OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4740–4751
« Show journal navigation

The effect of long timescale gas dynamics on femtosecond filamentation

Y.-H. Cheng, J. K. Wahlstrand, N. Jhajj, and H. M. Milchberg  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4740-4751 (2013)
http://dx.doi.org/10.1364/OE.21.004740


View Full Text Article

Acrobat PDF (2972 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Femtosecond laser pulses filamenting in various gases are shown to generate long- lived quasi-stationary cylindrical depressions or ‘holes’ in the gas density. For our experimental conditions, these holes range up to several hundred microns in diameter with gas density depressions up to ~20%. The holes decay by thermal diffusion on millisecond timescales. We show that high repetition rate filamentation and supercontinuum generation can be strongly affected by these holes, which should also affect all other experiments employing intense high repetition rate laser pulses interacting with gases.

© 2013 OSA

1. Introduction

Filamentation of femtosecond laser pulses in gases is an area of wide and increasing interest owing to applications such as harmonic generation, supercontinuum generation, and the possibility of generating greatly extended plasma conducting channels [1

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

]. Filaments are produced by the interplay between self-focusing induced by the bound electron nonlinearity in the atoms or molecules of the gas and defocusing from the plasma generated by the self-focused laser light. Typically, millijoule-level optical laser pulses are sufficient for extended filaments. A common application of filaments is broad frequency spectrum generation and pulse shortening [2

2. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57(18), 2268–2271 (1986).

5

5. 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]

] in sealed gas cells, where the laser driver is a high pulse repetition rate system, which can typically range up to 5 kHz.

In this paper, we demonstrate that femtosecond filaments can generate long-lived, radially localized and axially extended depressions in the gas density that gradually dissipate via thermal diffusion on a millisecond timescale. The effect is significant even with pulse energies as low as ~100 μJ. At sufficiently high laser pump repetition rates, we find that the long timescale gas dynamics can strongly influence the propagation of pulses in the pulse train. The drop in gas density caused by heating from nonlinear absorption of the laser is thought to play a role at the <100 ns timescale in the triggering of electrical discharges by filaments [6

6. F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pepin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28(2), 418–433 (2000). [CrossRef]

,7

7. S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, “Femtosecond laser-guided electric discharge in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 057401 (2001). [CrossRef] [PubMed]

], but to our knowledge the very long time scale behavior has not been recognized to affect filamentation at high pulse repetition rates.

The experiment consists of three parts. In the first part, we demonstrate the effect of laser pulse repetition rate on the self-focusing collapse and filament spectrum as a function of propagation distance in room air. In the second part, we examine the effect of pulse repetition rate on supercontinuum generation in a Xenon gas cell. In the third part, we present results of longitudinal interferometry measurements of long timescale gas evolution after femtosecond laser interaction. We then present simulations of the density hole evolution and use those results to gain physical insight and interpret our experiments.

2. Experiments

For all experiments, the laser pulses were generated by a 1 kHz Ti:Sapphire laser system capable of producing up to 3.5 mJ, 40 fs pulses centered at 800 nm. For the air filament experiment we used 0.9-1.5 mJ laser pulses focused at f/600 with a 3 m lens. The filament core spectrum was measured as a function of propagation distance by scanning a rail-mounted pinhole along the propagation path and collecting the forward emission on the exit side. The pinhole was prepared prior to the experiment by drilling a ~300 µm diameter hole in a thin Teflon sheet with the 1 kHz filamenting beam at multiple axial locations. This guaranteed negligible further pinhole erosion during a full axial scan. The filament was generated on an enclosed optical table to minimize shot-to-shot transverse position movement from air currents in the laboratory. The filament propagation terminates within ~2 mm past the pinhole exit. Simulations using the propagation code of ref [8

8. J. P. Palastro, T. M. Antonsen Jr, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86(3), 033834 (2012). [CrossRef]

]. show that no additional nonlinear frequency broadening is imparted beyond this point. Therefore, the collected spectrum is that of the propagating laser at the filament core. For this experiment, the laser was operated at 1 kHz but the repetition rate for focused pulses was controlled with chopper wheels synchronized to the laser timing. We found earlier that controlling the repetition rate with the laser’s regenerative amplifier Pockels cell resulted in slight thermally-induced changes to the beam intensity profile and phase front which were sufficient to affect the filamentation collapse location.

The filament core spectrum as a function of axial position for three laser repetition rates and pulse energies is shown in Fig. 1
Fig. 1 Filament core spectrum vs. propagation distance as a function of pump energy and repetition rate. Propagation distance is measured with respect to the vacuum focus. The laser pulse propagates from below in these panels. The white dotted line shows the position of beam collapse to a filament.
. The laser pulse propagates from below. In each panel, the axial location of beam collapse to a filament is shown with a dotted line. This was observed by recording the axial location where plasma fluorescence begins and is coincident with the onset of a strong blue shift owing to gas ionization. It is seen that the collapse position moves farther from the lens as the pulse repetition rate increases from 250 Hz to 1 kHz, and this axial shift increases with pulse energy. The onset of spectral blue wings, the signature of plasma generation, follows this axial shift, and the extent of the blue wings increases with repetition rate, especially for the higher energy pulses.

To understand the origin of these repetition rate dependent effects, we performed longitudinal interferometry on femtosecond filament-excited gas. For this experiment, we operated the pump laser at 20 Hz (50 ms between pulses) in order to measure the long timescale gas dynamics driven by a single pump pulse. Since the results from the filament and supercontinuum experiments (Figs. 1 and 2) indicate possible dependence on a gas evolution timescale ranging up to milliseconds, we could not use a standard optical pump-probe delay line. Instead, we used a gated CCD camera and a continuous probe beam from a 635 nm CW diode laser which counter-propagated through the pump-excited interaction region, overlapping the pump beam. The setup is shown in Fig. 3
Fig. 3 Interferometry setup. The CW diode probe laser counter-propagates with respect to the pump beam direction, passes through the pump focusing lens, and enters the folded wavefront interferometer.
.

The probe passed back through the pump focusing lens, was separated from the pump beam with a 800 nm dielectric mirror (M), and then was sent through a folded wavefront interferometer [9

9. T. R. Clark and H. M. Milchberg, “Time- and space-resolved density evolution of the plasma waveguide,” Phys. Rev. Lett. 78(12), 2373–2376 (1997). [CrossRef]

,10

10. T. R. Clark and H. M. Milchberg, “Time-evolution and guiding regimes of the laser-produced plasma waveguide,” Phys. Plasmas 7(5), 2192–2197 (2000). [CrossRef]

]. The vacuum focal plane of the pump laser beam was imaged onto a CCD camera at the exit of the interferometer. Temporal gating of the probe was obtained by triggering the CCD camera’s electronic shutter with an adjustable delay with respect to the pump pulse. We used the minimum temporal window of the electronic shutter of ~40 µs, which set the time resolution. As will be seen, this resolution is sufficient for measuring the long timescale gas response to the femtosecond pump pulse.

The linearly polarized 40 fs pump pulse was focused at f/65 into the chamber backfilled with various pressures of Kr, O2, N2, Ar, and air. The laser spot full width at half maximum (FWHM) diameter was ~60 μm. The pulse energy was adjusted using a waveplate and polarizer. Figure 4(a)
Fig. 4 (a) Gas average number density profiles vs. probe delay with respect to interaction of a 800 nm, 0.72 mJ, 40 fs pulse focused at f/65 into air at 1 atm. The inset shows electron density measured with spectral interferometry [11, 12]. (b) Lineouts of the air density profiles of Fig. 4(a). The blue curve is the measurement; the red curve is a Gaussian fit. The spatial resolution of the interferometric images is 10 µm. Density was extracted from phase shift maps using the linear polarizabilities of N2 and O2, βN2 = 1.76 × 10−24 cm3 and βO2 = 1.60 × 10−24 cm3 [14].
shows, for pump energy 0.72 mJ, a sequence of gas density profiles in 1 atm air extracted from the interferograms using well-known fringe analysis techniques [10

10. T. R. Clark and H. M. Milchberg, “Time-evolution and guiding regimes of the laser-produced plasma waveguide,” Phys. Plasmas 7(5), 2192–2197 (2000). [CrossRef]

]. The inset in the upper left of the figure shows the time-dependent phase shift imposed on a collinear spectral interferometry probe in a temporal window centered on the pump (our spectral interferometry diagnostic is described in references [11

11. Y.-H. Chen, S. Varma, A. York, and H. M. Milchberg, “Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O,” Opt. Express 15(18), 11341–11357 (2007). [CrossRef] [PubMed]

,12

12. J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett. 107(10), 103901 (2011). [CrossRef] [PubMed]

]). The initial electron density of ~1.4x1016 cm−3 is extracted from the phase shift ~0.6 ps after the pump pulse.

By the first frame shown in the sequence, at 40 µs delay after the pump, the plasma has long ceased to exist, as it will have recombined well before ~10 ns [13

13. S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181(1-3), 123–127 (2000).

]. The 2D gas density profile is an average over the CW probe laser’s interaction length. The density profile is extracted from the 2D phase shift profile, the known linear polarizabilities of nitrogen and oxygen [14

14. K. P. Birch, “Precise determination of refractometric parameters for atmospheric gases,” J. Opt. Soc. Am. A 8(4), 647–651 (1991). [CrossRef]

] and an interaction length of ~18 mm, determined by the axial extent of the filament’s plasma fluorescence. Simulations of the probe beam propagation using the BPM method [15

15. M. D. Feit and J. A. Fleck Jr., “Light propagation in graded-index optical fibers,” Appl. Opt. 17(24), 3990–3998 (1978).

] show negligible refractive phase front distortion that could complicate interpretation of our 2D phase extraction.

Corresponding lineouts of the gas density are shown in Fig. 4(b), with Gaussian fit curves overlaying the data curves. The profile sequence shows the gas density hole widening and becoming shallower. By ~0.5 ms, there is only a ~1% density depression remaining. Figures 5(a) and (b)
Fig. 5 (a) Number density profiles vs. probe delay with respect to interaction of a 800 nm, 0.72 mJ, 40 fs pulse focused at f/65 into N2 at 1 atm. (b) Lineouts of the N2 density profiles of Fig. 5(a). The blue curve is the measurement; the red curve is a Gaussian fit. The spatial resolution of the interferometric images is 10 µm. Density was extracted from phase shift maps using the linear polarizability of N2, βN2 = 1.76 × 10−24 cm3 [14].
show similar plots for 1 atm of N2. Qualitatively similar results occur for the other gases and pressures used.

3. Simulations of gas density hole evolution

To gain an understanding of the density hole evolution on gas type, pressure, and pump laser parameters, we performed simulations of the gas hydrodynamic evolution in cylindrical geometry using a one-dimensional Lagrangian one-fluid hydrocode, in which the conservation equations for mass, momentum and energy, ξi/t+(ξiv+ϕi)=Si, were solved numerically. The mass equation has ξ1 = ρ and ϕ1 = 0, the momentum equation has ξ2 = ρv and ϕ2=PI (where I is the unit tensor), and the energy equation has ξ3 = ε + ½ ρv2 and ϕ3 = Pv + q. Here, ξ is the volume density of the conserved quantity, ϕ is the flux of that quantity, and S refers to sources or sinks, while ρ is mass density, ε is fluid internal energy density, v is fluid velocity, P is gas pressure, and q is the heat flux. At all times, S1 = S2 = 0 owing to mass and momentum conservation, but S3≠0 because the thermal part of the energy density is changed by laser heating and by ionization/recombination of all the relevant species in the gas. Solving the full set of fluid plus species population equations from the femtosecond through millisecond timescales requires accurate microscopic rates, including those for inelastic collisions, ionization, attachment, and recombination from the initial plasma at ~5 eV down to room temperature. Many of these rates are not well known. Furthermore, in principle one must keep track of all the species involved (atoms, ions, molecules, molecular ions) and their various states of excitation.

We can, however, proceed by recognizing that at times >>10 ns after laser excitation, all of the energy initially stored in free electron thermal energy and in the ionization and excitation distribution has been repartitioned into an essentially fully recombined gas in its ground electronic state. If the gas is molecular, for the conditions of our experiments it will also be in the ground vibrational state and in a thermal distribution of rotational states. Because the thermal conductivity of neutral gas is much smaller than that of plasma, the total energy initially deposited by the femtosecond laser pulse remains contained within a diameter comparable to the original laser spot size. As the ambipolar diffusion during the recombination process is much less than the laser spot width of ~50 μm, the ‘initial’ radial pressure distribution driving the gas hydrodynamics at times >10 ns is set by the initial plasma conditionsP0(r)=N(r)kBT(r)(fe/fg)Ne(r)kBTe(r), where kB is Boltzmann’s constant, Ne(r) and Te(r) are the initial electron density and electron temperature profiles immediately after femtosecond laser pumping of the gas, and N(r) and T(r) are the neutral gas number density and temperature profiles. This expression depends on the thermodynamic degrees of freedom of the free electrons (fe = 3 translational degrees of freedom) and the gas, fg, which depends on the gas type and temperature. In addition, an initial radial velocity profile with a weak positive gradient is imposed to mimic the results of our full hydrodynamic simulations at times <10 ns. In practice, our long timescale simulation results are insensitive to the detailed shapes of either the initial pressure profile or the fluid velocity profile, and depend mostly on the peak initial electron density and temperature and the radial scale length. To simulate the neutral gas response at long timescales we solve the fluid equations for the ξi, using S3 = 0 and the initial pressure profile given by P0(r) above. We expect the fluid velocity field to relax over a timescale τrelax~R0/cs, where R0 is the initial radial scale of the laser heating, given by the laser spot radius, and cs = (kBT/m)1/2 is the gas sound speed, where m is the atom or molecule mass. For R0~50 μm, Ne~1.5x1016 cm−3 and kBTe ~5 eV (typical filament electron density and temperature (see below)), and N ~2.5x1019 cm−3 for a 1 atm ambient gas, we find ΔT~100 K as a result of repartitioning and τrelax ~1 μs. As we shall see, this timescale is borne out by the fluid simulations: for all gases and pressures of this experiment, by a few microseconds after the laser interaction, the fluid velocity field has relaxed and the pressure becomes constant with radial position. A quasi-equilibrium is reached where the gas density profile is then just the inverse of the temperature profile, and further evolution is described by thermal diffusion.

To understand the earlier time evolution of the gas before the thermal diffusion-dominated phase, Fig. 6
Fig. 6 Hydrodynamic simulation of the early phase of gas evolution of 1 atm N2. Initial conditions are Ne = 1.5 × 1016 cm−3 and kBTe = 5 eV. The density profile becomes quasi-stationary by ~2 μs.
shows simulation results in 1 atm N2 capturing the dynamics at times <10 μs after the pump pulse. We used Ne = 1.5 × 1016 cm−3 and kBTe = 5 eV as the initial plasma conditions as the source of thermal energy repartitioned into the atmospheric pressure neutral gas. While there are direct measurements of filament electron density (see Fig. 4(a) and ref [16

16. 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]

].), we rely on measurements of <10 eV electron spectra [17

17. C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5(5), 335–338 (2009). [CrossRef]

] from above threshold ionization in dilute nitrogen gas for laser intensity <1014 W/cm2. As will be seen, the good agreement between measurements and simulations of the gas density hole justify this choice of initial electron temperature. The repartitioning of the plasma energy to neutral gas assumes 3 degrees of translational freedom of the molecules (3×12kBT)plus 2 degrees of rotational freedom (2×12kBT), so that fg = 5. The resulting gas temperature change (ΔT~100 K) is insufficient for excitation of significant molecular vibration. It is seen that by ~1 μs, a sound wave has separated away from the interaction region and propagates to the simulation (absorbing) boundary, and by ~2 μs, a quasi-stationary density hole is established, in agreement with our earlier estimate for this timescale.

Figure 7(a)
Fig. 7 (a) Simulated evolution of the gas density hole at later times. (b) Hole FWHM d1/2 vs. time. The red curve is a fit tod1/2=(R02+4αt)1/2,indicating that the long time evolution of the gas is thermal diffusion dominated.
shows simulation results for times up to 1 ms for the same conditions as in Fig. 6. Good agreement is seen with the experimental N2 density profiles of Fig. 5. In Fig. 7(b), we plot the hole FWHM diameter d1/2 as a function of time. At these long times, the gas density profile evolution is governed completely by thermal diffusion, as indicated by the time dependence d1/2 ~t1/2. When there is no longer hydrodynamic motion (v~0), which is the case here after several microseconds as seen in Fig. 6, the energy conservation equationξ3/t+(ξ3v+ϕ3)=0becomesε/t=q. Using q=κT, where κ is the neutral gas thermal conductivity, this becomes T/t=α2T, the thermal diffusion equation, whereα=κ/cp, assuming constant κ and specific heat capacity cp. At the pressures used in our experiments, the gas dynamics are nearly ideal [18] with cp = 5NkB/2 for a monatomic gas and cp = 7NkB/2 for a gas of diatomic molecules. In the temperature range achieved after repartitioning of the initial plasma energy to the neutral gas (ΔT~100 K), the thermal conduction is only very weakly dependent on temperature. For an initial Gaussian temperature distribution with a 1/e radius of R0, the solution to the thermal diffusion equation is T(r,t)=T0(R02/(R02+4αt))exp(r2/(R02+4αt))+Tb, where T0 is the peak temperature and Tb is the background temperature (room temperature) of the gas. Because for our conditions the hydrodynamics has ceased after ~1 μs, the gas conforms to the pressure balance N(r,t)T(r,t) = NbTb, where Nb is the background gas density. For a relatively shallow depression, we get ΔN(r,t)=NbT0Tb1(R02/(R02+4αt))exp(r2/(R02+4αt)) for the density profile, where the width varies as ~(R02+4αt)1/2and the depth varies as~(R02+4αt)1, with the holes in heavier gases (smaller κ and α) expanding and decaying more slowly. For t>R02/4α (~10 µs for R0 = 50 µm and 1 atm air), the width and depth vary as ~(αt)1/2 and ~(αt)1. We note that the measured long timescale density profiles for all gases investigated are very well fit by Gaussians, of which Figs. 4(b) and 5(b) are examples.

The fact that thermal diffusion dominates the long timescale evolution of all of our tested gases is highlighted by Fig. 8
Fig. 8 Log-log plot of measured FWHM of density hole vs. time for our range of gases and conditions. The good fit to lines of slope ½ verifies that the long time gas evolution is dominated by thermal diffusion.
, which is a log-log plot of measured density hole FWHM diameter vs. time for a range of gases and pressures. All points are well fitted to lines with slope ½ as predicted by the thermal diffusion equation. The fitted lines were used to extract the thermal diffusion coefficients α of the gases, from which the thermal conductivities were determined byκ=αcp. These are compared to the literature values in Table 1

Table 1. Thermal Conductivities Extracted from Fits in Fig. 8 and Comparison to Literature Values

table-icon
View This Table
, showing good agreement.

4. Discussion and conclusions

What is the effect of this on laser pulse propagation? In general, the effect of the gas density hole, especially in the highly nonlinear filamentary regime, is best understood with detailed simulations [8

8. J. P. Palastro, T. M. Antonsen Jr, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86(3), 033834 (2012). [CrossRef]

], which are now underway. Such simulations will help interpret the details of Figs. 1 and 2. The goal of the present paper, however, is to present measurements of the density hole itself and some demonstrations of its effects on propagation. Below we present qualitative estimates in order to understand the main features of the propagation measurements.

For the case of a 1 kHz pulse train, the defocusing effect of the index hole on the propagating beam can be estimated using the hole refractive index shift Δn sampled across the beam, as seen in Fig. 9(b). The shift ranges from −10−6 to −10−5, depending on beam diameter. For higher repetition rates or pump pulse energies, the index shifts would be even larger. The effective f-number of the density hole which contributes to beam defocusing as strongly as natural beam diffraction is f# = ½(2∣Δn∣)−1/2, giving f# ~100 to ~350 for the above range of Δn. Our air filament experiment of Fig. 1 uses f/600 focusing, so it is clear that the cumulative density hole should have a significant defocusing influence. This is seen in Fig. 1, where the entire filament (initial collapse point and later termination) appears to move increasingly downstream from the lens and also lengthens with increasing pulse repetition rate. The increasing repetition rate effect of the long timescale density hole appears to be equivalent to using progressively weaker focusing lenses for filament generation. The supercontinuum generation experiment of Fig. 2 uses f/100 focusing, so the effect of the density hole should also be observable. This is borne out by the significant effect of repetition rate on the spectra, with appreciable blue wings added likely owing to increased filament length.

The mechanism considered thus far for gas density hole generation has been the initial plasma acting as a thermal pressure source. However, another channel for laser energy deposition in gases exists, namely 2-photon Raman excitation of molecular rotation [19

19. D. V. Kartashov, A. V. Kirsanov, A. M. Kiselev, A. N. Stepanov, N. N. Bochkarev, Y. N. Ponomarev, and B. A. Tikhomirov, “Nonlinear absorption of intense femtosecond laser radiation in air,” Opt. Express 14(17), 7552–7558 (2006). [CrossRef] [PubMed]

]. The excitation manifests itself as an ensemble average molecular alignment with respect to the pump laser polarization. The degree of alignment is expressed as cos2θt13, where t refers to a time-dependent average over the molecular ensemble [11

11. Y.-H. Chen, S. Varma, A. York, and H. M. Milchberg, “Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O,” Opt. Express 15(18), 11341–11357 (2007). [CrossRef] [PubMed]

] and θ is the angle between the molecular axis and the laser polarization. The average alignment decays due to collisional dephasing over several hundred picoseconds in room temperature, atmospheric pressure gas [11

11. Y.-H. Chen, S. Varma, A. York, and H. M. Milchberg, “Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O,” Opt. Express 15(18), 11341–11357 (2007). [CrossRef] [PubMed]

], with the potential energy stored in the alignment being converted to thermal energy. This energy can also be the source for gas density hole generation. In other experiments [11

11. Y.-H. Chen, S. Varma, A. York, and H. M. Milchberg, “Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O,” Opt. Express 15(18), 11341–11357 (2007). [CrossRef] [PubMed]

, 12

12. J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett. 107(10), 103901 (2011). [CrossRef] [PubMed]

], we have measured maximum alignments (cos2θt13)max ~0.05 in nitrogen for laser intensities in the range of 5x1013 W/cm2. The average energy stored per molecule in molecular alignment is roughly estimated as ualign~12γeffmaxE2, where E is the peak laser electric field and γeffmax=Δα(cos2θ13)max is the maximum effective molecular polarizability under alignment, where Δα is the polarizability anisotropy [11

11. Y.-H. Chen, S. Varma, A. York, and H. M. Milchberg, “Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O,” Opt. Express 15(18), 11341–11357 (2007). [CrossRef] [PubMed]

]. For a 100 fs pulse of peak intensity 5x1013 W/cm2 and ΔαN2 = 6.7 × 10−25 cm3 [20

20. J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85(4), 043820 (2012). [CrossRef]

], we get ualign~0.005 eV/molecule. Another estimate is obtained using our density matrix code [21

21. S. Varma, Y.-H. Chen, J. P. Palastro, A. B. Fallahkair, E. W. Rosenthal, T. Antonsen, and H. M. Milchberg, “Molecular quantum wake-induced pulse shaping and extension of femtosecond air filaments,” Phys. Rev. A 86(2), 023850 (2012). [CrossRef]

] to calculate the energy invested in the rotational state population transfer excited by the pulse. This gives an average stored energy of 0.004 eV/molecule, in agreement with the alignment-based estimate above.

By comparison, an initial plasma of density Ne~2 × 1016 cm−3 and temperature kBTe~5 eV generated in atmospheric density N2 repartitions its energy to give ~0.004 eV/molecule. So the effects are of similar size. We are currently investigating this molecular gas heating mechanism and its effect on filamentation in greater detail.

Acknowledgments

References and Links

1.

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

2.

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57(18), 2268–2271 (1986).

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).

3.

N. Zhavoronkov, “Efficient spectral conversion and temporal compression of femtosecond pulses in SF6.,” Opt. Lett. 36(4), 529–531 (2011). [CrossRef] [PubMed]

4.

C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. Dimauro, and E. P. Power, “Intense self-compressed, self-phase-stabilized few-cycle pulses at 2 microm from an optical filament,” Opt. Lett. 32(7), 868–870 (2007).

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).

5.

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]

6.

F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pepin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci. 28(2), 418–433 (2000). [CrossRef]

7.

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, “Femtosecond laser-guided electric discharge in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 057401 (2001). [CrossRef] [PubMed]

8.

J. P. Palastro, T. M. Antonsen Jr, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A 86(3), 033834 (2012). [CrossRef]

9.

T. R. Clark and H. M. Milchberg, “Time- and space-resolved density evolution of the plasma waveguide,” Phys. Rev. Lett. 78(12), 2373–2376 (1997). [CrossRef]

10.

T. R. Clark and H. M. Milchberg, “Time-evolution and guiding regimes of the laser-produced plasma waveguide,” Phys. Plasmas 7(5), 2192–2197 (2000). [CrossRef]

11.

Y.-H. Chen, S. Varma, A. York, and H. M. Milchberg, “Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O,” Opt. Express 15(18), 11341–11357 (2007). [CrossRef] [PubMed]

12.

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett. 107(10), 103901 (2011). [CrossRef] [PubMed]

13.

S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181(1-3), 123–127 (2000).

J. K. Wahlstrand, Y.-H. Chen, Y.-H. Cheng, S. R. Varma, and H. M. Milchberg, “Measurements of the high field optical nonlinearity and electron density in gases: application to filamentation experiments,” IEEE J. Quantum Electron. 48(6), 760–767 (2012).

14.

K. P. Birch, “Precise determination of refractometric parameters for atmospheric gases,” J. Opt. Soc. Am. A 8(4), 647–651 (1991). [CrossRef]

15.

M. D. Feit and J. A. Fleck Jr., “Light propagation in graded-index optical fibers,” Appl. Opt. 17(24), 3990–3998 (1978).

K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot measurement of laser-induced double step ionization of helium,” Opt. Express 10(26), 1563–1572 (2002).

16.

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]

17.

C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys. 5(5), 335–338 (2009). [CrossRef]

18.

http://webbook.nist.gov/chemistry/fluid/

W. M. Haynes, Handbook of Chemistry and Physics, 93rd edition (CRC Press, 2012), http://www.hbcpnetbase.com/

19.

D. V. Kartashov, A. V. Kirsanov, A. M. Kiselev, A. N. Stepanov, N. N. Bochkarev, Y. N. Ponomarev, and B. A. Tikhomirov, “Nonlinear absorption of intense femtosecond laser radiation in air,” Opt. Express 14(17), 7552–7558 (2006). [CrossRef] [PubMed]

20.

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85(4), 043820 (2012). [CrossRef]

21.

S. Varma, Y.-H. Chen, J. P. Palastro, A. B. Fallahkair, E. W. Rosenthal, T. Antonsen, and H. M. Milchberg, “Molecular quantum wake-induced pulse shaping and extension of femtosecond air filaments,” Phys. Rev. A 86(2), 023850 (2012). [CrossRef]

OCIS Codes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(260.5950) Physical optics : Self-focusing
(350.6830) Other areas of optics : Thermal lensing
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 16, 2013
Revised Manuscript: February 11, 2013
Manuscript Accepted: February 11, 2013
Published: February 19, 2013

Citation
Y.-H. Cheng, J. K. Wahlstrand, N. Jhajj, and H. M. Milchberg, "The effect of long timescale gas dynamics on femtosecond filamentation," Opt. Express 21, 4740-4751 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4740


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep.441(2-4), 47–189 (2007). [CrossRef]
  2. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett.57(18), 2268–2271 (1986).
  3. 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).
  4. N. Zhavoronkov, “Efficient spectral conversion and temporal compression of femtosecond pulses in SF6.,” Opt. Lett.36(4), 529–531 (2011). [CrossRef] [PubMed]
  5. C. P. Hauri, R. B. Lopez-Martens, C. I. Blaga, K. D. Schultz, J. Cryan, R. Chirla, P. Colosimo, G. Doumy, A. M. March, C. Roedig, E. Sistrunk, J. Tate, J. Wheeler, L. F. Dimauro, and E. P. Power, “Intense self-compressed, self-phase-stabilized few-cycle pulses at 2 microm from an optical filament,” Opt. Lett.32(7), 868–870 (2007).
  6. 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).
  7. 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]
  8. F. Vidal, D. Comtois, C.-Y. Chien, A. Desparois, B. La Fontaine, T. W. Johnston, J.-C. Kieffer, H. P. Mercure, H. Pepin, and F. A. Rizk, “Modeling the triggering of streamers in air by ultrashort laser pulses,” IEEE Trans. Plasma Sci.28(2), 418–433 (2000). [CrossRef]
  9. S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, “Femtosecond laser-guided electric discharge in air,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(5), 057401 (2001). [CrossRef] [PubMed]
  10. J. P. Palastro, T. M. Antonsen, and H. M. Milchberg, “Compression, spectral broadening, and collimation in multiple, femtosecond pulse filamentation in atmosphere,” Phys. Rev. A86(3), 033834 (2012). [CrossRef]
  11. T. R. Clark and H. M. Milchberg, “Time- and space-resolved density evolution of the plasma waveguide,” Phys. Rev. Lett.78(12), 2373–2376 (1997). [CrossRef]
  12. T. R. Clark and H. M. Milchberg, “Time-evolution and guiding regimes of the laser-produced plasma waveguide,” Phys. Plasmas7(5), 2192–2197 (2000). [CrossRef]
  13. Y.-H. Chen, S. Varma, A. York, and H. M. Milchberg, “Single-shot, space- and time-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O,” Opt. Express15(18), 11341–11357 (2007). [CrossRef] [PubMed]
  14. J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett.107(10), 103901 (2011). [CrossRef] [PubMed]
  15. S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun.181(1-3), 123–127 (2000).
  16. J. K. Wahlstrand, Y.-H. Chen, Y.-H. Cheng, S. R. Varma, and H. M. Milchberg, “Measurements of the high field optical nonlinearity and electron density in gases: application to filamentation experiments,” IEEE J. Quantum Electron.48(6), 760–767 (2012).
  17. K. P. Birch, “Precise determination of refractometric parameters for atmospheric gases,” J. Opt. Soc. Am. A8(4), 647–651 (1991). [CrossRef]
  18. M. D. Feit and J. A. Fleck., “Light propagation in graded-index optical fibers,” Appl. Opt.17(24), 3990–3998 (1978).
  19. K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot measurement of laser-induced double step ionization of helium,” Opt. Express10(26), 1563–1572 (2002).
  20. 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]
  21. C. I. Blaga, F. Catoire, P. Colosimo, G. G. Paulus, H. G. Muller, P. Agostini, and L. F. DiMauro, “Strong-field photoionization revisited,” Nat. Phys.5(5), 335–338 (2009). [CrossRef]
  22. http://webbook.nist.gov/chemistry/fluid/
  23. W. M. Haynes, Handbook of Chemistry and Physics, 93rd edition (CRC Press, 2012), http://www.hbcpnetbase.com/
  24. D. V. Kartashov, A. V. Kirsanov, A. M. Kiselev, A. N. Stepanov, N. N. Bochkarev, Y. N. Ponomarev, and B. A. Tikhomirov, “Nonlinear absorption of intense femtosecond laser radiation in air,” Opt. Express14(17), 7552–7558 (2006). [CrossRef] [PubMed]
  25. J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A85(4), 043820 (2012). [CrossRef]
  26. S. Varma, Y.-H. Chen, J. P. Palastro, A. B. Fallahkair, E. W. Rosenthal, T. Antonsen, and H. M. Milchberg, “Molecular quantum wake-induced pulse shaping and extension of femtosecond air filaments,” Phys. Rev. A86(2), 023850 (2012). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited