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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 16 — Aug. 3, 2009
  • pp: 13841–13850
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Supercontinuum generation and pulse compression from gas filamentation of femtosecond laser pulses with different durations

Zhanxin Wang, Jiansheng Liu, Ruxin Li, and Zhizhan Xu  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 13841-13850 (2009)
http://dx.doi.org/10.1364/OE.17.013841


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Abstract

Self-compression and spectral supercontinuum (SC) generated by filamentation of femtosecond laser pulses with duration from 45 fs down to 6 fs in argon gas have been numerically investigated. A 45-fs pulse can be self-compressed into a few-cycle pulse with duration of 12 fs at the post-filamentation region. By properly employing a high-pass filter to select the broadening high-frequency spectra which are almost in phase, the pulse can be further shortened to about 7 fs. By contrast, a 6-fs pulse cannot be further self-compressed into a shorter pulse by filamentation although it can generate much broader SC extending from 200 nm to 1300 nm. It is also found that a separate and strong SC in the ultraviolet (UV) region extending from 220 nm to 300 nm and peaked at about 255nm can be generated at proper propagation distances, which corresponds to a pulse with duration of about 5 fs.

© 2009 OSA

1. Introduction

It has been reported that SC generation from filamentation is highly dependent on the pulse duration [30

30. S. Trushin, S. Panja, K. Kosma, W. E. Schmid, and W. Fuß, “Supercontinuum extending from >1000 to 250 nm, generated by focusing ten-fs laser pulses at 805 nm into Ar,” Appl. Phys. B 80(4–5), 399–403 (2005). [CrossRef]

33

33. K. Kosma, S. A. Trushin, W. Fuß, and W. E. Schmid, “Characterization of supercontinuum radiation generated by self-focusing of few-cycle 800-nm pulses in Argon,” J. Mod. Opt. 55(13), 2141–2177 (2008). [CrossRef]

]. By focusing 10-fs laser pulses at 805 nm into argon, Trushin et al. have demonstrated that SC extends from >1000 to 250 nm [30

30. S. Trushin, S. Panja, K. Kosma, W. E. Schmid, and W. Fuß, “Supercontinuum extending from >1000 to 250 nm, generated by focusing ten-fs laser pulses at 805 nm into Ar,” Appl. Phys. B 80(4–5), 399–403 (2005). [CrossRef]

]. The UV cutoff wavelength can extend to 210 nm if a few-cycle pulse of 6 fs is employed [32

32. S. A. Trushin, K. Kosma, W. Fuss, and W. E. Schmid, “Sub-10-fs supercontinuum radiation generated by filamentation of few-cycle 800 nm pulses in argon,” Opt. Lett. 32(16), 2432–2434 (2007). [CrossRef] [PubMed]

]. Theoretical simulations indicate that third-harmonic spectra are not required to explain the observed UV spectra [31

31. N. Aközbek, S. A. Trushin, A. Baltuška, W. Fuß, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloeme, “Extending the supercontinuum spectrum down to 200nm with few-cycle pulses,” N. J. Phys. 8(9), 177 (2006). [CrossRef]

].

In this paper, by employing a model developed in the frequency domain, we simulated the spatial-temporal dynamics of filamentation in argon gas by 800-nm femtosecond laser pulses with different durations from 45 fs down to 6 fs. For a 45-fs input pulse with energy E in=1.3 mJ, the pulse will undergo self-compression and form a temporally compressed “light bullet” with a duration of ~12 fs at the post-filamentation domain as it is well-known [5

5. M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: A pressure dependence study,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(4), 4903–4910 (1998). [CrossRef]

,6

6. M. Nurhuada, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002). [CrossRef]

,28

28. L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100(11), 113902 (2008). [CrossRef] [PubMed]

]. By properly employing high-pass filters to cut out the out-phase low-frequency component, we found that the self-compressed pulse can be further shortened to about 7 fs, which is close to the Fourier transform limit of corresponding SC spectra. By contrast, the propagation dynamics of a 6-fs pulse is very different from that of a 45-fs pulse, which cannot be further self-compressed into a shorter pulse by filamentation although it can generate much broader SC extending from 200 nm to 1300 nm. It is interesting that a separate and strong SC in the ultraviolet region extending from 220 nm to 300 nm and peaked at about 255nm can be generated. If the SC generated at proper propagation distance is cut out by a high-pass filter, a pulse with duration of about 5 fs in deep UV can be numerically obtained.

2. Simulations

Our model for nonlinear propagation of an ultrashort laser pulse in optical medium is based on the model developed by Brabec et al. [34

34. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000). [CrossRef]

]. Assuming the pulse has radial symmetry and propagates along z axis with a wave vector k(ω)=n(ω)ω/c, where ω is the optical frequency, and n(ω) is the linear refractive index of the material, the equation of propagation of electric field has the following form [35

35. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. Lett. 92, 253901 (2004). [CrossRef] [PubMed]

38

38. J. Liu, H. Schroeder, S. L. Chin, W. Yu, R. Li, and Z. Xu, “Space-frequency coupling, conical waves, and small-scale filamentation in water,” Phys. Rev. A 72(5), 053817 (2005). [CrossRef]

]

zÊ=(i2k(ω)2+ik(ω))Ê+iω22k(ω)c2ε0P̂NLω2k(ω)c2ε0Ĵf.
(1)

Where Ê is the Fourier transform of the forward electric field component, P̂NL is the nonlinear polarization in frequency domain of PNL(r,z,t) given by PNL(r,z,t)=2ε 0 n b n 2 I(r,z,t)E(r,z,t), where n b and n 2 are linear refractive index and nonlinear coefficient at center wavelength λ 0, respectively. The current density Jf caused by free electrons can be expressed in frequency domain as [36

36. J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Z. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006). [CrossRef] [PubMed]

38

38. J. Liu, H. Schroeder, S. L. Chin, W. Yu, R. Li, and Z. Xu, “Space-frequency coupling, conical waves, and small-scale filamentation in water,” Phys. Rev. A 72(5), 053817 (2005). [CrossRef]

]

Ĵf=e2me(viω)ρ̂Ê+Ipβ(K)Î(K1)Êk0,
(2)

where k 0=0.5nb 0. The evolution of free electron density can be described as ∂t ρ=β (K) I K+ηcasρ-ηrecρ 2. The initial value of electron density is assumed as ρ 0≡109 cm-3 [39

39. L. Bergé and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7(1), 210–231 (2000). [CrossRef]

]. The input pulses are assumed to be Gaussian both in space and time domain, i.e.

E(r,t,z=0)=2Pinπw02×er2w02t2T02ik(0)r22fiω0t.
(3)

Where Pin, w 0, T 0, and f denote input peak power, beam waist, pulse duration, and effective focal length, respectively. k (0)=n b ω 0/c is the wave number at the laser frequency. Throughout the paper, we will use full-width at half maximum (FWHM) values with respect to the intensity and beam energy to characterize the pulses, namely, tFWHM=2ln2T0,wFWHM=2ln2w0,andEin=π2T0Pin..

The parameters for the propagation of 800-nm laser in argon at atmospheric pressure can be described as follows [14

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

]. The ionization potential is Ip=15.76 eV and the number of photons required for ionization is K=11. The multiphoton ionization (MPI) coefficient can be calculated as β (11)=1.34×10-114 S -1·m 19·W-11. The collision time can be taken as τc=190 fs. The linear refractive index n(ω) of argon is expressed as a formula given in Ref [40

40. 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), 424–434 (1960). [CrossRef]

]. The critical power takes the value =λ 2 0/2π nbn2 for a nonlinear coefficient n 2=3×10-19 cm2/W. ηcas=3.1×10-6 s -1·m 2·W -1 and ηrec=7×10-13 m 3·s -1 represent cascade ionization and electron-ion recombination rate, respectively. The Eq. (1) was solved by a fourth-order Runge-Kutta method with adaptive stepsize control. The transversal Laplace operator ∇2 is calculated here by a finite difference method [41

41. J. W. Thomas, Numerical partial differential equations: finite difference methods (Springer-Verlag, New York, 1995), Chap. 4.

] instead of Fourier transformation method used in Ref [38

38. J. Liu, H. Schroeder, S. L. Chin, W. Yu, R. Li, and Z. Xu, “Space-frequency coupling, conical waves, and small-scale filamentation in water,” Phys. Rev. A 72(5), 053817 (2005). [CrossRef]

].

3. Results and Discussions

In this section, we have investigated the self-guiding propagation of 800-nm pulses with different durations initially focused in argon at atmospheric pressure by a lens with a focal length f=60 cm. The beam waist of the pulse is assumed as w 0=2.5 mm (which corresponds to w FWHM=2.94 mm). When the input peak power is higher than the critical power for self-focusing, the beam collapse can be expected to occur near the so-called nonlinear focus zc, which can be expressed by the well-known Marburger formula

zc=0.367z0(PinPcr0.852)20.0219.
(4)

Where z 0=πn 0 w 2 0/λ 0 is the Rayleigh length of the beam. In the case of a convergent beam, the position of the collapse z c,f moves to z c,f=z c f/(z c+f).

Fig. 1. (Color online) Peak intensities (blue solid curves) and electron densities (red dashed curves) for 800 nm pulses (w0=2.5 mm) propagating in argon at various powers with durations of tFWHM=45 fs (a, b, c) and 6 fs (d).

Figure 1(a–c) show the peak intensities and electron densities, respectively, along the propagation axis z for 45-fs input pulses at different input pulse powers. The peak intensity and the plasma density of the laser pulse in the filament are sustained at ~57.5 TW/cm2 and about 1017 cm-3, respectively, which almost do not change with the input power. This phenomenon has been called intensity clamping. When the input pulse power increases from 5 Pcr to 12 Pcr, the filament and the plasma channel are elongated from 9 cm to 18 cm. As a comparison and shown in Fig. 1(d), we simulated the propagation of 6-fs pulse at 5 Pcr (Ein=0.11 mJ). The length of the filament is about 19 cm, which is much longer than the corresponding 45-fs pulse with the same input power. The peak intensity in the filament will alter from about 62 to 70 TW/cm2 along the propagation axis z, which is a little higher than that for the corresponding 45-fs pulse. As analyzed in ref [38

38. J. Liu, H. Schroeder, S. L. Chin, W. Yu, R. Li, and Z. Xu, “Space-frequency coupling, conical waves, and small-scale filamentation in water,” Phys. Rev. A 72(5), 053817 (2005). [CrossRef]

], the clamped intensity can be empirically expressed as Iclamping(ω02nbn26k(0)ππT0β(K))1(K1).. For a few-cycle pulse with a shorter duration T0, the clamped intensity will be higher than that for a long pulse.

Fig. 2. (Color online) On-axis temporal dynamics of 45-fs pulse propagating in argon at several input powers. (a) Pin=5 Pcr. (b) Pin=8.2 Pcr. (c) Pin=12 Pcr. (d) On-axis temporal dynamics of a 6-fs input pulse for Pin=5 Pcr.

In Figs. 2(a,b,c) we show the on-axis temporal dynamics of the 45-fs pulse in the (t, z) plane at input power 5 Pcr (Ein=0.8 mJ), 8.2 Pcr (Ein=1.3 mJ), 12 Pcr (Ein=2.0 mJ), respectively. As described extensively [5

5. M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: A pressure dependence study,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(4), 4903–4910 (1998). [CrossRef]

,6

6. M. Nurhuada, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002). [CrossRef]

,13

13. 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 Pt 2), 056604 (2006). [CrossRef]

], the front of the pulse firstly self-focuses near the nonlinear focus and produces plasma to defocus the trailing part of the pulse. On further propagation, the rear part of the pulse will refocus, which result in the pulse splitting on axis. This process can be repeated for each split pulse until the pulse front is completely exhausted. At the post-filamentation region, there is some difference for different input powers. When the input power is as low as Pin=5 Pcr, this single-sided depletion will eventually give rise to a few-cycle pulse with a duration of ~12 fs after z~63 cm, but the obtained few-cycle pulse is very weak (Fig. 2(a)). When the input power increases to Pin=8.2 Pcr, an intense temporal-compressed “light bullet” with duration about 12 fs can be obtained from z~63 cm and maintain over 30 cm as shown in Fig. 2(b). The pulse self-compression seems to be less effective with increasing input pulse power. When the input peak power is further increased to Pin=12 Pcr, a pulse with a duration of ~12 fs can still be obtained at z~65 cm. However, it is very interesting that the resulted few-cycle pulse can filament immediately because its peak power exceeds corresponding critical threshold for self-focusing. The self-compressed pulse will experience another splitting, which also can be seen from Fig. 1(c) and Fig. 2(c).

Fig. 3. (Color online) Typical intensity distribution in time and space domain at several different distances for a 45-fs input pulse at 8.2 Pcr. (a) 53.6 cm, (b) 62.6 cm, (c) 67.0 cm and (d) 86.5 cm, respectively.

In order to obtain a shorter few-cycle pulse, we choose input peak power Pin=8.2 Pcr and analyze the propagation dynamics in detail. Figures 3 shows the typical intensity distribution in time and space domain at z=53.6, 62.6, 67.0, 86.5 cm, respectively. Initially, the pulse is focused by a lens and self-focused due to Kerr effect. The peak intensity will gradually increase along with the way of propagation. The trailing edge of the pulse suffers trivial defocusing due to very weak ionization, which induces the slight asymmetry of the spatial-temporal profile. When the pulse reaches to the nonlinear focus (zc,f~53 cm), the pulse peak intensity quickly increases and reaches to about 57 TW/cm2 on axis, which causes intense ionization and plasma is generated at the trailing edge of the pulse which defocuses the light on-axis. The pulse forms a ‘light cone’ as shown in Fig. 3(a). Figure 3(b,c) show that the rear pulse may refocus, which will generate a typical double-peaked temporal distribution. Eventually, the energy of the leading edge of the pulse will deplete and cause strong pulse shortening as shown in Figs. 3(d), where a pulse with duration of ~12 fs is generated.

The on-axis spectral intensity generated at z=79.9 cm is shown in Fig. 4(a). Spectral SC from 2 to 3 PHz which corresponds to a Fourier transform limited duration of ~5.7 fs (Fig. 4(b)) is mainly induced by SPM and plasma behavior. The corresponding spectral phases are calculated relative to central wavelength 800 nm and shown in Fig. 4 (c) (black line). For clarity, we adjust the spectral phase by subtracting a linear phase shift. It merely corresponds to the shift of the envelope along the time direction and does not change the shape of the pulse envelope. Figure 4(c) (red line) shows the adjusted spectral phase which is detailed from 2.4 to 3.5 PHz by the inset in Fig. 4(c). It can be found that the spectral phase aberration in the region of high frequencies (ω>2.4 PHz) is very small while it is large in low frequency region. This kind of asymmetric spectral phase aberration is hard to compensate. However, when we properly cut out low-frequency spectra by using a high-pass filter, we can obtain a broad high-frequency spectrum whose phase aberration is small and can be compensated more easily because its spectral phase is almost quadratic. By using different spectral filters with different cut-off frequency to reshape the temporal profiles of the self-compressed pulses, we calculate the profiles of obtained pulses. As shown in Fig. 4(e), for the self-compressed pulse with a duration of ~12 fs at z=79.9 cm, shorter pulses with durations of about 9 fs, 7 fs, and 7 fs can be obtained by using high-pass filters with cut-off frequency of 2.4, 2.5, 2.6 PHz, respectively. However, when the cut-off frequency increases, the peak intensity of the obtained pulse will become lower.

Fig. 4. (Color online) (a) Spectral intensity and (c) spectral phase on axis at z=79.9 cm for a 45-fs input pulse at 8.2 Pcr. (b) The Fourier transformation-limited pulse for spectrum (a). (d) Spectral intensity distribution of the same pulse at z=79.9 cm. (e) On-axis temporal profiles of the pulse after selecting different spectral components by high-pass filters.
Fig. 5. (Color online) Spatial-temporal intensity profiles of 6-fs pulse at 800 nm propagating in argon at z=(a) 40.2, (b) 52.88, (c) 55.5, (d) 61.6 cm, respectively.

As a comparison, in the following paragraphs, we have also numerically simulated and analyzed the propagation of 6-fs pulse in argon at 5 Pcr. For lower input power such as 2 Pcr, the propagation dynamics is similar (not shown here). The on-axis temporal dynamics of 6-fs pulse was shown in Fig. 2(d). Figure 5 shows spatial-temporal intensity profile of 6-fs pulse at 800 nm propagating in argon at z=(a) 40.2, (b) 52.88, (c) 55.5, (d) 61.6 cm, respectively. The propagation dynamics is very different from that of 45-fs pulse as shown in Fig. 3. Initially, the input pulse is assumed as Gaussian both in space domain and time domain. The corresponding profile of spatial-temporal intensity looks like an ‘ellipse’. When the pulse propagates, the profile of the ‘ellipse’ becomes asymmetric (shown in Fig. 5(a)) along time axis mainly due to the external focusing that is numerically applied. When arriving at nonlinear focus (zc,f~52.9 cm) the pulse begins to filament (Fig. 5(b)). The trailing edge of the pulse suffers strong self-steepening which can bring about some trivial self-compression effect. When further propagating, the trailing part of the pulse will split and form many short temporal peaks, which will increase in number and peak intensity along with the increase of propagation distance (Fig. 5(c,d)). The short temporal splitting can be explained by the shock profile induced by self-steepening.

Fig. 6. (Color online) Spectral SC (normal spectral intensity in logarithmic coordinate) generated by 800-nm pulses with different durations at 5 Pcr at several typical positions. (a) tFWHM=6 fs, (b) tFWHM=45 fs.

Figure 6 (a) shows the spectral SC generated by 6-fs filaments at z=40.2, 52.9, 55.5 and 72.0 cm respectively integrated over the beam cross-section. It is clear that the spectrum SC can extend down to ~200 nm when filamentation begins at z~52.9 cm. On further increasing the path length z, the spectral intensity of the SC near the 255nm will gradually increase and shape into a separate spectral peak extending from 220 nm to 280 nm. This process can be more clearly seen from Fig. 7 where the on-axis spectral intensities generated at z=55.5, 61.6, and 64.0 cm, respectively, are shown.

Fig. 7. (Color online) On-axis spectral intensity of SC generated at z=(a) 55.5, (b) 61.6 and (c) 63.96 cm, respectively. Inset shows the SC spectral intensity (solid line) at 220 nm<λ<290 nm (6.5<ω<8.5 PHz) and spectral phase (dash line) relative to 7.4 PHz.

This separate SC is very interesting because it has small phase aberrations and can correspond to a few-cycle pulse. Figure 7(c) inset details the spectral intensity and phase from 220 nm to 290 nm generated at z=63.96 cm. The spectral phase aberration is small and can be further compensated easily. Figure 8 shows the corresponding temporal profiles generated by the UV SC at frequency window from 210 nm to 310 nm at several different propagation distances. A 5-fs pulse with peak intensity of about 40TW/cm2 can be obtained at propagation distances from 63.96 to 65.48 cm just by spectral filtering method.

The reason for generating the UV SC may come from the 4WM of 800-nm (ω0=2.36 PHz) pump pulse with a 400-nm (ωs=4.72 PHz) seed generated by intense self-phase modulation and self-steepening during filamentation following the scheme 2ωs-ω04WM. This is reasonable because the phase match can be satisfied as discussed by Bergé et al. [27

27. L. Bergé and S. Skupin, “Sub-2 fs pulses generated by self-channeling in the deep ultraviolet,” Opt. Lett. 33(7), 750–752 (2008). [CrossRef] [PubMed]

]. Interestingly, a completely analogous isolated blueshifted peak has been observed when the laser pulse filamentation in fused silica in the normal group velocity dispersion (GVD) region [17

17. D. Faccio, A. Averchi, A. Lotti, M. Kolesik, J. V. Moloney, A. Couairon, and P. D. Trapani, “Generation and control of extreme blueshifted continuum peaks in optical Kerr media,” 78, 033825 (2008).

], which has been explained as the blueshifted tail of X wave that is formed in the filaments.

Recently, Aközbek et al. have described the experimental observation of the spectral SC generated by different pulse duration in Ref [31

31. N. Aközbek, S. A. Trushin, A. Baltuška, W. Fuß, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloeme, “Extending the supercontinuum spectrum down to 200nm with few-cycle pulses,” N. J. Phys. 8(9), 177 (2006). [CrossRef]

], where the pulse was focused by a lens of focal length 1 m and accumulated many pulses by a broad-band spectrometer. Compared with their experimental results (Fig. 1(a) in Ref [31

31. N. Aközbek, S. A. Trushin, A. Baltuška, W. Fuß, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloeme, “Extending the supercontinuum spectrum down to 200nm with few-cycle pulses,” N. J. Phys. 8(9), 177 (2006). [CrossRef]

].), the experimentally observed SC generated by a 45-fs pulse is well consistent with our result by simulation as shown in Fig. 6(b). The observed SC generated by a 6-fs pulse can also extend down to 200 nm which is qualitatively consistent with our results shown in Fig. 6(a). However, for the 6-fs pulse, the observed SC intensity did not show an obvious separate peak near 255 nm in the UV but abruptly weakened from 300 nm down to 200 nm. This seems not to be a problem since self-phase modulation is very sensitive to the temporal shape, the spectrum and the spectrum chirp. The experimental pulses may be different from the pulses numerically used.

We have realized that the quadratic phase -ik (0) r 2/2f in the wavefront of the initial laser pulse has significant effect on the filamentation dynamics of femtosecond pulse, especially for few-cycle pulse. We also investigated the propagation dynamics of 45-fs and 6-fs pulses with different quadratic phase such as -ik(ω)r 2/2f � which in fact can result in much different femtosecond dynamics. Therefore, by adjusting the initial laser parameters, the filamentation process can be controlled. The control of filamentation process by changing the initial laser parameters will be discussed in detail in another paper.

Fig. 8. (Color online) On-axis temporal profile obtained by selecting spectral component at wavelength 210 nm<λ<310 nm at several positions when a 6-fs pulse is focused in argon by a lens with focal length 60 cm.

4. Conclusion

In conclusion, we have investigated the filamentation and self-compression of femtosecond pulses focused in argon by a lens of focus length 60 cm at different input powers and pulse durations from 45 fs down to 6 fs. The pulse can be self-compressed at the region of post-filamentation at Pin=8.2 Pcr and last over 30 cm. By properly employing high-pass filter, the pulse can be further shortened to about 7 fs which approaches to the Fourier transform limit of the corresponding spectral SC. As a comparison, the propagation dynamics of a 6-fs pulse is very different from that of a 45-fs pulse, which cannot be further self-compressed into a shorter pulse by filamentation although it can generate much broader SC extending from 200 nm to 1300 nm. It is also found that a separate and strong SC in the ultraviolet region extending from 220 nm to 300 nm and peaked at about 255nm can be generated, which can be explained as 4WM of a 800-nm pump pulse (i.e. input pulse) and a 400-nm seed pulse mainly generated by intense SPM and self-steepening during filamentation. The UV SC generated at proper propagation distance corresponds to a few-cycle pulse with duration of about 5 fs in time domain without spectral phase compensation.

Acknowledgements

This work was supported by the Chinese National Natural Science Foundations (Contract No 10674145) and the National Basic Research Program of China (Contract No 2006CB806000).

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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]

12.

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]

13.

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 Pt 2), 056604 (2006). [CrossRef]

14.

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

15.

X. Chen, Y. Leng, J. Liu, Y. Zhu, R. Li, and Z. Xu, “Pulse self-compression in normally dispersive bulk media,” Opt. Commun. 259(1), 331–335 (2006). [CrossRef]

16.

S. Henz and J. Herrmann, “Self-channeling and pulse shortening of femtosecond pulses in multiphoton-ionized dispersive dielectric solids,” Phys. Rev. A 59(3), 2528–2531 (1999). [CrossRef]

17.

D. Faccio, A. Averchi, A. Lotti, M. Kolesik, J. V. Moloney, A. Couairon, and P. D. Trapani, “Generation and control of extreme blueshifted continuum peaks in optical Kerr media,” 78, 033825 (2008).

18.

L. Bergé and A. Couairon, “Gas-Induced Solitons,” Phys. Rev. Lett. 86(6), 1003–1006 (2000). [CrossRef]

19.

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

20.

H. Ward and L. Bergé, “Temporal shaping of femtosecond solitary pulses in photoionized media,” Phys. Rev. Lett. 90(5), 053901 (2003). [CrossRef] [PubMed]

21.

L. Bergé, “Self-compression of 2 microm laser filaments,” Opt. Express 16(26), 21529–21543 (2008). [CrossRef] [PubMed]

22.

L. Bergé, S. Skupin, and G. Steinmeyer, “Self-recompression of laser filaments exiting a gas cell,” Phys. Rev. A 79(3), 033838 (2008). [CrossRef]

23.

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

24.

C. G. Durfee Iii, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22(20), 1565–1567 (1997). [CrossRef]

25.

C. G. Durfee Iii, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24(10), 697–699 (1999). [CrossRef]

26.

F. Théberge, N. Aközbek, W. Liu, A. Becker, and S. L. Chin, “Tunable ultrashort laser pulses generated through filamentation in gases,” Phys. Rev. Lett. 97(2), 023904 (2006). [CrossRef] [PubMed]

27.

L. Bergé and S. Skupin, “Sub-2 fs pulses generated by self-channeling in the deep ultraviolet,” Opt. Lett. 33(7), 750–752 (2008). [CrossRef] [PubMed]

28.

L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100(11), 113902 (2008). [CrossRef] [PubMed]

29.

Z. Wang, J. Liu, R. Li, and Z. Xu, “Spectral analysis and control to obtain sub-5 fs pulses by femtosecond filamentation,” Opt. Lett. 33(24), 2964–2966(2008). [CrossRef] [PubMed]

30.

S. Trushin, S. Panja, K. Kosma, W. E. Schmid, and W. Fuß, “Supercontinuum extending from >1000 to 250 nm, generated by focusing ten-fs laser pulses at 805 nm into Ar,” Appl. Phys. B 80(4–5), 399–403 (2005). [CrossRef]

31.

N. Aközbek, S. A. Trushin, A. Baltuška, W. Fuß, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloeme, “Extending the supercontinuum spectrum down to 200nm with few-cycle pulses,” N. J. Phys. 8(9), 177 (2006). [CrossRef]

32.

S. A. Trushin, K. Kosma, W. Fuss, and W. E. Schmid, “Sub-10-fs supercontinuum radiation generated by filamentation of few-cycle 800 nm pulses in argon,” Opt. Lett. 32(16), 2432–2434 (2007). [CrossRef] [PubMed]

33.

K. Kosma, S. A. Trushin, W. Fuß, and W. E. Schmid, “Characterization of supercontinuum radiation generated by self-focusing of few-cycle 800-nm pulses in Argon,” J. Mod. Opt. 55(13), 2141–2177 (2008). [CrossRef]

34.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000). [CrossRef]

35.

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. Lett. 92, 253901 (2004). [CrossRef] [PubMed]

36.

J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Z. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006). [CrossRef] [PubMed]

37.

J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74(4), 043801 (2006). [CrossRef]

38.

J. Liu, H. Schroeder, S. L. Chin, W. Yu, R. Li, and Z. Xu, “Space-frequency coupling, conical waves, and small-scale filamentation in water,” Phys. Rev. A 72(5), 053817 (2005). [CrossRef]

39.

L. Bergé and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7(1), 210–231 (2000). [CrossRef]

40.

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), 424–434 (1960). [CrossRef]

41.

J. W. Thomas, Numerical partial differential equations: finite difference methods (Springer-Verlag, New York, 1995), Chap. 4.

OCIS Codes
(320.5520) Ultrafast optics : Pulse compression
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Ultrafast Optics

History
Original Manuscript: June 10, 2009
Revised Manuscript: July 16, 2009
Manuscript Accepted: July 16, 2009
Published: July 24, 2009

Citation
Zhanxin Wang, Jiansheng Liu, Ruxin Li, and Zhizhan Xu, "Supercontinuum generation and pulse compression from gas filamentation of femtosecond laser pulses with different durations," Opt. Express 17, 13841-13850 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13841


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References

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  5. M. Mlejnek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: A pressure dependence study,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(4), 4903–4910 (1998). [CrossRef]
  6. M. Nurhuada, A. Suda, M. Hatayama, K. Nagasaka, and K. Midorikawa, “propagation dynamics of femtosecond laser pulses in argon,” Phys. Rev. A 66(2), 023811 (2002). [CrossRef]
  7. S. Champeaux and L. Bergé, “Femtosecond pulse compression in pressure-gas cells filled with argon,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 066603 (2003). [CrossRef]
  8. 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]
  9. 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]
  10. X. Chen, X. Li, J. Liu, P. Wei, X. Ge, R. Li, and Z. Xu, “Generation of 5 fs, 0.7 mJ pulses at 1 kHz through cascade filamentation,” Opt. Lett. 32(16), 2402–2404 (2007). [CrossRef] [PubMed]
  11. 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]
  12. 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]
  13. 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 Pt 2), 056604 (2006). [CrossRef]
  14. A. Mysyrowicz, A. Couairon, and U. Keller, “Self-compression of optical laser pulses by filamentation,” N. J. Phys. 10(2), 025023 (2008). [CrossRef]
  15. X. Chen, Y. Leng, J. Liu, Y. Zhu, R. Li, and Z. Xu, “Pulse self-compression in normally dispersive bulk media,” Opt. Commun. 259(1), 331–335 (2006). [CrossRef]
  16. S. Henz and J. Herrmann, “Self-channeling and pulse shortening of femtosecond pulses in multiphoton-ionized dispersive dielectric solids,” Phys. Rev. A 59(3), 2528–2531 (1999). [CrossRef]
  17. D. Faccio, A. Averchi, A. Lotti, M. Kolesik, J. V. Moloney, A. Couairon, and P. D. Trapani, “Generation and control of extreme blueshifted continuum peaks in optical Kerr media,” 78, 033825 (2008).
  18. L. Bergé and A. Couairon, “Gas-Induced Solitons,” Phys. Rev. Lett. 86(6), 1003–1006 (2000). [CrossRef]
  19. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84(16), 3582–3585 (2000). [CrossRef] [PubMed]
  20. H. Ward and L. Bergé, “Temporal shaping of femtosecond solitary pulses in photoionized media,” Phys. Rev. Lett. 90(5), 053901 (2003). [CrossRef] [PubMed]
  21. L. Bergé, “Self-compression of 2 microm laser filaments,” Opt. Express 16(26), 21529–21543 (2008). [CrossRef] [PubMed]
  22. L. Bergé, S. Skupin, and G. Steinmeyer, “Self-recompression of laser filaments exiting a gas cell,” Phys. Rev. A 79(3), 033838 (2008). [CrossRef]
  23. L. Bergé, S. Skupin, and G. Steinmeyer, “Temporal self-restoration of compressed optical filaments,” Phys. Rev. Lett. 101(21), 213901 (2008). [CrossRef] [PubMed]
  24. C. G. Durfee Iii, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Ultrabroadband phase-matched optical parametric generation in the ultraviolet by use of guided waves,” Opt. Lett. 22(20), 1565–1567 (1997). [CrossRef]
  25. C. G. Durfee Iii, S. Backus, H. C. Kapteyn, and M. M. Murnane, “Intense 8-fs pulse generation in the deep ultraviolet,” Opt. Lett. 24(10), 697–699 (1999). [CrossRef]
  26. F. Théberge, N. Aközbek, W. Liu, A. Becker, and S. L. Chin, “Tunable ultrashort laser pulses generated through filamentation in gases,” Phys. Rev. Lett. 97(2), 023904 (2006). [CrossRef] [PubMed]
  27. L. Bergé and S. Skupin, “Sub-2 fs pulses generated by self-channeling in the deep ultraviolet,” Opt. Lett. 33(7), 750–752 (2008). [CrossRef] [PubMed]
  28. L. Bergé and S. Skupin, “Few-cycle light bullets created by femtosecond filaments,” Phys. Rev. Lett. 100(11), 113902 (2008). [CrossRef] [PubMed]
  29. Z. Wang, J. Liu, R. Li, and Z. Xu, “Spectral analysis and control to obtain sub-5 fs pulses by femtosecond filamentation,” Opt. Lett. 33(24), 2964–2966 (2008). [CrossRef] [PubMed]
  30. S. Trushin, S. Panja, K. Kosma, W. E. Schmid, and W. Fuß, “Supercontinuum extending from >1000 to 250 nm, generated by focusing ten-fs laser pulses at 805 nm into Ar,” Appl. Phys. B 80(4-5), 399–403 (2005). [CrossRef]
  31. N. Aközbek, S. A. Trushin, A. Baltuška, W. Fuß, E. Goulielmakis, K. Kosma, F. Krausz, S. Panja, M. Uiberacker, W. E. Schmid, A. Becker, M. Scalora, and M. Bloeme, “Extending the supercontinuum spectrum down to 200nm with few-cycle pulses,” N. J. Phys. 8(9), 177 (2006). [CrossRef]
  32. S. A. Trushin, K. Kosma, W. Fuss, and W. E. Schmid, “Sub-10-fs supercontinuum radiation generated by filamentation of few-cycle 800 nm pulses in argon,” Opt. Lett. 32(16), 2432–2434 (2007). [CrossRef] [PubMed]
  33. K. Kosma, S. A. Trushin, W. Fuß, and W. E. Schmid, “Characterization of supercontinuum radiation generated by self-focusing of few-cycle 800-nm pulses in Argon,” J. Mod. Opt. 55(13), 2141–2177 (2008). [CrossRef]
  34. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000). [CrossRef]
  35. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations,” Phys. Rev. Lett. 92, 253901 (2004). [CrossRef] [PubMed]
  36. J. Liu, X. Chen, J. Liu, Y. Zhu, Y. Leng, J. Dai, R. Li, and Z. Xu, “Spectrum reshaping and pulse self-compression in normally dispersive media with negatively chirped femtosecond pulses,” Opt. Express 14(2), 979–987 (2006). [CrossRef] [PubMed]
  37. J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74(4), 043801 (2006). [CrossRef]
  38. J. Liu, H. Schroeder, S. L. Chin, W. Yu, R. Li, and Z. Xu, “Space-frequency coupling, conical waves, and small-scale filamentation in water,” Phys. Rev. A 72(5), 053817 (2005). [CrossRef]
  39. L. Bergé and A. Couairon, “Nonlinear propagation of self-guided ultra-short pulses in ionized gases,” Phys. Plasmas 7(1), 210–231 (2000). [CrossRef]
  40. 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), 424–434 (1960). [CrossRef]
  41. J. W. Thomas, Numerical partial differential equations: finite difference methods (Springer-Verlag, New York, 1995), Chap. 4.

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