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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
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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
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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
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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
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Nanosecond modeling (CHIC code)
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• 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
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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)
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2. Hydrodynamic motion ~ 100 ps
Difficulty• Water is transparent to visible wavelength
Solution• Control of laser energy absorption in dielectrics in previews studies (*)
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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
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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
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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
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Ionization by EM wave interactionCollisionnal ionization
eenionet nntntn colrec
1 )()( ντ
ν +−=∂
Radiative recombination
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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 ?
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⎟⎟⎠
⎞⎜⎜⎝
⎛= 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
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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
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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)
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Ionization rates comparison
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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
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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
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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
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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
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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
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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 %
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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)
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1/ Interaction in the bulkHydrodynamic process involved
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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
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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
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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
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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
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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)
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2/ Interaction near material boundaries
Hydrodynamic process involved
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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
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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
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Results from David Grojo (University of Ottawa):
Silica: Energy=155 nJ, bump= 7nm
45fs; NA=0.45
Experimental evidence of nanoLIFT in solids
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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
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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)
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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
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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
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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
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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
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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
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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
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Final hole shape
Final shape : combined plasma expansion / fragmentation processes