real-time electron dynamics in solids under strong

Real-time electron dynamics in solids under strong electromagnetic fields

ISSP-CMSI International WorkshopSymposium on Material Simulation in Petaflops era (MASP2012)

June 27 2012 ISSP Univ Tokyo

Kazuhiro Yabana Center for Computational Sciences University of Tsukuba

Y Shinohara U Tsukuba SA Sato U Tsukuba T Sugiyama U Tsukuba T Otobe JAEA J-I Iwata U Tokyo GF Bertsch U Washington

TDDFT First-principles tool for electron dynamics simulation

Absorption cross section

Collision of atoms and ions

E S0 S1

S2

+Ze

Electronic excitation + + + + + +

- - - - - -

E(t)

hν

3hν

e-

Multiple ionization

Intense ultra-short Laser pulses

Linear response regime (Perturbation theory)

Nonlinear nonperturbative regime (Initial value problem)

e- e-

soft X ray (High harmonic generation)

Dielectric function

Coherent phonon Electron-hole plasma Optical breakdown

Conductance of nano-wire

( )ωσ

Laser-solid interaction

Coulomb explosion

( ) ( )[ ] ( ) ( )

( ) ( )2

sum=

+=partpart

ii

iextKSi

trtr

trtrVtrhtrt

i

ψρ

ψρψ

3

CONTENTS

1 A frontier in light - matter interaction intense and ultrashort - Theories and computations required in current optical sciences - 2 Real-time and real-space calculation for electron dynamics in solid - time-dependent band calculation treatment of boundaries - 3 Electron and phonon dynamics in solid for a given electric field - Dielectric function coherent optical phonon optical breakdown hellip - 4 Coupled Maxwell + TDDFT multiscale simulation - First-principles simulation for macroscopic electromagnetic field in intense regime Dense electron-hole plasma induced by intense laser pulses -

4

Modern experiments on light-matter interactions

Requiring new theories and large-scale computations beyond ordinary electromagnetism and quantum mechanics

- Nano-sized material too large to calculate microscopically too small to calculate macroscopically large-scale microscopic calculation - Near field optics (resolution beyond diffraction limit) - Meta-material (negative refractive index) - Surface plasmon polariton (coupled light-electron dynamics) quantum effects () - Intense and ultrashort laser pulses (extreme nonlinear electron dynamics) requiring time-domain description coupled dynamics of electrons and electromagnetic fields

Frontiers in Optical Sciences Intense field

Nuclear reaction Particle Acceleration

QED Vacuum breakdown

Relativistic Classical

Nonrelativistic Quantum

Nonlinear electron dynamics

G Mourou

Intense laser pulse on solid

21513 Wcm1010 minus Laser intensity

Vacuum breakdown

Laser acceleration

Electron-hole plasma Optical breakdown Laser machining

Coherent phonon

HHG

Nonrelativistic Quamtum mechanics

Relativistic Classical mechanics

Nonlinear optics

eE(t)z z

nucleiby field electric Internal pulselaser by field electric External

asymp

7

Frontiers in Optical Sciences Ultra-short dynamics

s10 15minus Time

Nucleon motion in nucleus

s10 18minus s10 23minuss10 12minus

Attosecond Femtosecond Picosecond

Real-time observation of valence electron motion E Goulielmakis etal Nature 466 739 (2010)

Shortest laser pulse 80 as (2008)

Period of electron orbital in Hydrogen 150as

Period of Ti-sapphire laser pulse

Period of Optical phonon (Si 64 fs)

8

119879ph Period of optical phonon

M Hase et al Nature (London) 426 51 (2003)

pump probe

120549120549 119905120549 prop 119890minusΓ119905 sin Ωph119905 + 120601

Pump-Probe Measurement Coherent Phonon

Intense 1st pulse excites electrons and atoms Weak 2nd pulse measure change of reflectivity

Optical microscope image of waveguides written inside bulk glass by a 25-MHz train of 5-nJ sub-100-fs pulses CB Schaffer etal OPTICS LETTERS 26 93 (2001)

RR Gattass E Mazur Nature Photonics 2 220 (2008)

Micromachining ndash waveguide- Nanosurgery

Ablation of a single mitochondrion in a living cell N Shen etal Mech Chem Biosystems 2 17 (2005)

Femto-technology nonthermal machining by femtosecond laser pulses

10

CONTENTS


3D real-space grid representation high order finite difference

Time evolution 4-th order Taylor expansion

( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ

Calculation in real-time and real-space

Time-dependent Kohn-Sham equation

( ) ( )[ ] ( ) ( ) ( )2 sum==partpart

iiiKSi trtrntrtrnhtr

ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus

++nablaminus= int micro

Norm-conserving pseudopotential

12

Two key issues

Use (spatially uniform) vector potential instead of (spatially linear) scalar potential to express macroscopic electric field

Boundary effect (macroscopic shape effect) needs to be considered from outside of the theory

We assume a long wavelength limit lattice const ltlt light wavelength

Electron dynamics in a unit cell under time-dependent spatially uniform field

Treatment of optical electric field

Employing a vector potential replacing the scalar potential one may recover the periodicity of the Hamiltonian

( ) ( ) ( )ztEdtctAztE

tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2

Electron dynamics in crystalline solid under spatially uniform field

( )zteE

z

( )zVScalar potential spoils spatial periodicity of the Hamiltonian

( )zteE

( ) )(rharh ne+

( ) ( ) ( )rearrharh nkaki

nk

ψψ =+=+ )(

Time-dependent spatially uniform electric field

Time-dependent Bloch function

a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ

Equation for time-dependent Bloch function

Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

Assume Icosahedral shape

Electron dynamics in metallic clusters by TDDFT K Yabana GF Bertsch Phys Rev B54 4484 (1996)

16

＋＋

＋＋

＋＋

－－－－－

－

Collective electronic excitation plasmon

+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－

Longitudinal plasmon Mie plasmon

(Surface plasmon of spherical nanoparticle) 2124

=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－ Longitudinal

)()( tAtA ext= ( )tAtAtA onpolarizatiext += )()(

Choice of geometry (boundary condition)

- We solve electron dynamics in a unit cell inside a crystalline solid - The electric field in the unit cell depends on macroscopic geometry of the sample - We need to specify the lsquoboundary conditionrsquo in the calculation

Optical response of thin film

～ onpolarizatiext EEE +=

( )tEext

( )tAtAtA onpolarizatiextr += )()(


Longitudinal geometry Treatment of induced polarization

( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ

Equation for polarization

dielectrics ldquoparallel-plate-capacitor with dielectricsrdquo

( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA

Bertsch Iwata Rubio Yabana Phys Rev B62(2000)7998

18

19

CONTENTS


20

Linear response Two methods to calculate dielectric function from real-time electron dynamics

Transverse geometry Longitudinal geometry

( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2

For an impulsive external field

( ) ( ) ( ) ( )tkctAtktE θδ minus==

( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε

Comparison of numerical results for dielectric function of Si by two methods - Green longitudinal - Red transverse Re[ε]

Im[ε] J(t)A_0

Spatial grid 16^3 K-points 8^3 Distortion strength A_0 = 001 (with induced) 00005 (without)

22

Dielectric function of Si in TDDFT (ALDA) Transverse calculation

Dielectric function by TDDFT (ALDA) is not very good Too small bandgap (common problem with LDA)

23

Instantaneous pulse field is applied at t=0 the induced current as a function of time

G Onida L Reining A Rubio Rev Mod Phys 74(2002)601

PRL107 186401 (2011) arXiv11070199 S Sharma JK Dewhurst A Sanna EKU Gross Bootstrap approx for the exchange-correlation kernel of time-dependent density functional theory

Dots experiment Dash-dotted RPA Solid Bethe-Salpeter (electron-hole interaction considered)

TDDFT (ALDA)

25



pump probe




The two mechanisms for coherent phonon generation

Virtual electronic excitation (transparent material)

Real electronic excitation (opaque material)

Y Yan E Gamble and K Nelson J Chem Phys 83 5391 (1985) HJ Zeiger J Vidal TK Cheng EP Ippen G Dresselhaus and MS Dresselhaus Phys Rev B 45 768 (1992)

Impulsive Force appears only during laser irradiation

Displacive Change of equilibrium

119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876

120587 2frasl difference in the phase

( )qVFtΕV

partpart

minus== 21 2χ

Coherent phonon measurements in Sb - Most popular material for coherent phonon generation - Observed two modes A1g Eg

A1g

Eg

K Ishioka M Kitajima and O Misochko J Appl Phys 103 123505 (2008)

Eg A1g

Sb crystal structure and phonon mode - Semimetal - Rhombohedral structure

Having C3 symmetry axis parallel to vertical line in following figure

High density region Low density region

Eg

A1g

Bond

Each atom have three bonds Only one bond on plane Other two bonds are out of plane

There are two modes A1g and Eg (doubly degenerate)

Crystal structure Electron density at ground state Bond

Electron density under laser pulse Increasing Decreasing

119864

Electron density at ground state Density difference on plane-1 Density difference on plane-2

During laser pulse electrons moves atom to atom After laser pulse ends bonding electrons are reduced

Eg A1g

119916 Including electric field Out of electric field

Y Shinohara etal submitted to J Chem Phys

Density change and force

201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g

Including electric field Out of electric field

Force is dominated by real-excitation (removal of bonding electrons)


A1g

Eg


Eg A1g

However calculation is not consistent with measurement Experimentally A1g displacive Eg impulsive

TDDFT calculation for coherent phonon in Si

201265

119864

T2g

Direct bandgap 24 eV(calc)

225 eV below band gap

275 eV above band gap

250 eV around band gap

Pulse duration Virtual excitation Impulsive force

Real excitation Displacive force

Y Shinohara et al Phys Rev B 82 155110 (2010)

When laser frequency is below the direct gap impulsive (Raman tensor) force is visible

33

CONTENTS


Weak field regime Standard approach for light-matter interaction

[ ] ( )EEDD ωε==

Constitution relation Electromagnetism Maxwell equation for macroscopic fields E D B H

Quantum Mechanics Perturbation theory to calculate linear susceptibilities ε(ω)

Intense laser pulse induced nonlinear electron dynamics

[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε

Perturbative expansion is no more useful Dense electron-hole plasma Optical breakdown etc

Further increase of laser pulse intensity

We need to solve couple Maxwell + Schrodinger dynamics

Quantum mechanics is useful to calculate nonlinear susceptibilities as well

( )tri ψ( ) ( )trBtrE

ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2

2 =nablaminuspartpart eion enen minusminus=nabla πφ 42

Time-dependent Kohn-Sham eq

Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus

+nablaminus== sumsum ψψψ

external field

polarization

[μm] [nm] Different spatial scales

Multiscale simulation introducing two spatial grids

Maxwell equation describing electromagnetic field

Time-dependent density-functional theory describing electron dynamics

We solve coupled Maxwell + Schroedinger equations

Maxwell eq Propagation z-direction polarization x-direction

ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε

Laser pulse irradiation normal on bulk Si

Index of refraction ε=n

2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si

Laser frequency below direct bandgap

36

Ac

[microm]

Macroscopic grid

Multiscale simulation

( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart

Macroscopic grid points（μm） to describe macroscopic vector potential

ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(

πψψψψ minusnablaminusnabla=

=

sum

intΩ

At each macroscopic points Kohn-Sham orbitals are prepared and described in microscopic grids

Exchange of information by macroscopic current and macroscopic vector potential ( )tZA

( )tZJ

Zi ψ

At each macroscopic grid point We consider a unit cell and prepare microscopic grid

K Yabana etal Phys Rev B85 045134 (2012)

38

Each CPU calculates electron dynamics at different macroscopic position

CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn

Each CPU calculates nonlinear electron dynamics independently

Macroscopic vector potential requires A and j of nearby points to evolve in time (only tens of bytes exchanged)

( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN

Efficient parallelization

(We also parallelize with repect to k-points)

I=1010Wcm2

Z=0 [microm]

[microm]

Z=08 [microm] Z=16 [microm]

Propagation of weak pulse (Linear response regime separate dynamics of electrons and E-M wave)

Vacuum Si Laser frequency155eV lower than direct bandgap 24eV(LDA）

39

Ac

40

I=1010Wcm2


[microm]


Electron excitation energy per unit cell volume

Ac

41

Maxwell+TDDFT vs Maxwell only (constant ε)

Red = Maxwell + TDDFT Green = Maxwell

Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart

minuspartpart εε tzA

ztzA

tc

εcv =

In linear regime dispersion of dielectric function Induces Phase velocity vs group velocity Chirp effect is also seen

+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si

More intense laser pulse Maxwell and TDKS equations no more separate

42

43

I = 5 x 1012Wcm2

More intense pulse (2-photon absorption dominates)

[microm]



Ac

44

Vector potential and electronic excitation energy After the laser pulse splits into reflected and transmitted waves

Energy Conservation

Our multiscale equations can be derived from the Lagrangian We can derive conserved energy which is a sum of - energy of EM field - energy of electrons - interaction energy between them

46

Total energy Electron energy Energy of EM field

1010 Wcm2 1012 Wcm2 1014Wcm2

Energy conservation well satisfied in practical calculations

Computational aspect

ｘ

ｚ

35microm 256 points

Computational costs 1024 cores (MPI only) 10 hours at SGI Altix ICE 3800EX (ISSP Univ Tokyo) 20480 cores (MPI+openmp) 20 min at K-Computer

nm13=∆z

Microscopic (Schroedinger) spatial grid 163

k-points 83 (reduced by symmetry to 80)

Macroscopic (Maxwell) spatial grid 256

Time step (commom) = 16000 (too small)

47

48

Dense electron-hole plasma generation at the surface modifies dielectric properties at the surface

K Sokoowski-Tinten D von der Linde Phys Rev B61 2643 (2000)

Si

Pump-probe

λ=625nm 100fs pulse

Strong pump-pulse excites electrons at the surface forming dense electron-hole plasma

Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs

Probe-pulse measures change of Dielectric properties

Reflectivity change

Pump-pulse intensity

49

I=1x1011Wcm2 hv=155eV

Our Pump-Probe ldquoNumerical Experimentrdquo

Si Vacuum

Excited electron density at the surface

2-photon absorption

We can calculate excited electron density at the surface by pump-pulse reflectivity of probe pulse

Reflectivity of probe pulse

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50

We may extract ldquodielectric function of excited surfacerdquo from numerical pump-probe calculation

( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω

Decompose vector potential at the surface into incident and reflected components Ratio of two Fourier components gives us a reflectivity as a function of frequency

Dielectric function at the surface when irradiated by 1013Wcm2 pulse

Well described by Drude model (at least for real part)

( ) ( )( )ωεωε

ω+minus

=11R

51

Change of dielectric function as we increase the pump-pulse intensity


2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2

Increase of electron-hole density enhances metallic response

Computational Aspects and Future Prospects

Large computational resources required for multi-scale calculation

At present Normal incidence of linearly polarized pulse on Si crystal 1000 cores 10 hours 30000 cores 20 min (K-computer Kobe) More resources to achieve More complex dielectrics（SiO2 TiO2 ZrO2 hellip) x 10 Oblique incidence（2-dim） x 50 Self-focusing（3-dim） x 1000 Circular polarization（3-dim） x 1000 K-Computer Japan - 640000 cores yen100000000000

Electron dynamics in bulk periodic solid by real-time TDDFT - First-principles description of electron dynamics in femto- and atto-second time scale - Applications to - dielectric function (linear response) - coherent phonon generation - optical breakdown Coupled Maxwell + TDDFT multi-scale simulation - Promising tool to investigate laser-matter interaction - Requires large computational resources a computational challenge - Further developments necessary Surface treatment longitudinal electromagnetic wave 2D3D propagation collision effects (e-e e-v)

Summary

53

スライド番号 1


























Coherent phonon measurements in Sb

Sb crystal structure and phonon mode

Electron density under laser pulse

























TDDFT First-principles tool for electron dynamics simulation

Absorption cross section

Collision of atoms and ions

E S0 S1

S2

+Ze

Electronic excitation + + + + + +

- - - - - -

E(t)

hν

3hν

e-

Multiple ionization

Intense ultra-short Laser pulses

Linear response regime (Perturbation theory)

Nonlinear nonperturbative regime (Initial value problem)

e- e-

soft X ray (High harmonic generation)

Dielectric function

Coherent phonon Electron-hole plasma Optical breakdown

Conductance of nano-wire

( )ωσ

Laser-solid interaction

Coulomb explosion

( ) ( )[ ] ( ) ( )

( ) ( )2

sum=

+=partpart

ii

iextKSi

trtr

trtrVtrhtrt

i

ψρ

ψρψ

3

CONTENTS


4










G Mourou



Vacuum breakdown

Laser acceleration


Coherent phonon

HHG



Nonlinear optics

eE(t)z z


asymp

7


s10 15minus Time









8



pump probe









10

CONTENTS




( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ



( ) ( )[ ] ( ) ( ) ( )2 sum==partpart


ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus



12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































3

CONTENTS


4










G Mourou



Vacuum breakdown

Laser acceleration


Coherent phonon

HHG



Nonlinear optics

eE(t)z z


asymp

7


s10 15minus Time









8



pump probe









10

CONTENTS




( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ



( ) ( )[ ] ( ) ( ) ( )2 sum==partpart


ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus



12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































4










G Mourou



Vacuum breakdown

Laser acceleration


Coherent phonon

HHG



Nonlinear optics

eE(t)z z


asymp

7


s10 15minus Time









8



pump probe









10

CONTENTS




( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ



( ) ( )[ ] ( ) ( ) ( )2 sum==partpart


ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus



12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53




























































G Mourou



Vacuum breakdown

Laser acceleration


Coherent phonon

HHG



Nonlinear optics

eE(t)z z


asymp

7


s10 15minus Time









8



pump probe









10

CONTENTS




( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ



( ) ( )[ ] ( ) ( ) ( )2 sum==partpart


ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus



12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53
























































Vacuum breakdown

Laser acceleration


Coherent phonon

HHG



Nonlinear optics

eE(t)z z


asymp

7


s10 15minus Time









8



pump probe









10

CONTENTS




( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ



( ) ( )[ ] ( ) ( ) ( )2 sum==partpart


ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus



12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































7


s10 15minus Time









8



pump probe









10

CONTENTS




( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ



( ) ( )[ ] ( ) ( ) ( )2 sum==partpart


ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus



12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































8



pump probe









10

CONTENTS




( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ



( ) ( )[ ] ( ) ( ) ( )2 sum==partpart


ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus



12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53



























































10

CONTENTS




( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ



( ) ( )[ ] ( ) ( ) ( )2 sum==partpart


ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus



12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53
























































( ) ( ) ( ) ( ) ( ) 4

1exp0

=

∆

asymp

∆

=∆+ sum=

Nti

tthk

ti

tthtt iKS

N

ki

KSi ψψψ



( ) ( )[ ] ( ) ( ) ( )2 sum==partpart


ti ψψψ

( )[ ] ( ) ( )[ ] ( )trVtrnrr

erdrVm

trnh extxcionKS

2

2

22

++minus



12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































12

Two key issues








tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53
























































tA

cE

t

ˆ

1

int=hArr=

partpart

minusnablaminus=

φ

φ

( ) ( ) ( ) ( )ttrVtAcep

mt

ti ψψ

+

minus=

partpart

21 2


( )zteE

z


( )zteE

( ) )(rharh ne+


nk

ψψ =+=+ )(



a

14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































14

( ) ( ) ( ) ( )

( ) ( )2

2

21

sum=

+

minus+=

partpart

nkkn

knkn

trutrn

trutrVtAcekip

mtru

ti

( ) ( )( ) ( )trutaru

truetr

nknk

nkrki

nk

=+=ψ


Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































Na147+ Li147

+

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]

-30

-20

-10

0

10

20

30

Dipole moment

50403020100

Time [eV-1]



16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































16

＋＋

＋＋

＋＋

－－－－－

－


+ + + + + + + + + + + + + + +

－－－－－－－－－－－－－－



=

mne

pπω

n electron density

3p

Mie

ωω =

( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































( ) ( ) ( ) ( )ttrVtAcep

mt

ti nknk ψψ

+

minus=

partpart

21 2

( ) ( )ztEdtctAtA

cE

t

ˆ1int=

partpart

minus=

Transverse

+ + + + + + + + + + + + + + +







( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































( )tEext




( ) ( )trjrddt

tAd

cell

onpolarizati 4

)(2

2

intΩΩ

=π

2

2

21

sum=

+minus

+nablaminus=

partpart

ii

ixc

iii

n

nEeA

cei

mti

ψ

ψδ

δφψψψ

sum

minus

+=

iii ccA

cep

mj

21 ψψ



( ) )(

)(1)(

intminus=

partpart

minus=

tdttEctA

ttA

ctE

( )trj

( )tA


18

19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































19

CONTENTS


20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































20



( ) ( )

( ) ( )

( ) ( )ω

ωσπωε

σωσ

σ

ω

i

tedt

dtdA

cttdttJ

ti

t

41

1

+=

=

minusminus=

int

int ( ) ( ) ( )( ) ( )

( ) ( ) ( )

( )( )( )tAedt

tAedt

tAttdttA

tJdt

tAd

tAtAtA

extti

totti

ext

t

tot

pol

polexttot

ω

ω

ωε

ε

π

intint

int

=

minus=

=

+=

minus

1

4

1

2

2



( ) ( )tktJ σ= ( ) ( )tkdt

dAc

tE tottot

11 minus=minus= ε


Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































Im[ε] J(t)A_0


22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































22



23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53
























































23





TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53

























































TDDFT (ALDA)

25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































25



pump probe










119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53




























































119905

119905

119905

119905

119905

119905

119864(119905) 119864(119905)

119865(119905) 119865(119905)

119876(119905) 119876(119905) sin Ω119901119901119905

1 minus cos Ω119901119901119905

Δ119876


( )qVFtΕV

partpart

minus== 21 2χ


A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































A1g

Eg


Eg A1g




Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53

























































Eg

A1g

Bond





119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































119864



Eg A1g




201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































201265

119864


Plane-1 Plane-2

Ground state

Eg

A1g




A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































A1g

Eg


Eg A1g



201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































201265

119864

T2g









33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































33

CONTENTS



[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































[ ] ( )EEDD ωε==




[ ] ( ) ( ) ( ) +++== 3322 EEEEDD χχωε






ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































ixc

iii nEeA

cei

mti ψ

δδφψψψ +minus

+nablaminus=

partpart 2

21

jc

AtA

c

π41 2

2

2



Maxwell eq

21 2 ccA

cei

imjn i

ii

ii minus


external field

polarization







ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































ｘ

ｚ ( ) ( ) ( )

( ) ( )xtzAtrA

tzAz

tzAtc

z

ˆ

0 2

2

2

2

2

=

=partpart

minuspartpart

ε



2

11

+minus

=nnR

Reflectance

Velocity of wave

ncv =

Vacuum

ε=16

eV551nm800 == ωλ

Si


36

Ac

[microm]

Macroscopic grid


( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































( ) ( ) ( )tZJc

tZAZ

tZAtc

412

2

2

2

2π

=partpart

minuspartpart


ZeionZ

Zixc

ZiZZiZi

enenn

EeAcei

mti

2

2

421

minusminus=nabla

+minus

+nablaminus=

partpart

πφ

ψδ

δψφψψ

( ) Anc

emi

j

jrdtZJ

Zei

ZiZiZiZiZe

Ze

42

)(


=

sum

intΩ



( )tZJ

Zi ψ



38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































38


CPU1

( )tri 1 ψ

CPU2

( )tri 2 ψ

CPU3

( )tri 3 ψ

CPU4

( )tri 4 ψ

CPU-N

( )trNi ψ

( )tJ Z 1plusmn

( )tAZ 1plusmn



( )tA1 ( )tA2 ( )tA3 ( )tA4 ( )tAN



I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































I=1010Wcm2

Z=0 [microm]

[microm]




39

Ac

40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































40

I=1010Wcm2


[microm]



Ac

41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































41



Si Vacuum

( ) ( ) 160 2

2

2

2

2 ==partpart


ztzA

tc

εcv =


+

=

ωε

εωε

dd

cvg

21

[microm]

Ac

Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































Z=0 [microm]

[microm]


I =5 x 1012Wcm2

Vacuum Si


42

43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































43

I = 5 x 1012Wcm2


[microm]



Ac

44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































44


Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































Energy Conservation


46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































46


1010 Wcm2 1012 Wcm2 1014Wcm2



ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53























































ｘ

ｚ

35microm 256 points


nm13=∆z





47

48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































48



Si

Pump-probe



Drude model fit

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

m=018 τ=1fs


Reflectivity change


49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































49



Si Vacuum


2-photon absorption



( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

Fit by Drude model

50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































50


( ) ( ) ( )

( )( )( )int

int=

+=

tAedt

tAedtR

tAtAtA

iti

rti

ri

ω

ω

ω




( ) ( )( )ωεωε

ω+minus

=11R

51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

53






















































51



2-photon absorption

( )

+

minus=

τωω

πεε

imne

n phgsph

14

2

2x1012Wcm2

5x1012Wcm2

1x1013Wcm2






Summary

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Summary

53






















































real-time electron dynamics in solids under strong

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