s.l. chin et al- transverse ring formation of a focused femtosecond laser pulse propagating in air
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8/3/2019 S.L. Chin et al- Transverse ring formation of a focused femtosecond laser pulse propagating in air
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Transverse ring formation of a focused femtosecond laser pulse
propagating in air
S.L. Chin a, N. Akozbek b, A. Proulx a, S. Petit a, C.M. Bowden b,*
a Centre d'Optique, Photonique, et Laser (COPL) and Dept. de Physique, Universite Laval, Que., Qc, Canada G1K 7P4b US Army Aviation and Missile Command Research, Engineering and Development Center, Huntsville, AL 35898-5000, USA
Received 22 September 2000; accepted 20 November 2000
Abstract
We observe the formation of ring patterns of a focused femtosecond near IR laser pulse propagating in air before the
geometrical focal point. These rings are due to the combined eects of self-focusing and defocusing created by the
generated plasma via multiphoton/tunnel ionization of air. Qualitative agreement is found with numerical simulations,
using input conditions similar to those in the experiment. Ó 2001 Elsevier Science B.V. All rights reserved.
Keywords: Nonlinear optics; Self-focusing; Photoionization; Ultrafast processes; Nonlinear phenomena; Waves, Wave propagation
and other interactions
1. Introduction
The formation of ®laments in air by the use of
high-power femtosecond laser pulses has been the
subject of intense interest both experimentally and
theoretically [1±26] for the past several years. Po-
tential practical applications of this phenomenon
include lightning discharge control [1,2] and remote
sensing [12,14]. Besides its possible applications it
is also very interesting from a fundamental non-
linear dynamics point of view. The underlying
physical mechanism, which leads to the formation
of ®laments in air, is due to a dynamic competition
between self-focusing and defocusing created by the
generated plasma [22,23]. However, in general the
full dynamics of these pulses is complicated since
they undergo strong reshaping both temporally and
spatially. Due to the high intensity in the ®lament
incorporating measurement devices directly into
the beam is very dicult. To further elucidate this
phenomenon we use a focused laser pulse and re-
corded damage patterns on a silicate glass plate for
various propagation distances. We observe a com-
plicated ring formation on these plates, which are
attributed to self-focusing, and plasma defocusing.
To the best of our knowledge this is the ®rst ex-
perimental observation of ring formation with near
IR pulses, propagating in air. The damages are
scanned by a DekTak II pro®lometer. This allows
us to get a direct measure of the ablation pro®le,
which gives us a measure of the distributed trans-
verse ¯uence of the laser pulse. This in turn provides
information pertinent to the ®lament, which can be
compared with theoretical predictions. Numerical
simulations using similar laser input parameters
agree qualitatively with the experimental results.
1 February 2001
Optics Communications 188 (2001) 181±186
www.elsevier.com/locate/optcom
* Corresponding author. Fax: +1-256-9557216.
E-mail addresses: nakozbek@hotmail.com (N. Akozbek),
cmbowden@ws.redstone.army.mil (C.M. Bowden).
0030-4018/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.P II: S0 0 3 0 -4 0 1 8 (0 0 )0 1 1 2 9 -9
8/3/2019 S.L. Chin et al- Transverse ring formation of a focused femtosecond laser pulse propagating in air
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2. Experiment and results
The laser system consists of a Ti:sapphire os-
cillator followed by a regenerative and two multi-
ple pass Ti:sapphire ampli®ers that can deliver
pulses with energies of up to 100 mJ with a central
wavelength of 800 nm. In this experiment we used
a 350 fs (FWHM) pulse with energy of 85 mJ, and
a 320 fs (FWHM) pulse with energy of 75 mJ. The
beam diameter at 1=e2 of intensity was 1 cm. The
experimental setup is depicted in Fig. 1. The laser
pulse is focused by a lens with a focal length of
150 cm corresponding to an f -number F 150.
At various positions a silicate glass is inserted.
The photograph of the damage at the surface of
the plate was taken with a phase-contrast micro-
scope and the corresponding depth pro®le across
the diameter was taken with a DekTak scan. Fig.
2 shows the beautiful rings burnt into the glass at
a position of 149.5 cm just before the geometrical
focus. We observe in Fig. 2(a) a central damage
zone surrounded by a small unablated region
followed by a rather homogeneous ablated region,
which is then surrounded by a more complex
outer structure. The corresponding depth pro®le
across the damage diameter is shown in Fig. 2(b),
which exhibits indeed a strong central damagecrater followed by a secondary crater. The in-
tensity between the ®rst and secondary crater was
not high enough to create damage; thus the for-
mation of the damage pattern is a direct result
from the ¯uence pro®le of the laser pulse. The
outer ®ne rings do not show up on the pro®le due
to the resolution of the DekTak scanner, but a
third crater is slightly visible giving rise to another
ablated region. We show in Fig. 3, for slightly
dierent input parameters (320 fs (FWHM) and
75 mJ), the evolution of the depth pro®le fordierent propagation distances. Fig. 3(a) and (b)
are the depth pro®les before the geometrical
Fig. 2. Shown (a) is the damage pattern created by the laser pulse (350 fs, 85 mJ) at a position of 149.5 cm (before the geometrical
focus) and (b) the corresponding depth pro®le taken with a DekTek scan across the damage diameter, which is a direct measure of the
¯uence pro®le of the laser pulse.
Fig. 1. Shown is the experimental setup. The laser pulse is fo-
cused by a lens with a focal length of 150 cm. At various po-
sitions (before the geometrical focal point) a glass plate was
placed in front of the beam, creating a damage pattern on thesurface of the plate. The damage was then analyzed with a
phase contrast microscope.
182 S.L. Chin et al. / Optics Communications 188 (2001) 181±186
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focal point at 143.5 and 149.5 cm, respectively.
Note in Fig. 3(a) the small peak in the center of
the main crater. This would translate as a dip in
the ¯uence pro®le. As we approach the geomet-
rical focal point this center peak disappears as
seen in Fig. 3(b). However, such a dip in the
¯uence reappears beyond the geometrical focal
point shown in Fig. 3(c) at a distance of 157 cm,
but the secondary rings have signi®cantly dimin-
ished. This dynamic behavior of the ¯uence pro-
®le is qualitatively in agreement with numerical
simulations as we discuss in detail in the next
section.
3. Theoretical predictions and discussion
We consider the propagation of an input col-
limated paraxial Gaussian beam focused by a lens:
Ar ; s; z 0 A0 expÀr 2=w20 s
2=s20À ikr 2=2 f ,
where w0 and s0 are the initial beam radius and
pulse width, respectively, f is the focal length
of the lens, and k n0k 0 n0x=c with n0 % 1.
The propagation equation including diraction,
self-focusing and plasma defocusing, for the slowly
varying envelope function Ar ; s; z is given as,
(in the retarded time coordinate frame s t À z =m g )
Fig. 3. The depth pro®le taken across the damage pro®le with the DekTek scan is shown at positions (a) 143.5 cm (b) 149.5 cm and (c)
157 cm. Here the input laser pulse width was 320 fs with an input energy of 75 mJ. Initially, there is a strong central crater followed by a
secondary crater, which indicates the formation of rings. Note the peak in the center part of the damage pro®le in (a) which disappears
in (b) and reappears again in (c). This peak would translate as a dip in the center of the ¯uence pro®le.
S.L. Chin et al. / Optics Communications 188 (2001) 181±186 183
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io
o z
1
2k
o2
or 2
1
r
o
or
n2k 0j Aj
2 À2pe2 N e
kmec2 iC
 Ar ; s; z 0; 1a
N e is the generated electron density via multipho-
ton/tunnel ionization and is governed by
o N e
os N 0 R: 1b
Here, n2 is related to the third order nonlinear
susceptibility of air. N 0 is the number density of
neural air molecules and the ionization rate R 0:2rO2
j Aj2n 0:8rN2
j Aj2m
where rO2, rN2
, n, m are
the cross-sections and eective multiphoton num-bers, respectively for O2 and N2 obtained from ex-
perimentally measured ionization rates [27], (Here
we assumed that air is 20% O2 and 80% N2) and C
describes ionization losses. We have neglected the
eect of dispersion since the ratio of the diraction
length of the focused laser beam to the dispersion
length is much smaller than unity. In addition we
consider an instantaneous Kerr response.
We integrate Eqs. (1a) and (1b) with initial
conditions as close as possible to the experiment.
However, due to the ®xed grid points used in the
numerical scheme a smaller input beam diameter
and focal length of the lens is used such that the f -
number is the same as in the experiment. The peak
input power in the experiment was about 0:2 TW
which is about 35±20 times the critical power for
self-focusing in air (experimental estimation of the
critical power lies between 6 and 10 GW [3,8±11]).
The input parameters considered in the numerical
simulations are taken as, w0 0:2 cm, s0 297 fs,
f 60 cm ( f -number F 150), ( z 0 pw20=k0 is the
diraction length of the collimated input beam),
and P 0 20 P cr, where P cr k20=2pn0n2 is the critical
power for self-focusing in the CW limit, which is
about 3 GW for n2 5 Â 10À19cm2=W [28]. This
critical value is somewhat smaller than estimated by
experiment, which could be due to the fact that thenonlinear response is not purely Kerr-like. In Fig.
4(a) the simulated ¯uence (normalized to the peak
input ¯uence) is plotted as a function of the trans-
verse coordinates x and y (measured in units of the
initial beam radius) before the geometrical focal
point at a position of 59.75 cm. Alternatively, in
Fig. 4(b) the positions of the rings are plotted on a
2-D plot. We clearly see the formation of the rings
of the ¯uence pro®le, which agrees well with the
experimental observations. There is a central part
followed by a secondary ring and further out we see
Fig. 4. Shown in (a) are numerical results for the ¯uence (normalized to the peak input ¯uence) pro®le depicted in 3-D as a function of
the transverse coordinates x and y measured in units of the initial beam radius and (b) is the corresponding ring structure plotted in 2-
D, where only the peaks of the rings are shown. The ¯uence distribution in (a) is in good qualitative agreement with the experimentally
observed damage pro®le shown in Fig. 2(b) in which the ring formation is clearly observed. The outer rings depicted in Fig. 2(a) are
also apparent in (b).
184 S.L. Chin et al. / Optics Communications 188 (2001) 181±186
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4. Conclusion
In conclusion, we observed the formation of
ring structure during the propagation of a focused
femtosecond laser pulse. These rings are due to the
combined eects of self-focusing, and defocusing
by the plasma. Numerical simulations at least
qualitatively agree with the ring formation before
and after the geometrical focal point. We plan to
investigate more quantitatively the ring formation
by including re¯ections and interactions with the
surface into our present theoretical model.
Acknowledgements
N.A. would like to thank the ®nancial support
from the National Research Council and is grate-
ful to Dr. M. Scalora for helpful discussions.
S.L.C. acknowledges the support of NSERC, the
Department of National Defence Canada via the
Defence Research Establishment Valcartier and le
fonds FCAR and would like to thank Drs. A.
Talebpour, O.G. Kosareva, and V.P. Kandidov
for fruitful discussions. The authors also would
like to thank S. Lagace and J. Yang for their
valuable technical help.
References
[1] X.M. Zhao, J.-C. Diels, C.V. Wang, J.M. Elizondo, IEEE
J. Quant. Electron. 31 (1995) 599.
[2] X.M. Zhao, S. Diddams, J.-C. Diels, in: F.J. Duarte (Ed.),
Tunable Laser Applications, Marcel Dekker, New York,
1995, p. 113.
[3] A. Braun, G. Korn, X. Liu, D. Du, J. Squier, G. Mourou,
Opt. Lett. 20 (1995) 73.
[4] E.T.J. Nibbering, P.F. Curley, G. Grillon, B.S. Prade,M.A. Franco, F. Salin, A. Mysyrowicz, Opt. Lett. 21
(1996) 62.
[5] P.F. Curley, E.T.J. Nibbering, G. Grillon, R. Lange, M.A.
Franco, T. Lehner, B. Prade, A. Mysyrowicz, in: P.F.
Barbara, J.G. Fujimato, W.H. Knox, W. Zinth (Eds.),
Ultrafast Phenomenon X, vol. 62, Springer, Berlin, 1996, p.
103.
[6] H.R. Lange, G. Grillon, J.F. Ripoche, M.A. Franco, B.
Lamouroux, B.S. Prade, A. Mysyrowicz, Opt. Lett. 23
(1998) 120.
[7] S. Tzortzakis, M.A. Franco, Y.-B. Andre, A. Chiron, B.
Lamouroux, B.S. Prade, A. Mysyrowicz, Phys. Rev. E 60(1999) R3505.
[8] A. Brodeur, C.Y. Chien, F.A. Ilkov, O.G. Koserava, V.P.
Kandidov, Opt. Lett. 22 (1997) 304.
[9] O.G. Kosereva, V.P. Kandidov, A. Brodeur, C.Y. Chien,
S.L. Chin, Opt. Lett. 22 (1997) 1332.
[10] O.G. Kosereva, V.P. Kandidov, A. Brodeur, S.L. Chin,
J. Nonlinear Opt. Phys. Mater. 6 (1997) 485.
[11] S.L. Chin, A. Brodeur, S. Petit, O.G. Koserava, V.P.
Kandidov, J. Nonlinear Opt. Phys. Mater. 8 (1999) 121.
[12] L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein,
S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger,
H. Schillinger, R. Sauerbrey, Laser und Optoelektronik 29
(1997) 51.
[13] H. Schillinger, R. Sauerbrey, Appl. Phys. B 68 (1999) 753.[14] R. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez,
F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C.
Wedekind, H. Wille, L. Woste, C. Ziener, Appl. Phys. B 71
(2000) 593.
[15] M. Mlejnek, E.M. Wright, J.V. Moloney, Opt. Lett. 23
(1998) 382.
[16] M. Mlejnek, E.M. Wright, J.V. Moloney, Optics and
Photonics News, December 37, 1998.
[17] M. Mlejnek, M. Kolesik, J.V. Moloney, E.M. Wright,
Phys. Rev. Lett. 83 (1999) 2938.
[18] M. Mlejnek, E.M. Wright, J.V. Moloney, IEEE J. Quant.
Electron. 35 (1999) 1771.
[19] A. Chiron, B. Lamouroux, R. Lange, J.-F. Ripoche, M.
Franco, B. Prade, G. Bonnaud, G. Riazuelo, A. Mys-
yrowicz, Eur. Phys. J. D 6 (1999) 383.
[20] A. Talebpour, S. Petit, S.L. Chin, Opt. Commun. 171
(1999) 285.
[21] S. Petit, A. Talebpour, A. Proulx, S.L. Chin, Opt.
Commun. 175 (2000) 323.
[22] N. Akozbek, C.M. Bowden, A. Talebpour, S.L. Chin,
Phys. Rev. E 61 (2000) 4540.
[23] N. Akozbek, C.M. Bowden, A. Talebpour, S.L. Chin,
Laser Phys. 10 (2000) 101.
[24] B. La Fontaine, F. Vidal, Z. Jiang, C.Y. Chien, D.
Comtois, A. Desparois, H.P. Mercure, Phys. Plasma 6
(1999) 1615.
[25] S. Tzortzakis, B. Lamouroux, A. Chiron, M. Franco, B.Prade, A. Mysyrowicz, Opt. Lett. 25 (2000) 1270.
[26] J. Schwarz, P. Rambo, J.-C. Diels, M. Kolesik, E.M.
Wright, J.V. Moloney, Opt. Commun. 180 (2000) 383.
[27] A. Talebpour, J. Yang, S.L. Chin, Opt. Commun. 163
(1999) 29.
[28] E.T.J. Nibbering, G. Grillion, M.A. Franco, B.S. Prade,
A. Mysyrowicz, J. Opt. Soc. Am. B 14 (1997) 650.
186 S.L. Chin et al. / Optics Communications 188 (2001) 181±186
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