Q. Luo et al- Effect of beam diameter on the propagation of intense femtosecond laser pulses

8/3/2019 Q. Luo et al- Effect of beam diameter on the propagation of intense femtosecond laser pulses

http://slidepdf.com/reader/full/q-luo-et-al-effect-of-beam-diameter-on-the-propagation-of-intense-femtosecond 1/4

DOI: 10.1007/s00340-004-1692-2

Appl. Phys. B 80, 35–38 (2005)

Lasers and Optics

Applied Physics B

q. luo1,u

s.a.hosseini1

w.liu1

j.-f. gravel1

o.g.kosareva2

n.a. panov2

n. akozbek3

v.p.kandidov2

g. roy4

s.l.chin1

Effect of beam diameter on the propagationof intense femtosecond laser pulses1 Centre d’Optique, Photonique et Laser (COPL) et Departement de Physique,

de Genie Physique et d’Optique, Universite Laval, Quebec, QC, G1K 7P4, Canada2 International Laser Center, Physics Department, M.V. Lomonosov Moscow State University,

Moscow 119992, Russia3 Time Domain Corporation, 7057 Old Madison Pike, Huntsville, Alabama 35806, USA4 The Remote Sensing Group of the Defense Research and Development Center Valcartier (DRDC Valcartier),

Val-Belair, QC, G3J 1X5, Canada

Received: 21 July 2004/Revised version: 6 October 2004

Published online: 10 November 2004 • © Springer-Verlag 2004

ABSTRACT This paper describes the effects observed during the

propagation of intense femtosecond laser pulses in air follow-ing the modification of the laser beam diameter with a pair of convex–concave lenses placed/mounted in a telescopic config-uration. We observed that by reducing the diameter of the beamthe detected back-scattered nitrogen fluorescence from the fil-aments becomes more stable on a shot-to-shot basis while, fora larger beam size, greater fluctuations are observed that are notcorrelated to shot-to-shot fluctuations in the laser pulse energy.This result leads to a new method to control the fluorescence sig-nal which can be very important in remote-sensing applications.

PACS 42.65.Jx; 42.68.Ay; 42.68.Wt

1 Introduction

The propagation of intense femtosecond laserpulses in air is a relatively complex phenomenon involvingthe strong reshaping of the spatial and temporal profile of thelaser pulse through a combined action of linear and nonlin-ear effects [1–3]. The optical Kerr effect causes the beam toself-focus, resulting in an increase of the peak intensity. Athigh peak intensity, multiphoton/tunnel ionization (MPI/TI)of molecules and atoms in air takes place [4], resulting inthe creation of a low-density plasma causing the beam to bede-focused. The dynamic balance between self-focusing andplasma de-focusing repeats itself, resulting in the formation

of a plasma channel that is popularly called a filament. Thenonlinear fluorescence signal from nitrogen molecules (bothneutral and ion) inside the filament has been previously re-ported within the spectral range of 300–420 nm [5, 6]. It hasbeen demonstrated that nitrogen molecules are first ionizedinside the filament through the ejection of either an outermostelectron or an inner valence electron [6, 7]. Radiative relax-ation from excited states gives rise to nitrogen-ion fluores-cence. Electron–ion recombination then leads to the emissionof the second positive band of the neutral N2 molecule [8].

Previous studies of the propagation of terawattTi–sapphirefemtosecond laser pulses over a distance of 100 m in air have

u Fax: +1-418-6562623, E-mail: [email protected]

shown that the back-scattered nitrogen fluorescence signal(BSF) emitted from multiple filaments was clearly detectableover the whole range using a lidar system [9]. However, the

BSF signal fluctuated significantly on a shot-to-shot basis de-spite the rather stable laser pulse energy. By fluctuations, wemean that the signal intensity distribution along the propa-gation path as well as the starting point of the filamentationvaried randomly.

The physical origin of these fluctuations in the BSF signalcan be attributed to a competition among multiple filaments,which is a complex dynamical process evolving in the di-rection of the pulse propagation [10]. Numerical simulationsand experiments have recently shown that an inhomogeneousintensity distribution in the transverse cross section of thepulse, which can originate from either initial laser imperfec-tion or previous propagation through any non-homogeneousoptical medium, ultimately leads to the formation of mul-tiple filaments co-propagating in air [11–14]. Each initiallyindependent filament (or so-called parent filament) emits ra-diation conically with respect to the propagation axis, givingrise to the routinely observed ring structure [15]. The interfer-ence of the divergent fields of neighboring filaments initiatesthe formation and defines the position of new secondary fil-aments (or so called child filaments) if the resulting peak power of the perturbation formed due to the constructive in-terference is sufficient to induce self-focusing and filamentformation [16].

The scenario of multiple-filament competition is very sen-sitive to the relative location of the initial perturbations. If the parent filaments are initially far apart, the interferencewill be weak and the parent filaments will compete with eachother for energy with the surrounding (background) reser-voir [17–19]. Numerical simulations from different groupsshowed that when several filaments are confined in a smallvolume, they can interact and self-maintain over much longerdistances, whereas those distributed in a larger area decaymuch faster [10, 14, 17]. As a result, the plasma channels andthe amplified back-scattered fluorescence signal strongly de-pend on the intensity fluctuations in the beam profile and ontherelative distance between the initial filaments. On the otherhand, if the parent filaments are closely spaced, the inter-ference of the ring structure of these filaments will generatea larger number of child filaments, thus leading to a more



36 Applied Physics B – Lasers and Optics

intense plasma channel and therefore a stronger nitrogen flu-orescence signal.

In order to investigate more about the competition of fil-aments and ultimately have a better control of this process,we have forced the multiple filaments to be closer to one an-other. This was achieved by decreasing the beam diameterwith a convex–concave lens system. Since there is a close

correlation between the plasma density and the fluorescencesignal, the characteristics of the BSF signal of nitrogen weremonitored to follow the impact of these modifications on thefilamentation process.

2 Experimental setup

The experimental setup has been described else-where [9]. Briefly, a femtosecond laser beam with a repetitionrate of 10Hz, 42fs duration (FWHM), central wavelength of 800 nm with a bandwidth of 23nm (FWHM) and linearly po-larized is used in this experiment. The pulse energy can varyfrom a few mJ to 85mJ. The standard deviation of the fluctu-ations of the laser energy is 4.4%. The beam is guided from

a vacuum compressor (10−3 Torr) to a corridor (length 101m)through a 10 m vacuum pipe terminated with a 1.5 cm thick CaF2 window. In our experiments, a laser beam with two dif-ferent diameters is used. The output beam diameter after thevacuum pipe is 25mm (1/e2). A telescope system consistingof a convex lens and a concave lens with 100 cm and -30cmfocal lengths, respectively, is introduced to decrease the beamdiameter to 8 mm (1/e2). The divergence of the small beamcan be changed by varying the position of the concave lens.

The BSF of nitrogen is collected with a lidar systemand detected by a photomultiplier tube (PMT, HamamatsuR7400P, with 1 ns response time; gain= 7×106). Consider-ing that the lifetime of the N2 fluorescence signal is around

1–2 ns [20], the resolution of this detection system is around30–60cm. The field of view of the lidar is equal to 16 mrad.In most of our experiments, the lidar is put just behind thelast mirror of the laser beam path and set at an on-axis pos-ition. In this configuration, the field of view of the lidar systemcovers the whole range of the laser propagation, i.e. the ge-ometrical overlapping factor is always 1 for any distance. Inone of the experiments using the small-size laser beam, the li-dar was moved to an off-axis position and a pinhole is set infront of the PMT in order to detect only the fluorescence sig-nal after the first 35 m propagation distance of the laser pulse.The geometrical overlapping factor is 1 after 35 m.

Two broadband dielectric mirrors reflecting around 800±

25nm are placed in front of the PMT to eliminate any back-scattering of the fundamental laser light. These are followedby a band-pass filter (UG 11, 4 mm thick, band pass 200 to400 nm) transmitting the major spectral lines from nitrogenmolecules and ions in the 300–400 nm region.

3 Experimental results and discussion

Single-shot pictures of the laser beam cross sec-tion are shown in Fig. 1 for (a) a large beam diameter and (b)a small beam diameter. These pictures were taken by a com-mercial digital camera (Canon A40) after 35 m from the lastmirror, where the filaments just start to develop. A white-paper screen was inserted perpendicularly in the beam path

FIGURE 1 Two pictures of the filaments. a The large beam diameter with

40 mJ input laser energy is used. Image is taken at 35 m from the last mirrorwhere the filaments start to develop. b The small beam diameter with 25 mJinput laser energy is used. Image is taken at 2.5 m from the last mirror wherethe filaments start to develop

and the image created at the surface of the paper screen wascaptured by the camera. For the large beam (Fig. 1a), multi-ple filaments are clearly observed since they are far from eachother. One can clearly observe that one of the filaments (in thecenter) is much brighter than theothers. In contrast, in Fig. 1b,one can observe that the filaments are squeezed together andcannot be resolved. Thus only one very bright spot is observedin the center.

In Fig. 2, a three-dimensional graph of 300 shots at30mJ/pulse with large beam diameter (25mm) is presented.The experiment was done with different energies of the laserpulse. In this graph the x axis is the direction of propaga-tion of the beam that is calibrated from the time scale of theoscilloscope and the y axis represents the laser shot number.

The first small peaks at 0.0 m are due to the scattering of the pump pulse from the last mirror in the setup and the lastpeaks are from the beam stop that is fixed at the end of thecorridor. The middle peaks are BSF signals. A close analysis



LU O et al. Effect of beam diameter on the propagation of intense femtosecond laser pulses 37

of the BSF signal distributions shown in Fig. 2 demonstratesthat the fluorescence signals change drastically from shot toshot. This irregularity is well explained in our competitionmodel [10]. The BSF signal varies from shot to shot due to therandom fluctuation of the distance between the hot spots in thebeam cross-sectional area. This leads to either a favorable oran unfavorable situation for the plasma channel formation. In

the favorable case, the distances between the initial hot spotsare shorter; the interference of the ring structure of these fil-aments generates a larger number of child filaments. It thusresults in a large number of secondary plasma columns. Thus,moreintense plasma channels stretching over longer distancescan be observed. In the unfavorable case, the larger separa-tion distance between theinitial hot spots causes less powerfulperturbations arising due to the interference and more com-petition for energy between these perturbations. The resultingfluorescence signal is weaker.

In Fig. 3, the BSF signal with the smaller beam size(8 mm) at 30mJ/pulse is plotted. Here the telescope changesthe beam size and forces the initial perturbations in the beam

to be closer to each other. The signals show a dramatic changecompared to Fig. 2. The BSF signals appear closer to the de-tector, i.e. the filaments start earlier. This is due to the smallerbeam size. The most important thing is that the signals arequite stable and strong from shot to shot, as our theoreticalmodel predicted [10]. The beam size is so small that it forcesthe initial filaments to develop closer to each other. The dis-tance between the initial hot spots is shorter even than in thefavorable case of the relative location of perturbations in thelarge beam. Indeed, thevariation in theseparation distance be-tween the initial perturbations in the case of a large beam isof the order of 23% [10]. The beam is squeezed three times

FIGURE 2 300 shots of BSF waveform detected by PMT. The laser energy

was fixed at 30 mJ/pulse. The diameter of the beam is 25 mm

FIGURE 3 300 shots of BSF waveform detected by PMT. The laser en-ergy was fixed at 30 mJ/pulse. By using the telescope the beam diameter isreduced to 8 mm

when the diameter is decreased from 25 to 8 mm. Therefore,one might expect roughly a three times decrease in the sep-aration distance between the initial perturbations, which arethe seeds for the parent filaments. Smaller separation betweenthe parent filaments leads to earlier formation and closer lo-cation of child filaments. The average width of the filamentsand the corresponding plasma channels become larger. Asa consequence, in the case of a smaller beam diameter morefree electrons are generated. Hence, we can expect a muchstronger BSF signal (Fig. 3). Even with random shot-to-shotfluctuations in the separation distance between the initial per-turbations, the plasma density remains high enough to providea BSF signal at each shot. Thus, not only stronger but alsomore stable BSF signals are observed in the case of a smallerbeam size.

It is interesting to note that the strong signal lasts only upto a distance of around 10 m. After this region, it seems thatno more fluorescence signal can be detected. To further check the signal, we moved the lidar system to the off-axis positionand put a pinhole in front of the PMT. In this setup, the lidarsystem cannot collect the signal from the first 35 m of the laserbeam propagation, so that the strong signal at the beginningis not detected. A higher sensitivity is obtained by increasingthe high voltage of the PMTand using the more sensitive scaleof the oscilloscope. We observed a fluorescence signal for thewhole range limited by the corridor.

In Fig. 4, the average BSF signal of 300 shots is shownfor the case of a smaller input beam size. This signal consistsof two parts: the first 40 m is taken from the first set of ex-periments with an on-axis lidar position and the rest is fromthe second set of experiments with an off-axis lidar position.The signal is calibrated by taking into account the differentgain of the PMT with different high voltages, the different os-



38 Applied Physics B – Lasers and Optics

cilloscope scales and geometrical overlapping factors due todifferent lidar positions. The signal is corrected for differentdistances by multiplying the measured signal by r 2, wherer isthe distance between the signal and the lidar system. The BSFsignals are very strong at the beginning of filament forma-tion and decrease significantly after about 10 m. After that, theweak signal stays at almost the same amplitude and extends to

the end of the corridor.The weak signal shows that the plasma column could ex-tend to a very long distance. However, we are limited bythe corridor length and do not know what the total extent of the plasma column would be. The total extent of the plasmacolumn due to multiple filamentation starts from the initialself-focal point where the powerful pulse at several hundredcritical powers for self-focusing first self-focuses and, in prin-ciple, would end where the peak power inside the pulse isdecreased to just above the critical power for self-focusing.Even if the corridor is long enough, we might be limited bythe sensitivity of our system and might still not be able tomeasure the total extent. We thus estimate what our current

system could measure anddefine this measurable extent of theplasma column as the effective length. In order to estimate theeffective length in our current experiment, the average dataof 300 shots (without r 2 correction) taken from the off-axislidar position is plotted in the inset of Fig. 4. As describedin [9], we fit the tail partof the BSF signal using the lidar equa-tion exp (−αr )/r 2, where α is the attenuation factor (dashedline). This curve can be extrapolated to the baseline of theBSF signal, which corresponds to the limit of our detectionsystem. It suggests roughly an effective length of 564 m forfilaments that can be measured underthis experimental condi-tion provided that filaments exist for this whole range. For thelarge-beam case, the detectable maximum effective filamentlength at 60mJ is only 196 m [9].

It is important to note that a small region can be deter-mined at the beginning of the filament in which the signalis strong. This could be very important for locating the pos-ition of the pollutant precisely in a remote-sensing applica-tion. This small region at the beginning of self-focusing canbe moved, in principle, by varying any or all of the followingparameters: beam divergence, chirp, beam diameter and pulseenergy (peak power). More experimentation needs to be doneon this separate engineering subject.

FIGURE 4 The averaged BSF signal for 300 shots. The inset is the tail partof the signal, the dashed line is the fitted curve. Initial beam diameter is 8 mm

4 Summary and conclusions

We measured the back-scattered fluorescence sig-nal from nitrogen molecules in the filaments in air generatedfrom an intense femtosecond laser pulse with two differentbeam diameters, 25mm and 8 mm. When the beam size is de-creased, the separation of the initial perturbations gets closer.The interference of these initial filaments leads to the for-mation of a larger number of child filaments and, as a con-sequence, a more intense and stable plasma channel, whichgives rise to a higher fluorescence signal. The understandingof the initiations of multiple filaments, consequent propaga-tion and interaction dynamics is important in the control of random fluctuations of the input laser pulse that may leadto longer propagation distances. This is particularly import-ant for potential lidar applications in atmospheric sensing andpollutant measurement.

ACKNOWLEDGEMENTS We would like to acknowledge the

technical support of M. Martin. This work was supported in part by

NSERC, DRDC Valcartier, Canada Research Chairs, CIPI and FQRNT. O.G.

Kosareva, N.A. Panov and V.P. Kandidov acknowledge the support of theEuropean Research Office of the US Army under Contract No. N62558-

04-P-6051 the and Russian Foundation for Basic Research (Grant No. 03-

02-16939). V.P. Kandidov, O.G. Kosareva and S.L. Chin acknowledge the

support of the NATO Linkage (Grant No. PST.CLG.976981).

REFERENCES

1 A. Braun, G. Korn, X. Liu, D. Du, J. Squier, G. Mourou: Opt. Lett. 20,73 (1995)

2 S.L. Chin, A. Brodeur, S. Petit, O.G. Kosareva, V.P. Kandidov: J. Non-linear Opt. Phys. Mater. 8, 121 (1999)

3 S. Tzortzakis, L. Berge, A. Couairon, M. Franco, B. Prade, A. Mysy-rowicz: Phys. Rev. Lett. 86, 5470 (2001)

4 S.L. Chin: ‘From Multiphoton to Tunnel Ionization’. In: Progress in

Multiphoton Processes and Spectroscopy, ed. by S.H. Lin, Y. Fujimura,

A.A. Villaeys (World Scientific, Singapore 2004)5 A. Talebpour, M. Abdel-Fattah, A.D. Bandrauk, S.L. Chin: Laser Phys.

11, 68 (2001)6 A. Talebpour, M. Abdel-Fattah, S.L. Chin: Opt. Commun. 183, 479

(2000)

7 A. Becker, A.D. Bandrauk, S.L. Chin: Chem. Phys. Lett. 343, 345 (2001)8 Q. Luo, W. Liu, S.L. Chin: Appl. Phys. B 76, 337 (2003)9 S.A. Hosseini, Q. Luo, B. Ferland, W. Liu, N. Aközbek, G. Roy,

S.L. Chin: Appl. Phys. B: Lasers Opt. 77, 697 (2003)

10 S.A. Hosseini, Q. Luo, W. Liu, B. Ferland, S.L. Chin, O.G. Kosareva,

N.A. Panov, N. Aközbek, V.P. Kandidov: Phys. Rev. A 70, 033802(2004)

11 S.L. Chin, A. Talebpour, J. Yang, S. Petit, V.P. Kandidov, O.G. Kosareva,M.P. Tamarov: Appl. Phys. B 74, 67 (2002)

12 M. Rodriguez, R. Bourayou, G. Mejean, J. Kasparian, J. Yu, E. Salmon,

A. Scholz, B. Stecklum, J. Eisloffel, U. Laux, A.P. Hatzes, R. Sauerbrey,

L. Wöste, J.-P. Wolf: Phys. Rev. E 69, 036607 (2004)13 M. Mlejnek, M. Kolesik, J.V. Moloney, E.M. Wright: Phys. Rev. Lett. 83,2938 (1999)

14 L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian,

E. Salmon, J.P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, R. Sauer-brey: Phys. Rev. Lett. 92, 225002 (2004)

15 S.L. Chin, N. Aközbek, A. Proulx, S. Petit, C.M. Bowden: Opt. Com-

mun. 188, 181 (2001)16 S.L. Chin, S. Petit, W. Liu, A. Iwasaki, M.C. Nadeau, V.P. Kandidov,

O.G. Kosareva, K.Y. Andrianov: Opt. Commun. 210, 329 (2002)17 V.P. Kandidov, O.G. Kosareva, I.S. Golubtsov, W. Liu, A. Becker,

N. Aközbek, C.M. Bowden, S.L. Chin: Appl. Phys. B 77, 149 (2003)18 V.P. Kandidov, O.G. Kosareva, A.A. Koltun: Quantum Electron. QE-33,

69 (2003)

19 S.L. Chin: Phys. Can. 60, No. 5 (2004)20 A. Iwasaki, N. Aközbek, B. Ferland, Q. Luo, G. Roy, C.M. Bowden,

S.L. Chin: Appl. Phys. B 76, 231 (2003)

Documents

Q. Luo et al- Effect of beam diameter on the propagation of intense femtosecond laser pulses