Download A. Sate of the art

VOLUME 78, NUMBER 8
PHYSICAL REVIEW LETTERS
14 NOVEMBER 2003
Laser-Matter Interaction: Investigation using the MPIC Code
Julien Bertrand, Christian Jungreuthmayer and Thomas Brabec
Center for Research in Photonics, University of Ottawa, 150 Louis Pasteur Ottawa, Ontario K1N 6N5
(Received 14 November 2003)
In the last decade, laser intensities have reached the level of 10 20 Watt/cm2. Now, experiments are being
performed with laser intensities up to the order of 1020 Watt/cm2 [1]. The great interest for high-intensity
lasers is, of course, the huge discharge of energy they can provide but also because this energy is given by
pulses and can be well localized. For instance, the advantages of laser-surgery rely on those properties.
Still, energy absorption mechanisms in laser-matter interaction are not well known, this is specifically the
case for large-scale targets (several nm). In the last years, simulations of the interaction have been done
with various versions of the PIC (particle-in-cell) code. However, one basic principle of the PIC codes is to
regroup the particles simulated in boxes moving in a stationary grid divided in cubic cells. It consists on
working with the mean field approximation. Consequently, microscopic effects like impact ionization
electron-electron scattering, electron-ion scattering and charged enhanced ionization (CEI) [2] are ignored.
The code has been implemented to take full account of those effects; cells are shrunk to the atomic order
and each particle is represented by one moving box [2]. The concepts of the PIC codes will be explained in
the following. Therefore, taking in consideration microscopic effects, the Microscopic PIC (MPIC) code
allows us to look at laser-matter interaction more precisely. The essential is to expose the MPIC code as a
tool for laser-matter interaction, for large scale volumes (5-10nm).
PACS numbers: 07.05.Tp, 42.62.-b
I. INTRODUCTION
A. Sate of the art
The interaction of high-intensity lasers with a small amount
(1-10) of atoms or molecules is well known. The interaction
has been studied by experimentalists and theorists and both
sides agree; but the mechanisms driving the impact of highintensity lasers on macroscopic volume of bulk matter remain
ambiguous. For now, simulating bulk solid-state matter is
difficult and not achievable because the forces interacting in
the fine structure are not well known; the forces or potentials
acting between particles simulated (which can be electrons,
ions or neutral atoms) are key ingredients to simulating any
dynamics. One sees why intense lasers acting on simple
structures have been elucidated by the past.
Applications like laser-surgery or damaging of dielectric
surfaces, clearly indicates the hunch to understand large-scale
effects occurring on a macroscopic volume of matter
submitted to a high laser-field. Simulations of this are made
possible with PIC codes. To simplify the task, with regards to
what we pointed out above, matter is seen as a large
homogeneous atomic cluster. An atomic cluster consists of a
grouping of neutral atoms. Therefore, using large (1000025000 atoms) clusters to simulate laser-matter interaction is
the first step towards the study of the laser-‘’solid statematter’’ one.
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B. Matter irradiated by a strong Laser-field
Let’s look roughly at what happens when a high-intensity laser is
thrown in a cluster of neutral atoms. Suppose our laser linearly
polarized and focalized on the totality of the cluster. Each atom is
surrounded by its valence electrons. The laser can be seen as an
electromagnetic field oscillating in time with a Gaussian pulse
modulation (Fig. 1). At first, the beginning of the pulse will start
to propagate in the cluster. The oscillating strong laser electric
field applied on valence electrons will dramatically accelerate
them parallel to the polarization direction. Gradually, heated
electrons will escape the cluster because they absorbed enough
energy from the laser-field to tunnel out. The mother ions, which
are heavier and more inert, will then start to feel the absence of
the missing electrons causing a strong positive repulsive field. We
then assist to the coulomb explosion.
The cluster literally explodes. Now how electron heating did
happen or what are the mechanisms of absorption of energy? How
do the cluster behave during the explosion, is it a symmetric,
isotropic explosion? When does it really happen in the pulse
duration?
Answers can be given by the analysis of numerical experiments
done with PIC codes. Especially, the Microscopic PIC code [2],
taking in account most microscopic effects is used. Let’s first talk
about the principles of PIC codes.
© 2003 The American Physical Society
VOLUME 78, NUMBER 8
PHYSICAL REVIEW LETTERS
14 NOVEMBER 2003
Electric field (StatV/cm)
 
1
v2
1 2
c
(2)
The constant c is the speed of light and v is the actualized speed
of the box. For a little time step ’’dt’’, the box is allowed to
move. The laser electric field is also propagating in time in the
cluster. Now, a charge moving is inducing a current, well, it is
current. Then, in each cubic cell crossed by the moving box, a
current was generated. For each cell concerned a current J is then
calculated. After all the particles (boxes) moved in this time
step, the electromagnetic field is updated for each cubic cell of
the volume simulated using the Maxwell equations [5]:
Z axis (arbitrary units)
FIG.1. Picture of a Gaussian laser pulse propagating in the z
direction. In reality, the value of the standard deviation,
equivalent to the FWHM, is of the order of 100 fs.
 B 
dE
J
dt
(3)
 E 
dB
dt
(4)
II. EXPERIMENTS
A. PIC codes
In a PIC code, the volume simulated, which contains the
cluster of atoms, is a stationary grid divided in cubic cells. The
particles (electrons, ions or neutral atoms) are regrouped in
boxes with macroscopic dimensions that represent the average
over many particles. To allow particles to move, we solve
their relativistic equation of motion using the second law of
Newton and Lorentz’s force [3]:
F  m
dv
v
 q( E   B) (1)
dt
c
where q and m are the averaged charge and mass, E is the total
electric field and B the magnetic field acting on a box; they
basically come from the contribution of both the laser and the
cluster, we will see how E and B are obtained. However, the
laser is mostly a strong electric field, the B component from
the laser field is negligible. γ is the relativistic factor:
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Then for the next time step, the electromagnetic field is known
everywhere in the volume and particles can move again solving
their equation of motion. This is basically how PIC codes work.
To regroup particles in the same boxes results in a lack of
physical realism. The mean field approximation is used. In this
manner, all microscopic effects happening between single
particles like impact ionization, inverse Bremsstrahlung [4],
electron-electron scattering, electron-ion scattering are
neglected.
Impact ionization can be a fast electron hitting a neutral atom
and causing another electron to escape its mother ion.
Bremsstrahlung stands for “Radiation emitted by a charged
particle under acceleration” [4]. For example, a fast electron
running into another electron will be strongly decelerated and
then it will emit photons. The inverse Bremstrahlung is the
reverse mechanism: an electron leaving its mother ion will tend
to absorb photons from the laser. Different types of scattering
are also some other physical and microscopic effects going on in
a cluster. It is then clear that the study of a macroscopic media
needs to include all possible microscopic effects. The solution to
the PIC code is the MPIC code.
© 2003 The American Physical Society
VOLUME 78, NUMBER 8
PHYSICAL REVIEW LETTERS
14 NOVEMBER 2003
FIG. 2. These are pictures obtained with the MPIC code [2] for a 10000 Argon atoms. All pictures (a1), (a2) and (a3) correspond to
the time –92.9 fs, which means 92.9 fs before the electric laser field reaches its peak of intensity. At that time, I=4.4x10 14 W/cm2
(E=5.7x1010 V/m). In (a1) the enhanced ionization at the cluster poles is illustrated (ions only). Picture (a2) shows the cloud of
electron to move parallel to the laser polarization, along the x direction. Finally, (a3) shows the distribution of the electric field (ions
only), and PEI: Polarization Enhanced Ionization.
FIG. 3. All pictures (a1), (a2) and (a3) correspond to the time –25.9 fs, which means 25.9 fs before the electric laser field reaches its
peak of intensity. At that time, I=6.7x1015 W/cm2 (E=2.2x1011 V/m). The pictures (b1), (b2), (b3), correspond to the same as in
FIG.2. Now, the Coulomb explosion occurs. The cluster lost its spherical configuration, see red spots in (b2).
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© 2003 The American Physical Society
VOLUME 78, NUMBER 8
PHYSICAL REVIEW LETTERS
B. MPIC code:
To take full account of the microscopic interactions, the
dimensions of the cubic cells of the stationary grid are shrunk
to the atomic order, the edge of a cubic cell is reduced to the
dimension of the Bohr radius = 0.5 Å. In addition, every
particle is now a box of the same size as the cubic cells.
Consequently, all microscopic effects are taken in
consideration. Of course, the workload increased with
comparison to the normal PIC codes but a major advantage of
PIC codes versus normal molecular dynamics (MD)
simulations remains: the computational effort scale with N,
where N is the amount of particles simulated, while MD codes
scale with N2. Still, relativistic regime can be simulated. To
exploit efficiently the MPIC code the time step, discussed
before, has to be of the order of 10 -19 sec. This is the major pain
of the code.
Numerical experiments were performed with a laser linearly
polarized of maximum intensity of the order of 10 18 W/cm2.
Here, we specify maximum intensity because the laser field
used has a Gaussian pulse modulation. The Full Width at Half
Maximum (FWHM) of the intensity of the field is of the order
of 100 fs (10-17s).
III. RESULTS
We can see from FIG.2(a1), ionized atoms can be seen even at
the leading edge of the laser pulse. This means that some
electrons started to escape the cluster. Picture FIG.2(a2) shows
that the laser drives the electron cloud along its polarization axis
(x) which causes the atoms at the poles to get ionized. This
mecanism is denoted PEI [2] for Polarization Enhanced
Ionization, see FIG.2(a3). This mechanism induces at the poles
an electric field of one order higher than the laser one, see
FIG.2(a3). This will also start up the coulomb explosion along
the x axis because a strong repulsive force between ions at the
poles is induced. Later on, around time -50 fs, charge enhanced
ionization (CEI) will start to be obvious [2] . This is basically
the fact that consequently to PEI, a strong electric field is
induced between the outer ions and the core of the cluster, see
green shell in FIG.2(b1). This strong induced electric field,
which is in the opposite direction of the laser field, will cause a
chain effect on the cloud of electrons. Let’s say the electric field
reaches a maximum of intensity while oscillating (not the
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maximum of the gaussian modulation), then the cloud of
electron is moved downwards, see FIG.2(b2). Then the laser
field switch in the oppostie direction (it’s oscillating), this
will push the electron cloud upwards. The motion will be
accentuated because of the induced field we talked above.
That is the contribution of the ion charge distribution, it
causes CEI. One sees that PEI and CEI are correlated,
mutually dependent.
Another important fact to justify electron heating is
polarization dephasing heating (PDH), wich is suggested in
[2]. The laser can be seen as a harmonic force. The average
work of this kind of force on a particle should be zero.
Well,we still observe ionization: electrons submitted to the
laser field escape the cluster. Exploiting the MPIC code, a
plot of the laser field and the induced current J in the cluster
shows a dephasing between the two. Therefore, the average
work on electrons is not zero, wich agrees with the
explanation about PEI and CEI.
IV. CONCLUSION
To conclude, the main idea was to look at how matter can be
simulated: the MPIC is a powerful tool for the analysis of
large scale nano plasmas. The analysis of FIG.2 and FIG.3
are superficial. One would need to look at [2] for a deeper
study of large cluster explosion in intense laser fields. The
study of large clusters in intense laser fields is the first step
towards the one for solid-state matter, some applications like
laser-surgery and design of patterns in integrated circuits are
concerned. The laser-cluster explosion is also of interest for
the generation of x-rays and creation of nuclear particles.
_____________________________
[1] http://policy.iop.org/v1text.html
[2] C. Jungreuthmayer, M. Geissler, J. Zanghellini and T.
Brabec, Phys. Rev. Lett (refereed and accepted, but not
published, Dated; October 7, 2003).
[3] A. Serway, Modern Physics, 2nd edition, U.S.
press, 1994.
[4] http://rkb.home.cern.ch/rkb/PH14pp.html
[5] S.Hiziroglu, S.Guru, Cambridge University
Press, UK 1999.
© 2003 The American Physical Society
electrons
PEI
ions
VOLUME 78, NUMBER 8
NOVEMBER 2003
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PHYSICAL REVIEW LETTERS
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© 2003 The American Physical Society