Lumière ExtrêmeL’ Optique Relativiste

Et ses Applications

Gérard A. MOUROULaboratoire d’Optique Appliquée – LOA

ENSTA – Ecole Polytechnique – CNRSPALAISEAU, France

gerard.mourou@ensta.fr

Erik Power, Natalia Naumova, John Nees,Igor Sokolov*, Victor Yanovsky, Kyung-Han

Hong, Takeshi Matsuoka, Bixue Hou, AnatolyMaksimchuk, Gerard Mourou

Center for Ultrafast Optical Science, University of Michigan,

V. Malka, J. Faure, A. Rousse, K. Ta Phuoc

Laboratoire d’ optique Appliquée

EQ~hν

1MeV

1eV

1TeV

ElectronCharacteristic

Energy

1PeV

EQ=m0c2

100fs100fs

4

Chirped Pulse Amplification D. Strickland and G. Mourou 1985

Progress in Laser Peak Power

10TW 10TW

The Various Epochs of LaserPhysics

Ec =e

rb2 =

m 2 e5

h4

ER =m0 c 2

eλ=

hνD ce

ES =

2m0 c2

DC e1960

1990 2000

Coulombic Epoch

Relativistic Epoch Nonlinear QED

Sommaire• L’ intensité relativiste• L’ optique relativiste et son parallèle avec l’ optique

nonlinéaire de l électron lié• Le redressement optique relativiste: la clé de la

production d électrons, protons, rayonX et γ dehaute energie.

• Production d impulsions attosecondes de photons etd électrons

• X-ray cohérent par diffusion Thomson cohérente• Vers le champ critique(champ de Schwinger)

L’ optique relativiste

Bound Electron Nonlinear OpticsBound

• Harmonics

• Optical Rectification

•Self-focusing

Er

Br

−ex

x

t

EqFrr

=

The field necessary corresponds to hv/λ3

v << cF ∝ x

Nonlinear Optics (bound electron)

• Harmonic Generation Franken 1961• Sum and Difference Frequency Generation Bass et al. 1962• Optical Rectification Bass et al 1962• Parametric Generation and Amplification Giordmaine et al. 1965• Stimulated Raman Scattering Woodbury and Ng 1962• Stimulated Brillouin Scattering Chiao et al.1964• Two-Photon Absorption Kaiser et al. 1961• Four-wave Mixing Maker and Terhune 1965• Optical Kerr Effect Gires and Mayer 1964• Multiphoton Ionization Voronov and Delone 1965• G. Mainfray, P. Agostini, C. Manus, et al. 1967• N. Isenor and S. L. Chin 1969• Transient Coherent Effects: Photon Echoes Hartman et al. 1966, Self-Induced Transparencies Mc

Call and Hahn 1967

• P. Agostini, A. L’ Huillier, C. Manus, G. Mainfray High Harmonic Generation 1989 “Extreme (bound electron) nonlinear Optics”

RelativisticRelativistic Optics Optics

r F = q

r E +

r v c

∧r B

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟

a)Classical optics v<<ca)Classical optics v<<c, , b) Relativistic optics v~cb) Relativistic optics v~c

∆∆x~x~aaoo

∆∆z~az~aoo22

aa00<<1, a<<1, a00>>a>>a0022 aa00>>1, a>>1, a00<<a<<a00

22

a0 =eA0

mc2 =eE0 λmc 2

Relativistic Laser:Relativistic Laser: Helios Helios at LANL at LANLaa00~1, Rep. Rate~~1, Rep. Rate~mHzmHz

Carman et al 1981

Relativistic Relativistic λλ33 Laser CUOS Laser CUOSaa00~0.6, Rep.Rate kHz~0.6, Rep.Rate kHz

Seung-Whan Bahk

Relativistic λ3 regime

• Spatial focus (λ2)• Temporal focus (λ/c)• Relativistic intensity I=2 1018 W/cm2 (a=1),

wavelength λ=0.8µm, 1mJ, 1KHz

O.Albert, H.Wang, D.Liu, Z.Chang, G.Mourou (2000)

- 2 0 -1 0 0 1 0 2 00 .0 0

0 .2 5

0 .5 0

0 .7 5

1 .0 0

P u ls e D u r a t io nF W H M = 8 f s

Inte

nsity

(a.u

.)

1.3µm

“ Gérard Nonlinear optics started at 1 photon/pulse” (R. Chen, private communication during a nice party in Korea)

HERCULES

1022W/cm2

Φ =.8µm

DM Corrected

Uncorrected

Hercules: 1022W/cm2

a02=104

S. -W. Bahk, et al. ``Generations and characterization of the highest laser intensities (10^22W/cm^2),”Opt. Lett. Vol. 29, No. 24, p2837, Dec 15, 2004.

Redressement OptiqueRelativiste

(Wake Field Acceleration)

RelativisticRelativistic Optics Optics

r F = q

r E +

r v c

∧r B

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟

a)Classical optics v<<ca)Classical optics v<<c, , b) Relativistic optics v~cb) Relativistic optics v~c

∆∆x~x~aaoo

∆∆z~az~aoo22

aa00<<1, a<<1, a00>>a>>a0022 aa00>>1, a>>1, a00<<a<<a00

22

a0 =eA0

mc2 =eE0 λmc 2

Relativistic Rectification(Wake-Field Tajima, Dawson)

sEr

+ -

• pushes the electrons.

• The charge separation generates an electrostaticlongitudinal field. (Tajima and Dawson: Wake Fields orSnow Plough)

• The electrostatic field

r F Bz

= qr v c

∧r B

⎛ ⎝ ⎜

⎞ ⎠ ⎟

r v ∧

r B

Es=cγmoω p

e= 4πγmoc

2ne

E s ≈ E L

Relativistic Rectification

-Ultrahigh Intensity Laser is associated with Extremely large E field.

IZE LL *02 =

Medium Impedance Laser Intensity

218 /10 cmWIL =

223 /10 cmWIL =

mTVEL /2=

)/106.0(/6. 15 mVmPVEL =

The Relativistic Rectification:Total Serendipity

In the relativistic regime the laser transverse field becomes:

1) Totally rectified2) Longitudinal 3) As large as the transverse laser field4) The plasma can not be broken down.

Relativistic rectification could give access to TeV/m to PeV/m.

Million times higher fields than conventional technology.

Accelerator million times more compact.

Laser Acceleration:

At 1023W/cm2 , E= 0.6PV/m, it is SLAC (50GeV, 3km long) on 10µm The size of the Fermi accelerator will only be one meter(PeV accelerator that will go around the globe, based on conventional technology).

Relativistic Microelectronics

Petawatt ParticleAccelerators

Fermi PeV Accelerator

J. Faure et al., C. Geddes et al., S. Mangles et al. , in Nature 30 septembre 2004

e-beamThe Dream Beam

Recent results on electrons acceleration - Setup

J. Faure et al, Nature 2004

LOA – 100 TW

He gasne ~ 1019 cm-3

3D PICPukhov

Experiment

Recent results on electrons acceleration

J. Faure et al, Nature 2004

V. Malka et al, Science 2002

Divergence< 6 mrad

In collaboration with L. Le-Dain, S. Darbon from CEA Mourainvilier and DAM

Advantages: low divergence, point-like electron sourceApplication: high resolution γ-radiography

Applications

Higher resolution: of the order of 400 µm

In collaboration with L. Le-Dain, S. Darbon from CEA Mourainvilier and DAM

γ-radiography results

measured calculated

Applications

Secondary effects ofelectron acceleration:

X-rayBeam

The structure of the ion cavity

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

Longitudinal acceleration

Ex

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

⊥rapF

Transverse oscillation: Betatron oscillation

Laser 1.5 J/30 fs (Salle Jaune)

Electrons

Permanent magnets

Experiment Setup

Helium jet ne ~ 1019 cm-3

X-rays

A. Rousse et al.

Simultaneous measurements of X-ray and Electron Beams

X-ray CCD (taper) Roper Scientific6cm x 6cm CCD area with 500 µm Be filter

Magnets divergence

150 MeV10 MeV

+40

-40

ne = 1019 cm-3

Electron beam

X-ray beam

20 mradEX>3 keV

K. Ta Phuoc et al

Secondary effects ofelectron acceleration:

Proton Acceleration

Front and back acceleration mechanisms

Peak energy scales as : EM ~ (IL×λ)1/2

Large Laser results : Vulcan laser 50J:1ps & 1shot/20min.

In front of target– “blow-off”

direction5 cm

5 cm

BACK

5 cm

5 cm

Behind the target –“straight through”

direction

FRONT

Proton Beam Characteristics

Energy Collimation

Plastic TargetAluminum Target

In collaboration with K. Ledingham and P. Mc Kenna

p-beam

Attosecond Generation(photon)

Talks at this meeting by T. Tajima, S.V. Bulanov et al.Y.U. Mikhailova et al.

Attosecond byBond electron Nonlinear Optics

• P. Corkum, M. Ivanov and Burnett”Sub.femtosecond Pulses”Opt. Lett. 19, 1870 (1994)

• M. Hentschel et al. Nature 414, 509 (2001)• A. Baltuslka et al. Nature 421, 6111 (2001)

The technique relies on High harmonic Generation andnot very efficient.

It is limited to nJ and not scalable to high energy.

Relativistic self-focusing• Previously, relativistic

self-focusing hasbeen studied only inthe refractive regime.

A.G.Litvak (1969), C.Max,J.Arons, A.B.Langdon (1974)

ε = 1−ω 2

p

γ 0ω2 where γ 0 = 1+ a0

2

Single Mode Relativistic optics inReflection

r F = q

r E +

r v c

∧r B

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟

λUnder the action of the light pressure the critical surface will be pushed(curved) at relativistic speed at twice the laser frequency (2ω).

If the laser is focused on 1λ, it will act as a perfect “single mode” mirror, leading to well behaved reflection and deflection.

The restoration force is a function of the plasma density

3-D PIC simulation

attosecond pulseElectromagneticenergy density

Electrondensity

P-plane S-plane

2-D PIC simulation

Relativistic deflection of lightobserved in experiment

Experimental parameters:λ=0.8µm, τ=30 fs, d=1.2µm,I≈1.5·1018Wcm-2

Results:• Splitting of reflected beam

into two lobes• Divergence of the beam: 35o,

45o (input 40o)

Erik Power, APS DPP meeting, 2004

Simulation: ao=1, 20fs, f/1,plasma gradient 0.1λ

two e.m. trains

Spatio-spectral measurements

E

a0<<1 a0>1

2-D PIC simulation

Relativistic TemporalCompression

c

c

V~C

Scalable Isolated Attosecond Pulses

Amplitude, a

1D PIC simulations inboosted frame

Duration,

τ (as) 2D: a=3, 200as

τ(as)=600/a0

I=1022W/cm2

(Hercules)

λ=1019Ω/χµ2

(λ3 laser)

optimal ratio: a0/n0=2,or exponential gradientdue to ωcr=ω0a-1/2

n0= n/ncr

Isolated Attosecond Pulse Generationby

Relativistic Compression and Deflection

• It should be efficient

• Scalable

• Because it is a relativistic plasma, thehigher the intensity, the shorter and thebetter.

Attosecond Generation(electron)

2-D PIC simulation Attosecondelectron bunch generation:

Intensity: 2 1021 W/cm2 (a=30)

Pulse duration: 10fs

Wavelength: λ=0.8µµ

Polarization: linear

Focus spot: 1λ

Plasma density: 6.3 1022 cm-3 (36ncr)

Channel diameter: 1.4λ

Simulation setup

Attosecond Pulse of electrons

Attosecond Pulse of electrons

Attosecond Pulse of electrons

Attosecond Electron Bunches

N. Naumova, I. Sokolov, J. Nees, A. Maksimchuk, V. Yanovsky, and G. Mourou,Attosecond Electron Bunches, Phys. Rev. Lett. 93, 195003 (2004).

Attosecond pulse train

Attosecondbunch train

25÷30 MeV

a0=10, τ=15fs, f/1, n0=25ncr

Electron bunches of ~100 as durationwould produce backward

CoherentThomson scattering efficiency• Cross-section for the backward Thomson scattering: ~N+N(N-1)exp(-2(k’d’)2) depends on the factor in the exponent: k’d’=kd(1+V/c)2γ2 .• The resulting backward Thomson cross-section σTN2 exp(-8(kd)2γ4) ~ 10-4 exp(-8(kd)2γ4) cm2

is far above the channel cross-section σCh=10-8 cm2

• Limitation for d and γ: kd < γ-2( -0.125 ln(σCh/σTN2) )1/2

• Attosecond bunches with width d ~ 1/kγ2 ~ (100 as) . c

η~1 efficiency

Bunch:

N particleswith

Gaussiandistributionγ photon =

λ4γ 2 for γ =100

γ photon = 40 keV

For γ = 103 , γ photon = 6MeV

N. Naumova, I. Sokolov, J. Nees, A. Maksimchuk, V. Yanovsky, and G. Mourou, Attosecond Electron Bunches, Phys. Rev. Lett. 93, 195003 (2004).

EQ~hν

1MeV

1eV

1TeV

ElectronCharacteristic

Energy

1PeV

EQ=m0c2

Laser-Induced Nonlinear QEDE. Brezin and C. Itzykson Phys. Rev.D2,1191(1970)

W ∝ exp −πEs

E⎛ ⎝ ⎜

⎞ ⎠ ⎟

Es =

2m0 c2

eD c

with D c =h

m0 c 2Schwinger Field

Vacuum Tunneling

Es=1.3 1016 V/cm

Is=1030W/cm2

2 m0c2

Vacuum can be considered like a dielectric

e+e- Dirac sea

Talks of N.B. Narozni et al, C. H. Keitel

Towards the Critical Field

The pulse duration and the wavelength scaleas:

For I=1022W/cm2 a02 =104

The pulse duration τ= 600 /a0 ~ 6asThe wavelength ~ λ/1000The Focal volume decreases ~ 10-8

The Efficiency~ 10%

Intensity I=1022W/cm2 I=1028W/cm2

Ultra-high Intensity

General Relativity

and Black Holes

Equivalent to be near a Black Hole of Dimension?Temperature?

Laboratory Black Hole

Atomic Physics

Nuclear Physics

High Energy Physics

Astrophysics

Cosmology

eV

PeV

Moving from the Atomic Structureto the Quark Structure of Matter

Conclusion

The possibility to generate“Relativistic Intensities” with compactlasers is producing a revolution in the field of laser optics similar tothe one we experienced since the 1960’s.

Using the laser itself or “marrying” it with high energy particleaccelerators it suddenly extends the realm of optics from the eV tothe GeV regime to include Nuclear, High Energy Physics, GeneralRelativity, Cosmology.

It also brings back to the University Laboratory, Science that hasbeen traditionally done on large instruments.