11th IUVSTA School on

Lasers in Materials Science - SLIMS 8-15 July 2012,

Isola di San Servolo, Venice, Italy

Institute of Thermophysics, Siberian Branch of RAS

Main research directions:

Heat- and mass-transfer in one- and two-phase systems and in the systems with phase transitions;

Hydrodynamic instabilities and turbulence;

Wave dynamics in liquid and gas flows;

Low-temperature plasmas;

Thermodynamic properties of matter;

Laser ablation.

Diamond Jubilee of UK governing by the Queen Elizabeth II

100-year Memorial of Titanic

Diamond Jubilee of the University of Southampton

Olympic and Paralympic Games – 2012 in London

Mechanisms of matter excitations and ablation with ultrashort laser pulses

Several examples of continuum modeling in application to laser ablation

Volume modification of transparent materials

Concluding remarks

Target

Laser

Scales of laser-affected regions:

- spot size ~10 μm – 1 mm;

- depth ~10 nm - few μm

(depending on laser focusing and absorption properties of an

irradiated material)

Density, thermal capacity, thermal conductivity, viscosity, mechanical properties (Young

modulus, plastic yield, tensile strength), etc.

Continuum:

Interatomic potential of interaction

Atomistic: Mesoscopic:

Combines features of macroscopic and

atomistic approaches

Stoneham et al. APA 69, S81 (1999)

Continuum shell model in application to nanotubes

Yakobson et al. Phys.Rev.Lett. 76, 2511 (1996)

Axial compression Bending

Torsion

Hachisu et al., Astrophys. J. 368, L27 (1991)

Sakagami & Nishihara,

Phys.Fluids B2, 2715 (1990)

From: Physicists joke (in Russian), Multiple editions since 1966.

Hydrodynamic modeling:

Similarity between space and “laboratory” astrophysics

Steel, λ = 780 nm, left: τ = 200 fs, F0 = 0.5 J/cm2; right: τ = 3.3 ns, F0 = 4.2 J/cm2. From: Chichkov et al. Appl. Phys. A 63, 109 (1996).

Sapphire, λ = 800 nm, τ = 200 fs, F0 = 4 J/cm2; “gentle” (left) and strong ablation phases. From: Stoian et al. Nucl. Instr. Meth. B 166-

167, 682 (2000).

I. Electronic excitation Metals: - absorption of laser light by free electrons

- - impact ionization

+

-

+

+

All materials: - electron photoemission

. )()()()(

av tntItIt

tne

k

ke

Typical experimental setup to study laser ablation of solids

+

-

-

Dielectrics and semiconductors:

- generation of free electrons

by photo-ionization;

-

- free electrons absorb laser radiation

- +

+ -

+ -

Eg

+

+

-

+

+

3. Ultrafast melting (only semiconductors)

+

- -

-

at t ≥ 400 fs after the dense plasma excitation

(A. Rousse et al. Nature 410, 65 (2001))

4. Thermal melting (picosecond time scale)

+

+

- +

+

+

+

+

- -

-

2. Electron-phonon coupling

Eg = 9 eV

Eex = 5.2 eV

Fused silica, 800 nm

+

-

+

+

- + +

+ -

+ -

Trapping with defect formation

Photo-recombination

Dielectrics Semiconductors

Auger recombination

Eg Eex

+ - +

+

+

+ -

Easier excitation by next pulses

Target

Laser

M

(1) Heating, (2) melting, (3) thermal vaporization

(4) phase explosion

Recoil pressure Hydrodynamic instabilities

(Lecture by Professor Miotello)

Electron-lattice thermalization time ~ 10-100 ps

Near-threshold fluences: (1) Spallation

(2) Coulomb explosion

Lecture by Professor Zhigilei

Two-temperature model

Kaganov et al. Sov. Phys. JETP 4, 173 (1957)

Anisimov et al. Sov. Phys. JETP 39, 375 (1974)

.r

lel

t

TT

t

T

)(

, )exp()()1()( 0

lel

ll

l

lee

ee

e

TTgz

TK

zt

TC

ztIRTTgz

TK

zt

TC

Lecture by Professor Miotello

Theory of elasticity

Yakobson et al. Phys.Rev.Lett. 76, 2511 (1996)

Continuum shell model

Axial compression Bending

Hydrodynamics Colombier et al. Phys.Rev.B 74, 224106 (2006)

Povarnitsyn et al. Appl. Surf. Sci. 253, 6343 (2007)

Torsion

Experimental evidence for CE in sapphire R. Stoian, et al.

Phys. Rev. B 62, 13167 (2000)

t 100 – 200 fs, l 800 nm

Normalized velocity distributions for O+ (open triangles) and O2+ (closed diamonds):

Momentum scaling

O+ O2+

E

Ions are emitted and accelerated by the

electric field.

This leads to the momentum scaling

Eeam

tEevm

Laser pulse

MPI Photo-

emission

free-electron

absorption

avalanche

absorption

and reflection

dynamics

electric

field

carrier

drift and

diffusion

Objects for modeling: Au, Si, Al2O3

Regimes: t = 15-100 fs, l = 800 nm

Rate equation (continuity)

Rate equation (continuity)

Poisson equation

Drude formalism

iejLSx

J

et

njj

jj, ,

1

Dj = kBTeej /e

E

x

en ni e

0

jjjjj neDEneJ

t

1

1

1111

0

*

in

n

n

nn

cr

eege

Continuity equation:

Poisson equation:

Complex dielectric

function:

).(,4,2

3

),,()(

2

le

l

l

ee

ee

le

e

e

e

e

TTgt

TC

e

TkKkC

txTTgx

T

en

J

t

TC

Si:

Two-temperature model:

).,()/1(

),(),(

2)2()(

0

ab

2

21

txPEEnCn

nEtxItx

nn

nnE

IE

IE

t

E

e

ie

eg

ia

aeggg

f

t

),(),()(

),( abph

6

6 txItxanhnn

nItxI

x ia

a

Al2O3:

),(),(),(2),( ab21 txItxatxIhnhntxIx

aa

Si:

Attenuation of the laser beam:

Metals (Au):

e

e

e

es

kT

eTAIR

kT

hF

h

kTcJ

exp1

3

3

2 20

33

2

2

Semiconductors (Si):

e

e

e

e

PE

free

PE

Au

AuPE

SiPEAus

kT

eTAIR

kT

hF

h

kT

l

lcJ

exp1

3

3

2

13

13

2

0

33

2

2

Dielectrics (Al2O3): )/exp()(2

1 6

6 lxnn

nInIPE

ha

ae

N.M. Bulgakova et al. Phys. Rev. B 69, 054102 (2004); Appl. Phys. A 81, 345 (2005) W. Marine et al. J. Appl. Phys. 103, 094902 (2008)

Photoemission:

-0,1 0,0 0,1 0,2 0,3

0

1

2

3

Silicon x 30

Gold x 100

Al2O

3

ni-n

e [10

21 c

m-3]

Time [ps]

Laser fluence (slightly above the threshold of ion observation in plumes): 4, 0.8, and 1.2 J/cm2 for Al2O3, Si, and Au, respectively

t = 100 fs

l = 800 nm

-0,1 0,0 0,1 0,2 0,3 0,4 0,5-10

-8

-6

-4

-2

0

Critical electric field

Ele

ctr

ic fie

ld [1

01

0 V

/m]

Time [ps]

w = 0E2/2

Wat = 0E2Vat/2

For sapphire:

Eth 51010 V/m

Number of emitted electrons:

Al2O3 - 6.2108

Si - 5.941011

Au - 8.21010

Maximums of the electric field: Al2O3 - 8.71010 V/m; Si - 1.4108 V/m;

Au - 9106 V/m

0

00at

0

)3(2

nTknE l

xth

Al2O3

A.Weck et al. Appl.Phys. A 90,

537 (2008) Stainless steel

0,1 1 100,0

0,2

0,4

0,6

0,8

1,0

Ne

Ar

He

Pt

K

Laser fluence [J/cm2]

0,01 0,1 1 100,0

0,2

0,4

0,6

0,8

1,0

Pt

Laser fluence [J/cm2]

Ablation threshold

1-atm air

Vacuum

1.08-atm Ne

K

Dependence on ionization

potential of the ambient gas

A.Y. Vorobyev, C. Guo: Appl. Phys. Lett. 86, 011916 (2005) Opt. Express 14, 13113 (2006)

DCBAe QQQQt

n

)eV(/exp

9

32 10

3

eAraee

eB

B TInnemThk

Q

ie

eBe

C nnTkm

eQ 2

2/9

10

)K(9

24 )K(/10155.2 11

eieD TnnQ

,0

iiB Q

dt

Tkdn

2/3

2/14 2

3

80

e

ieie

B

iT

TTnn

kM

eQ

,e

eBe Qdt

Tkdn

*)1()1( EQTkQIQQQ DeBCArBie

kQ

z

sc

t

sA

)()(

kQ

z

sc

t

sA

)()(

a

k

A nAJQ

)(),( ctzJ

ct zzzzs /)(1)(

R

ctzs

tttrrF

L

LL

)(

)/)(/exp(

0

22

0

22

0

Ar Pt

0

Vdiv

t

ˆ)( divpVVt

V

TdivVpdivUVdiv

t

U

mn m

nmn

x

V

,

, ,

n,m = 1 – 3, n ≠ m

z

TJJ

gt

100% ionization in the focal spot r = 50 μm and

z = 100 μm

z

r

t = 650 ns

Tight focusing

t = 4.7 s

t = 2 s

F0 = 4 J/cm2, 65 fs

Long focus t = 2 s

N.M. Bulgakova et al. SPIE

Proc. 7005, 70050C (2008)

Critical power for self-focusing

Pcr = 3.2 GW for air Pcr = 2.8 MW in fused

silica

n = n0 + n2I

Volume nanogratings

M. Beresna, P.G. Kazansky

OPT.LETT., 35, 1662 (2010)

M. Beresna et al. Appl. Phys. Lett.

98, 201101 (2011)

However, the mistery

of nanogratings stays uncovered

Pulse energy 39 μJ/cm2

Translation speed 50 μm/s

Repetition rate 100 kHz

Pulse energy 43 μJ/cm2

Translation speed 10 μm/s

Courtesy of Peter G. Kazansky, University of Southampton

tr

av

t

e

e

n

n

en

InIt

n

Multiphoton ionization Avalanche ionization

Trapping

exciton

E’

Re-excitation

)/()2( 5.0

Leff eEEmg

Keldysh parameter:

(ratio of time necessary to an electron to tunnel through the potential barrier to the period of the laser field)

At > 1 multiphoton ionization dominates; at < 1 tunneling

dominates.

≈ 1 at I ≈ 5×1013 W/cm2

2/2

0EcI at I ≈ 5×1013 W/cm2 E ≈ 2×108 V/cm

+ + +

+ + +

+ - - -

- - -

at the level ≤ 5×1013 W/cm2

Intensity clamping upon volume modification

.)(

2

1)()1(

2

)()1(2

"1

2

2

PI1

0

22

0

20

2

2

2

21

0

EE

EE

EEEE

EE

g

ec

t

RR

EWnTi

dtRffn

Tnik

t

ik

rrrT

k

i

z

t

tt

I. Non-linear Schrödinger equation (NLSE)

tr

e

l

a

ger

ePI

e

t

n

n

n

Emm

nW

t

n

2

/1)( EE

+ + +

+ + +

+ - - -

- - -

coupled with the rate equation for free carriers

NLSE is obtained from the Maxwell equations in assumption of beam propagation

II. Maxwell equations

+ + +

+ + +

+ - - -

- - -

Equation for the electric field accounting free carrier generation and associated processes

12 2

2 2

0 *2 2

0 *

1 4 8 | |rot (1 /(4 ))a

PI

D e Ei D j H W E E E

c t c c mc E

m nl

m

D E P P 2 2 2

2

0

1 | | ( ) | ( ) |4

nl r r

cP n n f E f R E t d Et t t

coupled with hydrodynamic model for free carriers

c

( v) vv

e

ei E

t m

t

PI

tr

W Wt

t

vj e

Time scale: laser pulse propagation through a glass

sample (several ps); NA = 0.45

Only a small part of the pulse front is efficiently absorbed within the beam

focus region. The rest parts of the beam “flow over” the generated electron plasma

with rather small absorption.

J. Appl. Phys., 101, 043506 (2007)

Phys. Rev. B, 77, 104205 (2008)

Appl. Phys. Lett., 94, 041911 (2009)

Ti:sappire; beam energy is 2.5 μJ, beam waist 0.8 μm, pulse duration 80 fs, NA = 0.7

beam energy is 1 μJ, waist 1 μm, pulse duration 150 fs

Absorption of the laser energy by electrons

Electron-lattice thermalization

Formation of steep temperature gradients

Generation of thermoelastic waves

Heat conduction cooling of the laser-affected region

I. NLSE or Maxwell equations

Spatial distribution of absorbed

energy temperature map

II. Models of thermoelastoplastics

“Frozen jets” and “bubble belts” Impact of polarization on

energy delivery into modification region

Impact of laser pulse tilt on waveguide writing

Formation and motion of micro/nanovoids in glass Nanogratings in glass

“There's Plenty of Room at the Bottom”, Richard P. Feynman

Interaction of ultrashort laser pulses with materials is a fascinating phenomenon that is rich in

physical content and opens new unprecedented opportunities for technological applications.

It requires consolidating knowledge of optics, solid state physics and chemistry, plasma physics,

thermodynamics, theory of elasticity and plasticity.

“Physics lesson” by Sergei Korsun

I hope you do not feel like this poor student under information bombardment

“All these is outrageous lie! They lost power at hbar in the Schrödinger equation and drew electrons instead of muons in air shower!”

From an Internet forum of Russian students

By Sean Carroll

Instead your critical view is very welcome!

Insitute of Thermophysics

SB RAS

Dr. Alexander Bulgakov

Dr. Igor Burakov

Dr. Yuri Shukhov

Students: Olga Bulgakova

Anton Evtushenko

Sergey Starinski

Maxim Shugaev

Lev Zakharov

Prof. Peter Kazansky Optoelectronics Research Centre, University of Southampton, UK

Dr. Vladimir Zhukov Institute of Computational Technologies SB RAS, Novosibirsk, Russia

Dr. Yuri Meshcheryakov Institute of Hydrodynamics SB RAS, Novosibirsk, Russia

Prof. Eleanor Campbell Edinburgh University, UK

Dr. Arkadi Rosenfeld Max-Born-Institute, Berlin, Germany

Dr. Razvan Stoian Universite Jean Monnet, 42000 Saint Etienne, France

Dr. Anatoli Vorobyev Dr. Chunley Guo Rochester University, USA