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

W/cm

) are achieved in the focal

region, and electron plasma is generated (Potemkin

et al. 2014). The high temperatures (T

~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

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

 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

-3

) and the cavitation bubbles are

formed, when the electron density is about 10

-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

W/cm

). The energy stored in

shock waves and cavitation bubbles and, therefore,

amplitude and speed of shock waves and the

diameter (E~D

) 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

) 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

-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

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

W/cm

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



/4e

7.3×10

-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

=n

I≈800nm (n

=1,6×10

-16

/W), the

length scale for plasma defocusing

defoc

n

/n

≈5m, 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

124

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

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

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

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

O and H

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

()/

(10 1)

uc с

p с u







. Here c

are empirical

constants, c

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

1483 m/s, ρ

= 998 kg/m

, c

= 5190 m/s and c

= 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.

PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology

126

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

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.

WholeLife-cycleofSuperfilamentinWater-FromFemtosecondsuptoMicroseconds

127