Ludovic Hallo

INTERACTION LASER EN REGIME NANOSECONDE ET FEMTOSECONDE DANS

LES MILIEUX DIELECTRIQUES :

Quelques résultats de modélisation

Modélisation et Procédés Lasers Ultra- Brefs18-19 mars 2010, Carry-le-Rouet

Collaboration team

Candice Mézel, Jérôme Breil, Vladimir TikhonchukCELIA, Université Bordeaux 1, CNRS, CEA, France

Olivier SautInstitut de Mathématiques de BordeauxUniversité Bordeaux 1, France

Antoine Bourgeade, David HébertCEA CESTA, Le Barp, France

2

Fabien Guillemot, Agnès SouquetINSERM U577 – Biomatériaux et Réparation TissulaireUniversité Bordeaux 2, France

David Grojo*, Benoit ChimierLP3 + *University of Ottawa

Laser/dielectrics at very high intensities (TW/cm2)

1) Nanocavity formations in dielectrics

• Ablation in the bulk• Improvement of ionization models (Keldysh, etc...)

Context

2) Toward a new Laser Induced Forward Transfer process

• Ablation in the bulk + matter expansion• Understanding of transfer mechanisms• Contribution to experiment interpretations

3) Applications

• Optic laser dammages• Calibration of Equation of State• Validation of CHIC modeling tool

laser

M. Duocastella et al. Appl. Phys. A, 93 (2), 453-456, 2008

Jet radius : Φ = 4.5 mmJet speed : V = 90 m/s

- Tissue Engineering- BioPrinting- Cells deposit on prosthesis- Micropatterning

λ = 355 nmτ = 10 nsEpulse = 0.7 μJ

4

Objective• Proceed smaller particules like molecules• Control the amount of transferred material

Femtosecond regime

Nanosecond

Typical Laser-Induced Forward Transfer (LIFT) techniquewell known... in nanosecond regime

Nanosecond modeling (CHIC code)

5

• Silica transparent during interaction time

• Rear face deformation is the same with or without air on jet formation scale time.

Thermal flux

• No hydrodynamic effect on silica

Pinit

Water Titanium

Jet radius : Φ = 4.5 μmJet speed : V = 90 m/s

λ = 355 nmt = 10 nsF = 20 J/cm2

C. Mézel et al, PoP 15 123112 (2009)

Modeling results (CHIC code)

2. Hydrodynamic motion ~ 100 ps

Difficulty• Water is transparent to visible wavelength

Solution• Control of laser energy absorption in dielectrics in previews studies (*)

7

Laser

water

Shock wavepropagation

éjection

New scheme: - no more ablator- control of the jet diameter

1. Short time scale : laser energy absorption ~ 100 fsSfoc = 0.55 μm2

Ifoc = 50 TW/cm2

Pfoc = 0.3 MW

w0 = 300 nmRL = 350 nmEllipsoïdal absorption zone:

Typical laser caracteristics: λ = 800 nm, τ = 100 fs, E = 30 nJ

Plasma formationIfoc > Ith = 29.3 TW/cm²Pfoc < Pcr = 1.87 MW

L. Hallo et al., Phys. Rev. B 76, 024101 (2007)(*) C. Mézel et al, PoP 15 093504 (2008)

From nanosecond to femtosecond

Short time scale: laser energy absorption ~ 100 fs

Laser propagation description with Maxwell equationsAbsorption of laser energy with an ionization model

1D/2D/3D model including:

SUCCESSION OF PROCESS IN LASER AFFECTED MATERIAL

9

Ionization threshold and critical powerIntensity and power estimates at the focal plane

Ifoc = 90 TW/cm2, Pfoc ≈ 0.3 MW MW 87.1

2P

20

2

cr ≈=nnπ

λ

Set of laser parameters

Wavelength: λ = 800 nmLaser energy: E = 30 nJPulse duration: τ = 100 fsBeam waist: ω0 = 0.3 μm

Focal area: Sfoc = πω0RL= 0.33 μm2

Ith = 29.3 TW/cm2

A plasma is formed in the focal plane which enhances laser absorption (like in a metal).Non-linear effects are neglectable.

λπω2

0=LRRayleigh length = 0.35 μmω0 < λ

2D estimate of intensity at the focal plane

Ionization by EM wave interactionCollisionnal ionization

eenionet nntntn colrec

1 )()( ντ

ν +−=∂

Radiative recombination

10

Density balance of the free electrons:

NN Iσν =ionMPI rate:

σN : effective cross section derived from Keldysh theory 1.

MPI scheme

Valence band

Conduction bandħω Egap

Ex/ λ = 800 nm in silica (Egap = 9 eV) : N = 6 photons

1 L.V. Keldysh, JETP 47 p. 1945-1957 (1964)

• 2D/3D model solving Maxwell equations + ionization model

Overestimation of the electron density

Question about the ionization regime

Multiphoton ionization (MPI) regime ?

⎟⎟⎠

⎞⎜⎜⎝

⎛= 22

2

EemE e

gapωγ

Egap : dielectric band gap energyme : electron massω : laser frequencyE : electric field

For silica irradiated by IR laser : [ ]V/m E10 43.1 10

=γ

11

Keldysh theory on ionization regime

• γ >> 1, weak field: multiphoton regime

• γ << 1, strong field: tunnel regime

γ = 1 for I = 36 TW/cm2

Ionization regime not clearly defined

Comparison of: - MPI estimated from Keldysh formula- Tunnel ionization estimated from Keldysh formula - Exact Keldysh formula (no approximation)

Ionization regimes

Keldysh theory [1]

σ6 = 2 1025 cm-3 s-1

(cm2/TW)6 [2]

σ6 = 6 1020 cm-3 s-1

(cm2/TW)6 [3]

Tunnel ionization

• Multiphoton limit is not correct at high intensities (beyond 50 TW/cm2).• Varying the cross section of MPI is not a good solution because νmpi ~ I6.

Tunnel ionization could provide better quantitative results at high intensities.[1] L.V. Keldysh, JETP 47 p. 1945-1957 (1964)[2] J.R. Penano et al. PRE 72 036412 (2005)[3] M. Lenzner et al. PRL 80 p. 4076-4079 (1999)

12

Ionization rates comparison

2D Maxwell’s equations coupled to ionization model

EtB rr

∧−∇=∂∂

{ {⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+−∧∇=∂

currentionisation

current electronic0

1mpiJJB

dtD

e

rrrr

μ

colrec

1( ) ( )Nt e N n e en t I n t n nσ ν

τ∂ = − +

Density and energy balance

Laser propagation and absorption

)()()(23.)( tnUtntTkEJtUW ecolgap

rec

eeBempigapet ν

τν −⎟

⎠⎞

⎜⎝⎛−+=∂

rr

laserMaxwell’s equations

λ = 800 nmω0 = 0.3 μmτ = 100 fs

Elaser = 50.5 nJ

Elaser = 5.6 nJ

Emax = 5 109 J/m3 Emax = 1.2 1010 J/m3

Elaser = 22.4 nJ

Emax = 1.1 1010 J/m3

Absorbed laser energy in silica

15

Silica Water

ρ = 2,2 g/cm3

Ugap = 9 eV6 photons ionizationσ6 = 9,8 10-70 s-1 (cm2/W)6

Ith = 28.9 TW/cm2

Pcr = 1.98 MW

ρ= 1 g/cm3

Ugap = 6,5 eV4 photons ionizationσ4 = 4.635 10-43 s-1 (cm2/W)4

Ith = 29.3 TW/cm2

Pcr = 1.87 MW

λ = 800 nmω0 = 300 nmτ = 100 fsE = 50 nJ

Required threshold intensity is lower in water than in silica, but water and silica look very similar.

Ionization parameters: water vs silica

16

λ = 800 nm, τ = 100 fs, I = 300 TW/cm2

Electronic density (m-3)

Electronic temperature (K)

Transmitted beam (J/m)

Threshold intensity reached earlierMore electrons are generated

Transmitted beam is strongerElectrons are more energetic

Multiphoton regime

Tunnel regime

Absorption zone shapes depend on the ionization processes.

Tunnel

MPI

2D results in water

2D results in micaAbsorbed energy distribution : ionization and heating

Absorbed energy (nJ)

MPI + COL

E_abs totalE_abs ionizationE_abs heating

MPIE_abs totalE_abs ionizationE_abs heating

λ = 800 nmτ = 45 fsI = 83 TW/cm2

w0 = 637 nmE_abs = 33 nJ

2. MPI and COL ionization

- 9.8 % for ionization- 90.2 % for electron heating

1. MPI ionization

- 4 % for ionization- 96 % for electron heating

Efficiency of laser heating ( > 90 % laser absorbed energy)

39 % of electrons generated by MPI ; 61 % generated by collisions.

Screening of laser beam due to collisionnal ionization

2D results in micaInfluence of multiphotonic cross-section σ3

Absorbed energy (nJ)Electronic density (m-3)

σ3

4*σ3

MPI σ3

E_abs totalE_abs ionizationE_abs heating

MPI 4*σ3

E_abs totalE_abs ionizationE_abs heating

λ = 800 nm, τ = 45 fs, I = 83 TW/cm2, w0 = 637 nm

Screening of laser beam due to MPI with high cross-section

E_abs (nJ) Elecrons MPI Electrons COL

σ3 33 39 % 61 %

4∗σ3 37 45 % 55 %

Hydrodynamic motion ~ 100 ps

HYDRODYNAMIC SIMULATIONS

Initial condition: Absorbed energy from 2D/3D Mawxell modeling.

Hydrocode CHIC : 2D axisymetric- Separated temperature for electrons and ions- Ion-electrons energy exchange- Thermal conductivity- Tabulated equations of state (SESAME, BLF,QEOS, home-made designs…)-Two points to adress : in the bulk or near boundaries

P.-H Maire et al, IJNMF 56 p. 1161-1666 (2008)P.-H Maire et al, SIAM 29 p. 1781-1824 (2007)

1/ Interaction in the bulkHydrodynamic process involved

Array of voids in sapphire produced by single pulses at 6 µm depth

E. Gamaly et al. Phys. Rev. B 73, 214101(2006)

Laser energy = 100 nJDiffraction angle θ = 100°Waist ω0 = λ/πθ = 0.15 μm

Laser

Peak laser power = 0.5 MWCritical power = 2 MWIntensity = 40 TW/cm2

Ionization threshold = 30 TW/cm2Sfoc = 0.15 μm2

Vfoc = 0.3 μm3

dt = 220 nm

Motivations: experiments in sapphire

Shock and rarefaction waves generationDensity (kg/m3) on radius (mm) for a 30 nJ uniform energy release

t = 20 ps

t = 50 ps

t = 100 ns

Shock wave

Rarefactionwave

Diverging shock wave created by the energy release in the focal volumeConverging rarefaction wave collapses and forms the cavity

Nouvelles voies pour la modélisation de l’interaction laser-matière – Marseille 29 octobre 2008

Nanocavity modelling in Silica

Nouvelles voies pour la modélisation de l’interaction laser-matière – Marseille 29 octobre 2008

• 40 nJ laser shot

• 80 nJ laser shot

Density

Propagation axis

600 nm

1100 nm

rmod = 130 nmLaser

Laser

Density

Propagation axis

rmod = 220 nm

rexp= 110 nm

rexp= 300 nm

Usual setups: shock impact : Gaz gun, electron generators...

Sabot

Tantale

Velocity IDL Pérot-Fabry

V = 1000 m/sSilica

Polyéthylène

• Gaz gun (CEA/CESTA)

Mesure de vitesse par IDL Pérot-Fabry

Silica LIF

e-

E

• CESAR (CEA/CESTA)

• Laser setup ?

Hugoniot datas ?

Toward a new experimental setup for EOS calibration

Characteristics of a laser setup

E

E- to ions transfer

Shock and expansion waves formation

Cavity

Absorption by e-

Large (P,T) domain

Laser domain

High pressure

L. Hallo et al., Applied Physics A 92, 4, 837-841 (2008)

2/ Interaction near material boundaries

Hydrodynamic process involved

27

Suggested jet formation process1. Just after laser pulse (tens of fs)

2. Cavity formation and expansion

3. Cavity collapse: jet formation

Absorption zone μm3

Axisymetry

1. Shock wave expansion.Slight deformation of the rear interface.

2. Rear interface deformation under the cavity expansion.

3. Cavity collapses, the fluid rushes into the already deformed interface and forms a jet.

Jet formation

13.2 ns

Maximum cavity expansion

5 ns

Shock wave formation1rst backsurface deformation

Cavity expansion similar to silica2nd deformation

7.5 ns

Cavity collapse Jet formation

λ = 800 nmω0 = 0.3 μmτ = 100 fsElaser = 50.5 nJ

500ps 1 μm

2DComputed hydrodynamic response in water

A confined volume is needed to form a jet.Jet radius ~ 300 nm << 3 μm (ns regime)

LASER

Results from David Grojo (University of Ottawa):

Silica: Energy=155 nJ, bump= 7nm

45fs; NA=0.45

Experimental evidence of nanoLIFT in solids

30

300nJ, 100fs and energy located 0.3µm below rear surface

Energy variation

200nJ 400nJ

Computed hydrodynamic response in silica

Uncertainties : energy location, laser absorption, but jet formation is shown

Modeling results in Mica

Transmission (%)

T code with a sinusoidal temporal beamT experimental (results from University of Ottawa)T code with a gaussian temporal beam (order 2.8)

Transparent dielectric

Fs microjoulelaser

Ejected matterSolid densification

Hole

Femtosecond laser interaction with dielectric surfaces

1. Surface ionization , laser propagation and energy absorption2. Front surface deformation, pressure increase, ablation and hole formation3. Solid densification around hole, final shape of the hole

Physical processes

λ = 800 nmτ = 17 fsE = 1 μJ

Traitement du cas en surfaceDensité (m-3)

Déphasage

Fréquences d’ionisationMultiphoton ionization

Collisionnal ionization

Electron trapping

• Collisionnal ionization plays no role

Silica femtosecond LP3 experiments (2009)W0=4.65 μm, 28 fs (Gaussienne 3.15 μm, 17 fs)

Energy (μJ) Electric field (V/m) Fluence (J/cm2)1 2.4 1010 1.6

1.3 2.74 1010 2 (claquage)

2 3.39 1010 3.2

3 4.16 1010 4.8

5 5.37 1010 8.6

6 5.88 1010 10.3

1 μJ 3 μJ

5 μJ 6 μJ

Specific energy contours after laser shot (after relaxation)

Shielding of laser propagation for high flux → Top hat, « bi-corne » shape of energy contours

1 μJ 3 μJSeuil de claquage

5 μJ 6 μJ

5 μm

10 μm

375 ps

325 ps 275 ps

Density contours after hydrodynamic expansion

Density contours after hydrodynamic expansion3 μJ 5 μJ 6 μJ

2

1.1

2

2

Hole : low density region, densification by lateral shock compressionbut hydrodynamic expansion not efficient enough

Final hole shape

Final shape : combined plasma expansion / fragmentation processes