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
PHOTOPTICS2015-InternationalConferenceonPhotonics,OpticsandLaserTechnology
124