Laser-Matter Interaction: Investigation Using the MPIC Code

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, OntarioK1N 6N5

(Received 14 November 2003)

In the last decade, laser intensities have reached the level of 1020 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

VOLUME 78, NUMBER 8 PHYSICAL REVIEW LETTERS 14 NOVEMBER 2003

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 high-intensity 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 (10000-25000 atoms) clusters to simulate laser-matter interaction is the first step towards the study of the laser-‘’solid state-matter’’ one.

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.

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.

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]:

(1)

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:

(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]:

(3)

(4)

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.

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=4.4x1014 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).

VOLUME 78, NUMBER 8 PHYSICAL REVIEW LETTERS 14 NOVEMBER 2003

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 1018 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 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 accentuatedbecause 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.

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[1]

[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]

[5] S.Hiziroglu, S.Guru, CambridgeUniversityPress, UK 1999.

VOLUME 78, NUMBER 8 PHYSICAL REVIEW LETTERS 14 NOVEMBER 2003