filamentation,” Opt. Express 16(1), 466–493 (2008). [CrossRef] [PubMed]

6

6. L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]

]. The basic physics of filaments is generally considered as the dynamic balance between the focusing caused by Kerr effect and lens and the plasma-induced defocusing, although many controversies have recently arisen [7

7. P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104(10), 103903 (2010). [CrossRef] [PubMed]

13

13. P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106(24), 243902 (2011). [CrossRef] [PubMed]

]. In most of the works on filaments, the transparent media such as fused silica, water, air, and/or argon are employed. Filamentation of ultrashort pulses in argon has been widely used to obtain few-cycle laser pulses by employing the now well-known effect of pulse self-compression [14

14. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000). [CrossRef] [PubMed]

28

28. M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103(4), 043901 (2009). [CrossRef] [PubMed]

]. The self-compression effect in the argon filamentation occured in two stages: When the optical Kerr effect focuses the pulse until the peak intensity is clamped, an ionization front is generated that will defocus the trail of the pulse and shortens its leading edge, which is the first stage of self-compression [14

14. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000). [CrossRef] [PubMed]

,15

15. L. Bergé and A. Couairon, “Gas-induced solitons,” Phys. Rev. Lett. 86(6), 1003–1006 (2001). [CrossRef] [PubMed]

]. Furtherly, the pulse front can be exhausted, leaving one isolated and shortened pulse behind due to refocusing in the rear part of the pulse [17

17. 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 Stat. Nonlin. Soft Matter Phys. 74(5), 056604 (2006). [CrossRef] [PubMed]

22

22. 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(2), 274–276 (2006). [CrossRef] [PubMed]

], that is the so-called split-isolation cycle [19

19. L. Bergé, S. Skupin, and G. Steinmeyer, “Temporal self-restoration of compressed optical filaments,” Phys. Rev. Lett. 101(21), 213901 (2008). [CrossRef] [PubMed]

21

21. C. Brée, J. Bethge, S. Skupin, L. Bergé, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12(9), 093046 (2010). [CrossRef]

]. Experimentally, the few-cycle pulse is extracted by termination of the filaments at proper position using a exit window [17

17. 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 Stat. Nonlin. Soft Matter Phys. 74(5), 056604 (2006). [CrossRef] [PubMed]

,19

19. L. Bergé, S. Skupin, and G. Steinmeyer, “Temporal self-restoration of compressed optical filaments,” Phys. Rev. Lett. 101(21), 213901 (2008). [CrossRef] [PubMed]

21

21. C. Brée, J. Bethge, S. Skupin, L. Bergé, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12(9), 093046 (2010). [CrossRef]

] or a movable aperture [26

26. O. G. Kosareva, N. A. Panov, D. S. Uryupina, M. V. Kurilova, A. V. Mazhorova, A. B. Savel’ev, R. V. Volkov, V. P. Kandidov, and S. L. Chin, “Optimization of a femtosecond pulse self-compression region along a filament in air,” Appl. Phys. B 91(1), 35–43 (2008). [CrossRef]

,27

27. H. S. Chakraborty, M. B. Gaarde, and A. Couairon, “Single attosecond pulses from high harmonics driven by self-compressed filaments,” Opt. Lett. 31(24), 3662–3664 (2006). [CrossRef] [PubMed]

]. In the case of movable aperture, the filament is terminated abruptly or smoothly depending on the size of aperture where a density gradient occurs. Experimental results show that a double increase in the aperture diameter can result in an approximately three-fold increase in the pulse duration [26

26. O. G. Kosareva, N. A. Panov, D. S. Uryupina, M. V. Kurilova, A. V. Mazhorova, A. B. Savel’ev, R. V. Volkov, V. P. Kandidov, and S. L. Chin, “Optimization of a femtosecond pulse self-compression region along a filament in air,” Appl. Phys. B 91(1), 35–43 (2008). [CrossRef]

]. This proposed the question of sensitivity of the nonlinear pulse dynamics to the gas density gradient. Recently, Diels group [29

29. J.-C. Diels, J. Yeak, D. Mirell, R. Fuentes, S. Rostami, D. Faccio, and P. Trapani, “Air filaments and vacuum,” Laser Phys. 20(5), 1101–1106 (2010). [CrossRef]

] has employed an aerodynamic window as a new diagnostic tool to experimentally investigate this question. From the point of view of numerical simulation, although A. Couairon et al. [23

23. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005). [CrossRef] [PubMed]

] have numerically shown that self-compression to the single-cycle limit can be achieved by using argon with a pressure gradient, there is still the need to improve the understanding on the dynamics in the filamentation of non-uniform argon when considering the complexity of the nonlinear propagation.

In this paper, we numerically investigated the dynamics of the femtosecond filamentation in argon with non-uniform density. Different with the traditional split-isolation cycle where the pulse front is eventually exhausted, we find that the pulse-splitting appear earlier in the non-uniform case than the uniform case because the refocusing effect is sensitive to the plasma density. During the pulse-splitting, the spatio-temporal intensity profile takes on a double Λ shape.

2. Models and parameters

In our numerical experiments, a transform-limited Gaussian laser pulse with the duration of 35fs (FWHM) and beam radius of 4.4mm (1/e2) was focused in a cell filled with argon by a lens with a focal length f=1m. The length of the argon cell is 30cm, which is so placed that the focus of the lens is located at the center of the cell. The input plane of our numerical simulation is just located at the front surface of the cell. The area between the lens and the cell is assumed as vacuum. Therefore, the spectra of the electric field in the input plane can be analytically expressed as
E˜(r,ω,z=0)=πT0exp(T02(ωω0)24)1pqexp(r2q).
(1)
Where,p=1/w02+ik0/2f and q=1/p+i2d/k0,ω is the angular frequency of the electric field, w0=4.4mm is the beam radius, T0=tFWHM/2ln2 is the pulse duration, λ0=800nm is the center wavelength of the laser pulse in vacuum, ω0=2π/λ0 is the angular frequency, k0=2π/λ0 is the wave number, d=85cm is the distance between the lens and the front surface of the cell. In Eq. (1), the Fourier transform and its reverse are defined as E˜(ω)=+E(t)eiωtdt and E(t)=(1/2π)+E˜(ω)eiωtdω, respectively.

The propagation of the axially symmetric laser pulse in the argon cell is described by the scalar unidirectional pulse propagation equation as [6

6. L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]

]
zE˜=(i2k(ω)+ik(ω))E˜+ω2k(ω)c2ε0F˜NL.
(2)
Where E˜E˜(r,ω,z) is the spectra of the forward electric field, k(ω)=n(ω)ω/c is the frequency-dependent wave number, F˜NL=iωP˜NLJ˜ contains the Kerr nonlinear polarization PNL and the current density J. The evolution of free electron density can be described as zρ=W(|E|)ρnt+σ|E|2ρ/Ip, where W(|E|) is the ionization rate, Ip is the ionization potential, and ρnt is the gas density.

3. Results and discussion

In this section, we show the propagation dynamics in the gas cell filled with argon of uniform and non-uniform density, respectively. In the case of uniform density, the gas pressure is taken as 3 bar, which corresponds to the gas density of ρnt=8×1019cm3. In the another case, the gas density distribution is assumed as Gaussian profile along the propagation axis and the peak density is the same as it in the uniform case, i.e., ρnt=8×1019×exp(-z2/wz2)cm3, where z is the distance from the center of argon cell, wz=5cm is the half width (1/e2) of gas density distribution.

Figures 1(e), 1(f) show the evolution of on-axis temporal intensity profile along the propagation axis. Firstly, we discuss the dynamics in the uniform density case as shown in Fig. 1(e). The rear of the pulse is defocused all the while along the propagation axis from z = −5 to 0 cm where the pulse intensity is well clamped. In this region, the spatio-temporal profile takes on a Λ shape as shown in Fig. 2(a)
Fig. 2 Intensity distribution in time and space domain at two typical distances. (a,b) in the case of uniform density, (c,d) in the case of non-uniform density.
, which in fact has been shown in many published works [17

17. 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 Stat. Nonlin. Soft Matter Phys. 74(5), 056604 (2006). [CrossRef] [PubMed]

23

23. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005). [CrossRef] [PubMed]

]. When the peak intensity of the pulse begins to decline near the position of z = 0, the rear of the pulse can refocus and therefore the pulse splitting appears. Figure 2(b) shows the typical dynamics of on-axis pulse-splitting. By contrast, we show the on-axis temporal profile as a function of propagation distance in the non-uniform case in Fig. 1(f), the typical spatio-temporal intensity distributions are shown in Fig. 2(c), 2(d). The refocusing effect appears very early due to its sensitivity to the plasma density, which result in the co-propagation of intense on-axis double pulses. In fact, the refocusing begin to appear when the plasma density decline to just half of its peak value. The spatio-temporal profile takes on a double Λ shape in the typical co-propagation region as shown in Fig. 2(c), which is different with the traditional refocusing dynamics as shown in Fig. 2(b) and some previously published works [17

17. 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 Stat. Nonlin. Soft Matter Phys. 74(5), 056604 (2006). [CrossRef] [PubMed]

23

23. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005). [CrossRef] [PubMed]

]. In the non-uniform density case, it is the rear of the pulse that is firstly exhausted rather than the pulse front. The pulse self-compression is achieved by isolating the pulse front. Although the pulse rear can refocus when the pulse front is exhausted, there is almost no self-compression in this region. Figure 2(d) show the typical dynamics in the region from z = −1 to 0 cm where the rear part of the pulse has been exhausted and the self-compression effect is achieved.

To obtain a deeper insight into the filamentation dynamics in the non-uniform case, we show the on-axis temporal profile in Fig. 3(a)
Fig. 3 (a,d) Temporal profiles, (b,e) spectral intensity, and (c,f) spectrograms of on-axis pulse in the non-uniform argon at two typical distances consistent with Fig. 2(c,d), respectively. The values are normalized relative to its maximum in (c,f).
, 3(c) and the on-axis spectral intensity in Fig. 3(b), 3(d) corresponding to two typical distances of z = −1.6 and −0.5 cm, respectively. Figure 3(a) shows the process of pulse-splitting into two intense pulses, which can sustain about 1 cm along the propagation direction. Their corresponding spectra extend from 700 to 1000 nm and show a complete splitting. The front pulse corresponds to the low-frequency components and the back pulse the high-frequency components, which can be furtherly confirmed from the calculated XFROG spectrograms (see Ref [34

34. S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16(22), 17626–17636 (2008). [CrossRef] [PubMed]

] for the calculation method) shown in Fig. 3(c), where the gate function is a Gaussian with 30 fs FWHM. When the rear of the pulse is exhausted, an intense isolated self-compressed pulse appears, which corresponds to the low-frequency components of the generated supercontinuum as confirmed from Fig. 3(f).

4. Summary

In summary, we numerically investigated the dynamics of filamentation in an cell filled with argon of uniform and non-uniform density distributions, respectively. The non-uniform density distribution is assumed as Gaussian profile along the propagation axis in the argon cell. We found the pulse-splitting appeared earlier due to the sensitivity of rear-part refocusing to the plasma density and the pulse self-compression is achieved mainly by the exhausting of pulse rear in the case of non-uniform density distribution. In the double-peak pulse splitting region, a double Λ shape can appear in the spatio-temporal intensity profile in the non-uniform density case, which is a kind of novel spatio-temporal dynamics.

Acknowledgments

Z. Wang gratefully thanks Prof. Ya Cheng for his fruitful discussions. This work was supported by the National Basic Research program (Contract No. 2010CB923203), the National Natural Science Foundation (Contracts No. 11104236, 61008061, 10974214), Jiangsu Province Natural Science Foundation (Contract No. BK2010173), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) of China.

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(1), 73–75 (1995). [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(1), 62–65 (1996). [CrossRef] [PubMed]

3.

J. Kasparian and J.-P. Wolf, “Physics and applications of atmospheric nonlinear optics and filamentation,” Opt. Express 16(1), 466–493 (2008). [CrossRef] [PubMed]

4.

J. Schwarz and J.-C. Diels, “UV filaments and their application for laser-induced lightning and high-aspect-ratio hole drilling,” Appl. Phys., A Mater. Sci. Process. 77(2), 185–191 (2003).

5.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2–4), 47–189 (2007). [CrossRef]

6.

L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]

7.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett. 104(10), 103903 (2010). [CrossRef] [PubMed]

8.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Femtosecond filamentation in air and higher-order nonlinearities,” Opt. Lett. 35(15), 2550–2552 (2010). [CrossRef] [PubMed]

9.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett. 106(15), 153902 (2011). [CrossRef] [PubMed]

10.

Z. Wang, C. Zhang, J. Liu, R. Li, and Z. Xu, “Femtosecond filamentation in argon and higher-order nonlinearities,” Opt. Lett. 36(12), 2336–2338 (2011). [CrossRef] [PubMed]

11.

O. Kosareva, J.-F. Daigle, N. Panov, T. Wang, S. Hosseini, S. Yuan, G. Roy, V. Makarov, and S. L. Chin, “Arrest of self-focusing collapse in femtosecond air filaments: higher order Kerr or plasma defocusing?” Opt. Lett. 36(7), 1035–1037 (2011). [CrossRef] [PubMed]

12.

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105(21), 215005 (2010). [CrossRef] [PubMed]

13.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106(24), 243902 (2011). [CrossRef] [PubMed]

14.

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000). [CrossRef] [PubMed]

15.

L. Bergé and A. Couairon, “Gas-induced solitons,” Phys. Rev. Lett. 86(6), 1003–1006 (2001). [CrossRef] [PubMed]

16.

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(6), 673–677 (2004). [CrossRef]

17.

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 Stat. Nonlin. Soft Matter Phys. 74(5), 056604 (2006). [CrossRef] [PubMed]

18.

A. Mysyrowicz, A. Couairon, and U. Keller, “Self-compression of optical laser pulses by filamentation,” New J. Phys. 10(2), 025023 (2008). [CrossRef]

19.

L. Bergé, S. Skupin, and G. Steinmeyer, “Temporal self-restoration of compressed optical filaments,” Phys. Rev. Lett. 101(21), 213901 (2008). [CrossRef] [PubMed]

20.

Z. Wang, J. Liu, R. Li, and Z. Xu, “Supercontinuum generation and pulse compression from gas filamentation of femtosecond laser pulses with different durations,” Opt. Express 17(16), 13841–13850 (2009). [CrossRef] [PubMed]

21.

C. Brée, J. Bethge, S. Skupin, L. Bergé, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys. 12(9), 093046 (2010). [CrossRef]

22.

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(2), 274–276 (2006). [CrossRef] [PubMed]

23.

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett. 30(19), 2657–2659 (2005). [CrossRef] [PubMed]

24.

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(1–2), 75–85 (2006). [CrossRef]

25.

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, “Spatio-temporal characterization of few-cycle pulses obtained by filamentation,” Opt. Express 15(9), 5394–5404 (2007). [CrossRef] [PubMed]

26.

O. G. Kosareva, N. A. Panov, D. S. Uryupina, M. V. Kurilova, A. V. Mazhorova, A. B. Savel’ev, R. V. Volkov, V. P. Kandidov, and S. L. Chin, “Optimization of a femtosecond pulse self-compression region along a filament in air,” Appl. Phys. B 91(1), 35–43 (2008). [CrossRef]

27.

H. S. Chakraborty, M. B. Gaarde, and A. Couairon, “Single attosecond pulses from high harmonics driven by self-compressed filaments,” Opt. Lett. 31(24), 3662–3664 (2006). [CrossRef] [PubMed]

28.

M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett. 103(4), 043901 (2009). [CrossRef] [PubMed]

29.

J.-C. Diels, J. Yeak, D. Mirell, R. Fuentes, S. Rostami, D. Faccio, and P. Trapani, “Air filaments and vacuum,” Laser Phys. 20(5), 1101–1106 (2010). [CrossRef]

30.

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, E. Hertz, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82(3), 033826 (2010). [CrossRef]

31.

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components: erratum,” Opt. Express 18(3), 3011–3012 (2010). [CrossRef]

32.

A. Dalgarno and A. E. Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. R. Soc. Lond. A Math. Phys. Sci. 259(1298), 424–431 (1960). [CrossRef]

33.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199(1), 5–76 (2011). [CrossRef]

34.

S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express 16(22), 17626–17636 (2008). [CrossRef] [PubMed]

OCIS Codes
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.2250) Ultrafast optics : Femtosecond phenomena

ToC Category:
Ultrafast Optics

History
Original Manuscript: February 28, 2012
Revised Manuscript: March 28, 2012
Manuscript Accepted: April 2, 2012
Published: April 11, 2012

Citation
Zhanxin Wang, Chaojin Zhang, Jiansheng Liu, and Zhizhan Xu, "Dynamics of femtosecond laser filamentation in argon with non-uniform density distribution," Opt. Express 20, 9558-9563 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-9558


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References

  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(1), 73–75 (1995). [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(1), 62–65 (1996). [CrossRef] [PubMed]
  3. J. Kasparian and J.-P. Wolf, “Physics and applications of atmospheric nonlinear optics and filamentation,” Opt. Express16(1), 466–493 (2008). [CrossRef] [PubMed]
  4. J. Schwarz and J.-C. Diels, “UV filaments and their application for laser-induced lightning and high-aspect-ratio hole drilling,” Appl. Phys., A Mater. Sci. Process.77(2), 185–191 (2003).
  5. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2–4), 47–189 (2007). [CrossRef]
  6. L. Berge, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys.70(10), 1633–1713 (2007). [CrossRef]
  7. P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-order Kerr terms allow ionization-free filamentation in gases,” Phys. Rev. Lett.104(10), 103903 (2010). [CrossRef] [PubMed]
  8. M. Kolesik, E. M. Wright, and J. V. Moloney, “Femtosecond filamentation in air and higher-order nonlinearities,” Opt. Lett.35(15), 2550–2552 (2010). [CrossRef] [PubMed]
  9. P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett.106(15), 153902 (2011). [CrossRef] [PubMed]
  10. Z. Wang, C. Zhang, J. Liu, R. Li, and Z. Xu, “Femtosecond filamentation in argon and higher-order nonlinearities,” Opt. Lett.36(12), 2336–2338 (2011). [CrossRef] [PubMed]
  11. O. Kosareva, J.-F. Daigle, N. Panov, T. Wang, S. Hosseini, S. Yuan, G. Roy, V. Makarov, and S. L. Chin, “Arrest of self-focusing collapse in femtosecond air filaments: higher order Kerr or plasma defocusing?” Opt. Lett.36(7), 1035–1037 (2011). [CrossRef] [PubMed]
  12. Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett.105(21), 215005 (2010). [CrossRef] [PubMed]
  13. P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett.106(24), 243902 (2011). [CrossRef] [PubMed]
  14. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett.84(16), 3582–3585 (2000). [CrossRef] [PubMed]
  15. L. Bergé and A. Couairon, “Gas-induced solitons,” Phys. Rev. Lett.86(6), 1003–1006 (2001). [CrossRef] [PubMed]
  16. 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. B79(6), 673–677 (2004). [CrossRef]
  17. 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 Stat. Nonlin. Soft Matter Phys.74(5), 056604 (2006). [CrossRef] [PubMed]
  18. A. Mysyrowicz, A. Couairon, and U. Keller, “Self-compression of optical laser pulses by filamentation,” New J. Phys.10(2), 025023 (2008). [CrossRef]
  19. L. Bergé, S. Skupin, and G. Steinmeyer, “Temporal self-restoration of compressed optical filaments,” Phys. Rev. Lett.101(21), 213901 (2008). [CrossRef] [PubMed]
  20. Z. Wang, J. Liu, R. Li, and Z. Xu, “Supercontinuum generation and pulse compression from gas filamentation of femtosecond laser pulses with different durations,” Opt. Express17(16), 13841–13850 (2009). [CrossRef] [PubMed]
  21. C. Brée, J. Bethge, S. Skupin, L. Bergé, A. Demircan, and G. Steinmeyer, “Cascaded self-compression of femtosecond pulses in filaments,” New J. Phys.12(9), 093046 (2010). [CrossRef]
  22. 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(2), 274–276 (2006). [CrossRef] [PubMed]
  23. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Lett.30(19), 2657–2659 (2005). [CrossRef] [PubMed]
  24. 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(1–2), 75–85 (2006). [CrossRef]
  25. A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, A. Couairon, M. Franco, A. Mysyrowicz, and U. Keller, “Spatio-temporal characterization of few-cycle pulses obtained by filamentation,” Opt. Express15(9), 5394–5404 (2007). [CrossRef] [PubMed]
  26. O. G. Kosareva, N. A. Panov, D. S. Uryupina, M. V. Kurilova, A. V. Mazhorova, A. B. Savel’ev, R. V. Volkov, V. P. Kandidov, and S. L. Chin, “Optimization of a femtosecond pulse self-compression region along a filament in air,” Appl. Phys. B91(1), 35–43 (2008). [CrossRef]
  27. H. S. Chakraborty, M. B. Gaarde, and A. Couairon, “Single attosecond pulses from high harmonics driven by self-compressed filaments,” Opt. Lett.31(24), 3662–3664 (2006). [CrossRef] [PubMed]
  28. M. B. Gaarde and A. Couairon, “Intensity spikes in laser filamentation: diagnostics and application,” Phys. Rev. Lett.103(4), 043901 (2009). [CrossRef] [PubMed]
  29. J.-C. Diels, J. Yeak, D. Mirell, R. Fuentes, S. Rostami, D. Faccio, and P. Trapani, “Air filaments and vacuum,” Laser Phys.20(5), 1101–1106 (2010). [CrossRef]
  30. W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, E. Hertz, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A82(3), 033826 (2010). [CrossRef]
  31. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components: erratum,” Opt. Express18(3), 3011–3012 (2010). [CrossRef]
  32. A. Dalgarno and A. E. Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. R. Soc. Lond. A Math. Phys. Sci.259(1298), 424–431 (1960). [CrossRef]
  33. A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top.199(1), 5–76 (2011). [CrossRef]
  34. S. Akturk, A. Couairon, M. Franco, and A. Mysyrowicz, “Spectrogram representation of pulse self compression by filamentation,” Opt. Express16(22), 17626–17636 (2008). [CrossRef] [PubMed]

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