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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.
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