Whole Life-cycle of Superfilament in Water
From Femtoseconds up to Microseconds
F. V. Potemkin, E. I. Mareev, A. A. Podshivalov and V. M. Gordienko
Faculty of Physics and International Laser Center M.V. Lomonosov Moscow State University, Moscow, Russia
Keywords: Femtosecond Superfilament, Laser-induced Shock Waves, Laser-induced Cavitation, Aberrations, Linear
Absorption.
Abstract: A whole life-cycle of the superfilamentation in water in tight focusing geometry was investigated. In this
regime a single continuous plasma channel is formed. To achieve this specific regime the principal
requirement is the usage of tight focusing and supercritical power of laser radiation. They together clamp
the energy in the ultra-thin (approximately several microns) channel with a uniform plasma density
distribution in it. The superfilament becomes a center of cylindrical cavitation bubble area and shock wave
formation. The length of the filament increases logarithmically with laser pulse energy. The linear
absorption decreases the incoming energy delivered to the focal spot, which dramatically complicates the
filament formation, especially in the case of loose focusing. Aberrations added to the optical scheme lead to
multiple dotted plasma sources for shock wave formation, spaced along the axis of pulse propagation.
Increasing the laser energy launches the filaments at each of the dot, whose overlapping leads to enhance
the length of the whole filament.
1 INTRODUCTION
When a femtosecond laser pulse is tightly focused
inside the water cell, extreme for the medium
intensities (I~10
13
W/cm
2
) are achieved in the focal
region, and electron plasma is generated (Potemkin
et al. 2014). The high temperatures (T
e
~10eV),
achieved in the laser plasma lead to a thin layer of
water vapor generation. The layer begins to expand
with a supersonic speed, than emits a shock wave
and at last forms a cavitation bubble. After
separation from the layer, shock wave begins
propagation through the medium until it dying. The
cavitation bubble comes over several oscillations
until it collapse. Because the energy is transmitted
from the plasma to the medium through electron-ion
collisions, initially the cavitation bubble and the
shock front shape replicates the shape of the laser-
induced plasma (Lauterborn & Vogel 2013). Thus,
the shock wave profile replicates the initial pressure
distribution in plasma, and therefore in order to
control the shock wave shape, one must take care of
the distribution of the energy conserved in the
plasma (Noack and Vogel 1999). The processes,
which could affect on the initial plasma density and
intensity distribution dramatically changes the
evolution of the superfilament and its post-effects. In
the work we investigate the role of focusing regimes,
laser parameters and medium properties (linear
absorption) in the process of ultra-short laser pulse
superfilamentation in water as the most convenient
prototype of condensed medium. This work is a
pioneering attempt to investigate the superfilament
and its post-effects in water under tight focusing
geometry. Additionally for the first time we found
out the unique experimental conditions demonstrated
controllable reversible transition from the regime of
multiple filamentation to superfilamentation in
condensed matter
2 EXPERIMENTAL SETUP
In the experiments, a Cr:forsterite femtosecond laser
(wavelength of 1240 nm, pulse duration about 140
fs, laser energy up to 150 µJ, intensity contrast
about 5x10
9
ASE, and repetition rate of 10Hz) was
employed. Shadow photography technique was
applied for probing the dynamics of laser-induced
shock waves and cavitation bubbles. In this
technique, the probe pulse (used as a strobe) passes
through the sample and creates a uniform
122
Potemkin F., Mareev E., Podshivalov A. and Gordienko V..
Whole Life-cycle of Superfilament in Water - From Femtoseconds up to Microseconds.
DOI: 10.5220/0005403801220127
In Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS-2015), pages 122-127
ISBN: 978-989-758-093-2
Copyright
c
2015 SCITEPRESS (Science and Technology Publications, Lda.)
Figure 1: Experimental setup. The incoming femtosecond laser pulse splits into two channels. The pump pulse is tightly
focused by an aspheric lens into the water cell. The energy of the pump pulse is varied by half-wave plate and Glan prism.
The second harmonic is used as a probe pulse. It is scattered in a ground glass plate. Passing through the water cell with a
shock wave, the probe radiation is collected by the microscopic objective on the CCD matrix. Temporal resolution of this
scheme is about 200 fs; optical delay can be changed with adjusting mirror position from zero to 25 nanoseconds.
illumination on a CCD camera. The perturbations in
the refractive index, induced by the pressure waves,
act as scattering centers and are seen as dark areas
on the CCD matrix. The experimental scheme is
sketched in Fig.1. The beam splitter divided the
initial laser beam into two beams: pump and probe.
The half-wave plate with Glan prism was used for
attenuation of the incident pulse energy. In the
incident wavelength, water strongly absorbs laser
radiation due to resonance with molecular
vibrations, which lead to significant linear
absorption.
Therefore, taking into account linear absorption
of water at 1240 nm about 0.9 cm
-1
only 74%
(3.3mm focusing lens) and 69% (4.6mm focusing
lens) of incoming energy was delivered to the focal
waist. Tight focusing of the laser beam into the
water cell leads to the strong spherical aberrations.
Placing the focusing lens inside the water cell
allowed us to minimize these aberrations.
3 RESULTS AND DISCUSSION
Filamentation usually defines, as a dynamical
balance among self-focusing, plasma defocussing
and diffraction, when supercritical laser radiation
propagates through a nonlinear medium (Couairon
and Mysyrowicz 2007). On the one hand, the optical
Kerr effect acts against diffraction and tends to focus
the beam on itself. On the other hand, multiphoton
absorption limits the intensity, because the laser-
induced plasma acts as a defocusing center. Usually
filamentation is accompanied by the conic emission
and strong luminescence from multiple
“filaments”(Couairon and Mysyrowicz 2007). In a
normal wisdom, in a tight focusing regime (NA>0.3)
the diffraction sufficiently overcomes the Kerr self-
focusing just after the focal spot, therefore the
filament can`t be fired. The formation of laser-
induced shock waves and cavitation bubbles inside
the condensed medium is a threshold effect: shock
waves are formed, when the electron density is high
enough (~10
19
cm
-3
) and the cavitation bubbles are
formed, when the electron density is about 10
18
cm
-3
(Vogel et al., 2008). When laser radiation was
focused by 3.3mm focusing lens, threshold of shock
wave formation could be measured at 4±0.5µJ (laser
intensity is about 10
13
W/cm
2
). The energy stored in
shock waves and cavitation bubbles and, therefore,
amplitude and speed of shock waves and the
diameter (E~D
3
) of cavitation bubbles strongly
depend on the electron concentration. Thus, they are
WholeLife-cycleofSuperfilamentinWater-FromFemtosecondsuptoMicroseconds
123
perfect tools for probing the plasma density
distribution.
3.1 Role of the Focusing Geometry in
the Filament Formation
The first series of the experiments were carried out
with comparatively loose focusing (NA=0.1). This
close to classical regime enables a bright conical
emission and multifilamentation.
Figure 2: The cavitation bubble pattern induced by the
laser filament in water (laser pulse energy 190±10µJ, time
delay 2µs). (a) There is a plasma channel in the right part
of the picture, which transforms into several randomly
distributed cavitation bubbles. No visible luminescence or
conical emission is observed (b) There are multiple
randomly distributed cavitation bubbles, but there is no
plasma channel. In this case the visible luminescence from
the filament and conical emission were observed.
Only at high (about 40 P
cr
) power of the laser beam
the multiple filaments could be visually observed,
due to the high linear absorption, which sufficiently
complicate the process of filament formation. The
intensity clamping limits the electron density, which
is not exceeding 3x10
18
cm
-3
(Minardi et al., 2008).
Therefore, loose focusing of a laser beam cannot
achieve high electron densities due to the intensity
clamping in the filament, and additionally, the
breaking of one filament into multiple filaments
diffuses the laser energy over a huge area. In these
conditions no shock waves are formed, because
there is not enough energy localization characterized
by electron density (Vogel et al., 2008). In this case,
the shadow photographs show no shock wave
formation. However, if we increase the laser energy
(in this case the time delay is varied electronically
by the delay generator), a random distribution of
cavitation bubbles can be observed (Fig.2). The
energy distribution along the filament axis is
stochastic and a significant amount of energy is
deliver to the non-linear Kerr foci. These Kerr foci
become centres of the cavitation bubble formation.
Thus, the radii and position of the bubbles change
from pulse to pulse, because the energy issued in
each focus determines the diameter of each bubble
(E~D
3
).
The opposite case is tight focusing (NA>0.3) of
the laser beam (Fig.3). In this regime the shadow
pictures show plasma channels much longer than the
Rayleigh length. Now let us discuss in detail the
physical processes that take place under tight
focusing of intense laser radiation into fresh water.
The intensity in condensed matter is strongly limited
by the nonlinear absorption (Mikheev and Potemkin
2011). In the case of tight focusing, the laser
intensity in the focal spot can reach values up to 10
14
W/cm
2
this is an upper limit of a rough estimate;
such experimental values were estimated based on
the CE broadening in filament under tight focusing
in water (Couairon and Mysyrowicz 2007).
Therefore the electron density is about 0.1n
cr
(n
cr
=m
e
2
/4e
2
7.3×10
20
cm
-3
) and the plasma
electron energy is sufficiently larger than in loosely
focusing geometry. In this regime the energy is
localized in the microvolume with 4 µm in diameter,
and multiple filaments interact with each other and a
single continuous filament is created (Point et al.,
2014). To determine the contribution of different
processes (plasma defocusing, Kerr self-focusing
and diffraction), simple estimates can be made. The
length of self-focusing can be estimated as
L
sf
=n
2
I≈800nm (n
2
=1,6×10
-16
cm
2
/W), the
length scale for plasma defocusing
L
defoc
=L
pl
n
at
/n
e
=n
0
n
cr
/n
e
≈5m, and the diffraction
length is a Rayleigh length which is about 15 µm.
Therefore, the Kerr self-focusing does not allow the
laser radiation to leave the optical axis, and one
continuous filament with approximately uniform
distribution of electron concentration along the
optical axis can be formed. This can be confirmed
by the fact that the radius of the shock wave and
cavitation bubble is uniform along the filament axis,
and its radius strongly depends on the plasma
electrons’ mean energy and density. The shape and
the size of the cavitation area and shock waves do
not change from pulse to pulse. To simplify, when
the laser beam is tightly focused into the bulk of the
condensed matter, it cannot deliver all the energy to
one point and then transmit energy further until it
will be absorbed. The nonlinear processes limit
intensity in each point of such a channel, as will be
shown in the text. With the energy increase the
electron concentration is limited in the channel
(Fig.3a), but the length of the filament continues its
growth (see Fig.3d). Therefore, the superfilament
continues its life on the femtosecond time-scale.
For 0.2<NA<0.3 the energy localization on the
PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology
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optical axis grew, and competition with strong
energy exchange between different filaments
occurred. This led to random filament distribution
across the laser beam, and each filament launched a
shock wave, but in sum they do not form one
contrast wave (Abraham et al., 2000). Nonetheless,
laser-induced cavitation bubbles can be a better
indicator for filament characterization. Initially, the
array of laser-induced cavitation bubbles form one
cylindrical cavitation area (Fig.2a), as in the case of
tighter focusing. But after an approximate 1mm
distance, the superfilament breaks into multiple
filaments and multiple bubble formation can be
observed. These multiple bubbles, as in the case of
loose focusing, are randomly disturbed.
3.2 Role of Linear Absorption
Cr:Forsterite laser wavelength (1240nm) falls in the
absorption band of water molecules vibrations
cantered at 1200nm, which leads to a high linear
absorption (about 0.9cm
-1
); such high absorption
strongly violates the processes of filament formation
and further shock wave and cavitation bubble
generation. To identify the role of the linear
absorption, additional experiments were carried out
with heavy water (D
2
O). Heavy water has similar
physical properties to water, but the vibrational
frequencies are different. The fact allowed us to
avoid resonant interaction between the laser
radiation and water molecules.
The amount of the absorbed energy is
proportional to the distance travelled by the laser
beam inside the water. Therefore, to achieve high
intensities in the focal spot, it is necessary to use
lenses with small focusing distance or alternately
focus the radiation near the water boundary. The
most significant role the absorption of the laser
energy will play in the case of loose focusing. When
the laser radiation was focused into a cell with D
2
0,
the visibility of the filament and the number and size
of the cavitation bubbles (the volume of the
cavitation area determines the energy delivery to the
medium) was greater than in the case of H
2
0.
In the case of tight focusing into the water cell,
the nonlinear absorption starts to play the main role
and the difference between the D
2
O and H
2
O
becomes less significant. To compare the length of
the plasma channels it is easy to use the cavitation
bubble area. The experiments show that with a
decrease of focusing distance, the length of the
plasma channel grows.
3.3 The Evolution of Filament-induced
Shock Wave
Now let us concentrate on the filament-induced
shock wave evolution, taking place on the
nanosecond timescale. The shadow photographs,
provided in Fig.3(a-c), show that instead of a
spherical shock wave, the cylindrical shock wave
was generated, because the each point of the
superfilament becomes a centre of spherical shock
waves and cavitation bubble formation.
Figure 3: (a-c) The shadow pictures of the filament-
induced shock waves (time delay 15ns, NA=0.4,
f=3.3mm) at different energies, (d) the length of the
filament on the laser pulse energy, (e) the diameter of the
shock wave on the laser pulse energy.
At energies just above the threshold, one spherical
shock wave was formed (Fig.3a). With the increase
of laser energy a single, stable (from pulse to pulse),
cylindrical shock wave was generated. As was
discussed above, the shock waves were generated
WholeLife-cycleofSuperfilamentinWater-FromFemtosecondsuptoMicroseconds
125
only in the areas where the electron density was
greater than the threshold. The amplitude and the
initial speed of the shock wave were fully described
by the initial pressure distribution inside the laser-
induced plasma. In our case, the extreme intensity in
the focal spot leads to a stable continuous
superfilament formation. Initially the cavitation
region in the centre of the picture replicates the
shape of the filament, and therefore the length of the
filament can also be restored from the pictures; the
errors of such rough estimates do not exceed the
diameter of each cavitation bubble. The filament
length has a logarithmic dependence on laser pulse
energy (Fig.3d). The pressure on the front of the
shock wave can be restored from the shock wave
speed using the semi-empirical equation
02
()/
10
(10 1)
s
uc с
ss
p с u

. Here c
1
,c
2
are empirical
constants, c
0
is the speed of sound in the medium,
is the density of the undisturbed medium, and us is
the speed of the shock wave front. In water c
0
=
1483 m/s, ρ
0
= 998 kg/m
3
, c
1
= 5190 m/s and c
2
= 25
306 m/s. Thus assuming the exponential decay of the
shock wave speed, we can calculate the shock wave
speed. For incident laser energy of 130µJ, shock
wave front velocity is 2300±200m/s. The shock
pressure can be estimated as 1.0±0.1 GPa.
We performed another series of experiments to
investigate the dynamics of filament-induced shock
waves on the laser pulse energy. The results are
shown in Fig.3e. We found, that shock wave
diameter tends toward saturation as a square root of
incident pulse energy. The saturation of the shock
wave energy (which is proportional to its speed), is
caused by the intensity clamping. With the increase
of the laser pulse energy the plasma electron density
tends toward saturation, due to a limitation of
electrons in the effected volume (Mikheev &
Potemkin 2011). Thus the energy, that can be
transferred from laser radiation to plasma and then
from plasma to each shock wave in the optical
breakdown volume, is limited. Nevertheless, the
length of the filament continues to increase, because
there is still enough energy in the energy reservoir.
Thus, varying only the energy of laser pulse shape,
we can change the spatial characteristics of the laser-
induced shock wave.
3.4 Role of Aberrations
The last way to control the shock wave shape is
using the aberrations. The aberrations often limit the
possibilities of laser beam tight focusing inside the
medium. Briefly, when the laser beam tightly
focuses into the bulk of the medium, the
convergence angles are big; due to the Snell`s law
the different rays are focused in different points of
the medium, leading to significant spherical
aberrations. A more complicated theory of the
process can be found in (Marcinkevičius et al.
2003). In our case the most important result is
formation of intensity maxima along the optical axis,
which becomes the centres of filament generation.
Figure 4: The evolution of the shock waves and cavitation
bubbles on the laser pulse energy with aberrations. (a)-(f)
shadowgrams of shock waves and cavitation bubbles,
delayed on 18.6 ns from optical breakdown at different
incident laser pulse energy: (a) 6.8, (b) 13.7, (c) 15.8, (d)
20.5, (e) 35.6 and (f) 51.3 µJ. The laser radiation was
focused by the 4.6mm focusing lens (NA=0.3). (g,h) The
numerical calculation of the intensity profiles after
focusing of the laser beam into water for NA=0.3,
d=1,3mm and the shadow picture of the corresponding
laser-induced shock waves and cavitation bubbles.
In this regime, complex spatial patterns of shock
waves can be generated. The intensity profile
maxima become the centres for cavitation bubble
and spherical shock wave generation. At low laser
pulse energy only single spherical shock waves are
generated (Fig. 4a), while at higher laser pulse
energy several dotted sources, isolated from each
other, create a complex envelope of shock wave
(Fig. 4c-e). With the increase of laser energy
additional shock waves are generated from new
plasma, forming a cylindrical shock wave (Fig. 4f).
Such aberrations could effectively increase the
length of the laser filament and the laser-induced
shock impact on the material.
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4 CONCLUSIONS
In conclusion, we investigated the whole life (from
femtoseconds to microseconds) of the superfilament,
fired in water under a supercritical power regime
from the laser pulse energy, focusing and linear
absorption. The high intensity clamps the energy
into a thin layer along the filament axis. It leads to
the channel formation with extreme and quasi-
uniform electron density distribution. The increase
of the laser pulse energy does not change plasma
density but sufficiently enlarges the superfilament
length. The superfilament became a centre of
cylindrical cavitation area formation and shock wave
generation. The maximal velocities and pressures
achieved for the incident laser energy of 130µJ on
the shock wave front were 2300±200m/s and
1.0±0.1 GPa, respectively. The length of the
filament was logarithmically dependent on laser
pulse energy. The diameter of the filament grew as a
square root of laser pulse energy and tended toward
saturation, which was caused by the saturation of
plasma electrons’ density. When the looser
(NA<0.1) focusing was employed there was no
continuous plasma channel and shock wave
generation, but instead a conical emission and
randomly-generated cavitation bubbles were
observed, as the energy delivered to the medium by
plasma electrons was not high enough for contrast
shock wave generation. In the case of medium
focusing (0.1<NA<0.3) the superfilament, once
created close to the water-air boundary, breaks up
into a randomly distributed pattern of cavitation
bubbles. The linear absorption significantly
increased the threshold of filament ignition due to
the effective laser energy transferring to the
vibrational modes of H
2
O molecules. Aberrations
added to the optical scheme led to multiple dotted
plasma sources for shock wave formation, spaced
along the axis of pulse propagation. Increasing the
laser energy launches the filaments at each of the
dot, whose overlapping provides to enhance the
length of the whole filament and resulted in growth
of shock impact on the material.
ACKNOWLEDGEMENTS
This research has been supported by the Russian
Foundation for Basic Research (Projects No. 14-02-
00819a and No. 14-29-0723) and partly by the M.V.
Lomonosov Moscow State University Program of
Development.
REFERENCES
Abraham, E., Minoshima, K. & Matsumoto, H., 2000.
Femtosecond laser-induced breakdown in water : time-
resolved shadow imaging and two-color
interferometric imaging. Optics and Spectroscopy,
176, pp.441–452.
Couairon, A. & Mysyrowicz, A., 2007. Femtosecond
filamentation in transparent media. Physics Reports,
441(2-4), pp.47–189.
Lauterborn, W. & Vogel, A., 2013. Bubble Dynamics and
Shock Waves C. F. Delale, ed., Berlin, Heidelberg:
Springer Berlin Heidelberg.
Marcinkevičius, a. et al., 2003. Effect of refractive index-
mismatch on laser microfabrication in silica glass.
Applied Physics A: Materials Science & Processing,
76(2), pp.257–260.
Mikheev, P.M. & Potemkin, F. V., 2011. Generation of
the third harmonic of near IR femtosecond laser
radiation tightly focused into the bulk of a transparent
dielectric in the regime of plasma formation. Moscow
University Physics Bulletin, 66(1), pp.19–24.
Minardi, S. et al., 2008. Time-resolved refractive index
and absorption mapping of light-plasma filaments in
water. Optics letters, 33(1), pp.86–8.
Noack, J. & Vogel, a., 1999. Laser-induced plasma
formation in water at nanosecond to femtosecond time
scales: calculation of thresholds, absorption
coefficients, and energy density. IEEE Journal of
Quantum Electronics, 35(8), pp.1156–1167.
Point, G. et al., 2014. Superfilamentation in Air. Physical
Review Letters, 112(22), p.223902.
Potemkin, F. V et al., 2014. Laser control of filament-
induced shock wave in water. Laser Physics Letters,
11(10), p.106001.
Vogel, A. et al., 2008. Femtosecond-Laser-Induced
Nanocavitation in Water: Implications for Optical
Breakdown Threshold and Cell Surgery. Physical
Review Letters, 100(3), p.038102.
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