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a) Manipulation of high power laser pulses by plasma gratingsb) Powerful terahertz emssion from laser wakefield in plasma
Zheng-Ming Sheng
Institute of Physics, CAS, China
Sino-Germany Symposium on Quantum Engineering Celebrating the Einstein Year of Physics, Nov. 23-27, 2005, Beijing, China
Sino-Germany Symposium on Quantum Engineering Celebrating the Einstein Year of Physics, Nov. 23-27, 2005, Beijing, China
H. C. Wu: Institute of Physics, CAS, ChinaJ. Zhang: Institute of Physics, CAS, ChinaK. Mima: Institute of Laser Engineering, Osaka University, Japan
H. C. Wu: Institute of Physics, CAS, ChinaJ. Zhang: Institute of Physics, CAS, ChinaK. Mima: Institute of Laser Engineering, Osaka University, Japan
Outline
• Motivations
• Formation of plasma grating by intersecting laser pulses
• Dispersion of the plasma Bragg grating
• Manipulation of intense laser pulses by plasma Bragg grating
• THz emission from laser wakefields
• Summary
h
GeV electrons
GeV protons
G. Mourou et al., Physics Today 1998Relativistic Laser-Plasma Interaction
100 years after Einstein´s papers on special relativity, they create macroscopic relativistic plasma on the table top with exciting applications..He would have liked it !
Few-cycle laser pulses produce 100 MeV – 1 GeV electron pulses comparable to conventional accelerators, but on mm rather than km distances
J. Meyer-ter-Vehn, MPQ Garching
Motivation
Current high power lasers are produced by the CPA technology. The maximum power is limited significantly by the damage threshold of gratings, which is usually less than 1J/cm2.
Current high power lasers are produced by the CPA technology. The maximum power is limited significantly by the damage threshold of gratings, which is usually less than 1J/cm2.
All optical elements for ultra-high intensity laser will be made by plasma -----J. Meyer-ter-Vehn
Plasma doesn’t have such limit. Does such a grating exist that can serve for pulse stretching and compressing?
Formation of Plasma Bragg Grating
The ponderomotive force of the interference fields of the two pump pulses pushes the electrons, which further drag the heavy ions through Coulomb force. Finally, an electrically neutral PBG forms, which can last as long as a few picoseconds.
Z.-M. Sheng et al., Appl. Phys. B 77, 673 (2003).
Pump Light IPump Light I Uniform PlasmaUniform PlasmaPump Light IIPump Light II
Interaction of intersecting laser beams in plasma
)cos(2/2/
)cos()cos(
2122
21
221
kykxaaaa
etkyaetkxaI zz
x-y
I
kx
ky
Strong ponderomotive force
meVkmc
KXaa
kmc
F
KXaaaaI
I
Xmc
XmcF
p
p
/10*2.3
)sin(2
)cos(22
1
74.2
74.21
122
212
2122
21
218
2/121822
Formulations of the problem
)2cos(24
11
),)(/(/
,0/)(/
),/(//)/(/
,0/)(/
),/(//)(/
2122
21
2222
,
,
,
,
kxaaaa
nncx
xvnctn
McnxPxMmctp
xvnctn
mcnxPxctp
iep
xiii
iixi
xeee
eexe
Approximate stationary solution
Assuming that quasi-charge-neutrality is fulfilled at long time, ni ≈ne, ∂pe,x/∂t=0, ∂pi,x/∂t=0, one obtains
2
21
22/1
/,/
,1)]1(2/[
),1/()1(
)],(cos2exp[)2(
mcTkTT
aa
kxnn
eBeei
e
ie
If a1=a2=0.1, Te=10eV, Ti=1eV, one obtains nmax=38.2n0. This proves to be overestimated as compared to the numerical results.
1D PIC simulation parameters
Two identical pulses:
a=a0sin2(t/), 0≤t≤
a0 ~ 0.1, ~600,
Te=10eV, Ti=1eV,
n0/nc=0.3
Initial Conditions in 1D-PIC Simulation: n0=0.3nc, L=100 λ0; a=0.03, T=
200τ0.
The PBG begins to build up at t=300 τ0 and stays at the deepest modulation almost unchanged during 700-1300 τ0. The PBG begins to attenuate after t=1600 τ0, and completely disappears at t=2000 τ0.
The PBG begins to build up at t=300 τ0 and stays at the deepest modulation almost unchanged during 700-1300 τ0. The PBG begins to attenuate after t=1600 τ0, and completely disappears at t=2000 τ0.
Theory of Light Propagation in an Uniform PBG
Bragg principle: The light with λ=2Λ is fully reflected by PBG. Frequency of this light is named as Bragg frequencyBragg frequency ωB.
Key property of a grating: Bragg reflection occurs over a range of frequencies centered about ωB. This frequency range is photonic baphotonic ba
ndgapndgap (i.e. forbidden gap).
Λ
Transmission Spectrum of UPBGTransmission Spectrum of UPBG
Bandgap width: 0.12 ωB, i.e. 96nm for λ0=800nm.Bandgap width: 0.12 ωB, i.e. 96nm for λ0=800nm.
1D wave equation in underdense plasma:
a
ca
tczp
2
2
2
2
22
2
)1
(
where: ..exp,exp,ˆ2
1cctiziktzatiziktzaea BBBBx
21 a
Electron density of PBG: nnn 0
m
Bm zimknn )2exp(where:
Bk Bragg wave number
Nonlinear coupled-mode equations (NLCME) :
0)2(
)2()1
(
*22
*21
22
1
22
010
aaaaaaa
aaaaaztv
ig
0)2(
)2()1
(
*22
*21
22
1
22
010
aaaaaaa
aaaaaztv
ig
where:cg
B
n
n
v1
01 2
c
m
g
Bm n
n
v
08
cNvg 00 cnnN /1 00
Linearized coupled-mode equations (LCME):
0)1
( 10
aaztv
ig
0)1
( 10
aaztv
ig
Dispersion relation: 22 q
where:
Bkkq 0/)( gB v
2
20
22
2222
2)()(
c
BgBB
p
n
nvkk
kc
In homogeneous plasma:
In homogeneous plasma gratings:
In homogeneous plasma:
In homogeneous plasma gratings:
220 /1 gg vv
Group-velocity dispersion (GVD)
2/322
20
2
2 )(
/)sgn(
gv
The grating dispersion is normalnormal on the lower branch of the bandgap; the dispersion is abnormalabnormal on the upper branch. Moreover, the grating dispersion approaches infinite at the bandgap edges.
Light Speed Reduction
Signal light of ω=0.93ωB propagates in the PBG at a group velocity of 0.34c only, which corresponds to 40% of the light speed in the uniform plasma (n0=0.3nc).
Signal light of ω=0.93ωB propagates in the PBG at a group velocity of 0.34c only, which corresponds to 40% of the light speed in the uniform plasma (n0=0.3nc).
0.85 0.90 0.95 1.00 1.05 1.10 1.150.0
0.2
0.4
0.6
0.8
1.0
/B
Vg/c PIC
Theory NG
Pulse Stretching
Signal light: a0=0.04, T0= 10τ0, a0exp(-t2/T02).
0 20 40 60 80 100
10
20
30
40
50
60
70
T/ o
z/0
0.92(NG)
0.90
0.92
0.93
The pulse is stretched faster when the light frequency is closer to the bandgap edge (0.935ωB). This is due to the increasing dispersion at the bandgap edge.
The pulse is stretched faster when the light frequency is closer to the bandgap edge (0.935ωB). This is due to the increasing dispersion at the bandgap edge.
800 900 1000 11000
4
8
12
16
|a|2 *1
04
t/o
Input PIC NLCME
=0.92B
Chirped Pulse Compression (CPC)
0 20 40 60 80 100
20
30
40
50
60
0.90(NG)
0.89
0.90
0.91
T/ o
0.92
z/0
800 900 1000 1100 12000.0
0.5
1.0
1.5
2.0
=0.9B
Input PIC NLCME
|a|2 *1
04
t/o
Signal light: a0=0.01, T0=50τ0, C=-4, a0exp[-(1+iC)t2/T02)].
The pulse is compressed faster when the light frequency is closer to the bandgap edge (0.935ωB).
The pulse is compressed faster when the light frequency is closer to the bandgap edge (0.935ωB).
Fast Compression of Bragg Grating Soliton (BGS)
Mechanism of soliton formation in abnormal medium: Compensation between the abnormal GVD and SPM leads to the formation of optical soliton.
Abnormal GVD: Making the pulse negative chirped.
Self-phase modulation (SPM):
Stretching the pulse spectrum, and making its center positive chirped.
Large grating dispersion on the upper branch of bandgap can reduce the length of soliton evolution. So one can compress the intense pulse in PBG faster than in uniform plasma.
900 950 1000 1050 1100 1150 12000.00
0.02
0.04
0.06
0.08
t/o
|a|2
Input PIC NLCME L=130
0 20 40 60 80 100
4
6
8
10
12
14
16
18
20
22
1.11
1.12
1.10
1.13
1.12(NG)
z/0
T/ o
In PBG, the pulse can be effiently compressed in the distance less than 100λ0. However, in the uniform plasma, the pulse have a maximum compression at z=500λ0.
In PBG, the pulse can be effiently compressed in the distance less than 100λ0. However, in the uniform plasma, the pulse have a maximum compression at z=500λ0.
Signal light: a0=0.15, T0= 20τ0, a0exp(-t2/T02).
Formation of NUPBG
Pump Light IPump Light I Pump Light IIPump Light II
Uniform PlasmaUniform Plasma
Pump lights meet togetherPump lights meet together
Nonuniform ponderomotive force leads to NUPBG
Perfect chirped-pulse compression in NUPBG
Bandgap width: Δω/ωΔω/ωBB=δ=δnn11(x)/n(x)/ncc
n smalln small
n largen large
Compressing positive chirped pulses
Compressing positive chirped pulses
Compressing negative chirped pulses
Compressing negative chirped pulses
Compression of positive chirped pulses
Reflection for high frequency components
Reflection for low frequency components
Signal light: a0=0.01, T0=60τ0, C=4,ω0 = 0.975ωB
Compression efficiency: ≥90%
Energy loss: ≈0%.
PBG can be a novel tool for ultra-intense light control
PBG can be a novel tool for light control, and fast compression in the high intensity regime, because of their ultrahigh damage threshold >1000J/cm2.
PBGPBGPBGPBG
ShaperFilterStrecherCompressor
H.C. Wu et al., Phys. Plasmas 12, 113103 (2005); Appl. Phys. Lett. 87, 201502 (2005).
B. Ferguson and X.-C. Zhang, Nature Materials 1, 26 (2002)
Terahertz wave
Applications:
Material characterization by THz spectroscopy; Tomographic imaging; Biomaterial applications.
THz Wave Emitters
• Photoconductive dipole antenna• Optical rectification in Electro-optic crystals with femtosecond
laser• Upconversion of radio frequency sources or downconversion o
f optical (Gunn, Bloch oscillator, gas lasers, optical parametric generators and oscillators)
• Semiconductor THz laser
“The lack of a high-power, low-cost, portable room-temperature THz source is the most significant limitation of modern THz system.”
--- B. Ferguson and X.-C. Zhang, Nature Materials 1, 26 (2002).
An electron plasma wave is potentially a high-power THz source
• Plasma waves that can be driven by ultrashort laser pulses oscillate typically at the THz range (e.g., ne=1018cm-3, p/2=9THz).
• The field strength before wave-breaking is as high as 100 GV/m for ne=1018cm-3.
• How can an electrostatic wave be converted to an electromagnetic wave?
THz radiations from a vacuum-plasma interface by introducing an inhomogeneous plasma region
22 4/
/2
emn
Lp
L
~2/L
3161011.1,12 cmnTHz e
pe
ZM Sheng, HC WU, K Li, J Zhang, Phys. Rev. E 69, 025401(R) (2004). ZM Sheng, K Mima, J Zhang, H Sanuki, PRL 94, 095003 (2005).ZM Sheng, K. Mima, and J. Zhang, to appear in Phys. Plasmas.
Model calculation: schematic view
Plasma oscillations in inhomogeneous plasmas
00
000
000
/
/),(
),/)((),(
)],,(cos[),(
x
t
ktxv
vxtxtx
txtx
ph
gp
Wave vector of a plasma wave in inhomogeneous plasmas
3/0
2
3),(
,)/(),/(
0
0
00
2/10000
tvxfork
x
tvxtxk
LxLxnn
g
pg
pp
g
pg
pp
vxtSincek
xL
xtvxLtxk
LxLxnn
/0
)(2
)()(2),(
,)/1(),/1(
0
0
000
2/10000
Dispersion of electromagnetic waves and electron plasma waves
2222peck
kDe
pe
1
Slope c
Langmuir waves Slope 31/2vte
2222 3 peevk
They meet each other only at k=0They meet each other only at k=0
EM waveEM wave
ES waveES wave
Evolution of plasma waves in inhomogeneous plasmas from simulations
x=ct/3
Mode conversion theory
644.2,sin)/(
),3
4exp(
2
2
3/2
2/3
cLq
q
Conversion efficiency from electromagnetic waves into electrostatic waves is the same as its inverse problem
nccos2 nc
EM
ES
nccos2 nc
ES
EM
)~()]~([),,,~( 2 mL EqdLS
Emission spectrum from wakefield is calculated by
1D simulation at oblique incidence
=15, L=60, dL=10, a0=0.5
Comparison with model
Energy conversion efficiency scaling
C mainly depends upon the incident angle and the pulse profile.
dLL
n0
3
00
20
20
00
5
0 ~~
L
aan
n
L
dC c
Lenergy
Controlling of the bandwidth
0.00 0.05 0.10 0.15 0.200.0
4.0x10-8
8.0x10-8
1.2x10-7
1.6x10-7
|E(
)|2
/0
300 400 500 600 700 800-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
Ey-
Bz
t/
n1
n2
12
2
12
4nn
m
epp
Effect of laser beam diameters
8
)tan~(exp
cos
~
2)~,(
,)()(~
,/tan
).8/exp()2/()(~
,
:),(
)/2exp()(),()(
20
2
0
2
222/12
22221
20
2
WkWkS
dSdkkfkkLet
WkWkfkk
kkvectorWave
Wyyfyfctxfaa
ppW
wyyxy
yypx
yx
L
Laser Beam Fourier transform of beam profile
Wakefield of an ultrashort laser pulse: the longitudinal electric field
n
(a=0.5, T=20, n/L=0.01nc/60)
Laser
The local phase velocity is changing with time!
Transverse magnetic field
ZM Sheng, HC WU, K Li, J Zhang, Phys. Rev. E 69, 025401(R) (2004). (a=0.5, T=20, n/L=0.01nc/60)
Radiation pulse and spectra
a0=0.5, L=600, T=200, w0=200
Two-dimensional simulation of oblique incidence
W=10t
W=20t
E. Miura, K. Koyama et al., APL 86, 251501 (2005).
@2TW, 50fs, 5m, 1020cm-3
J. Faure et al., Nature 431, 541 (2004).S. P. D.
Mangles et al., Nature 431, 535 (2004).
C. G. R. Geddes et al., Nature 431, 538 (2004).
Experimental observation of quasi-monoenergetic electron beams from laser wakefield acceleration
Emission from a plasma channel (produced for GeV energy gain)
100
50 50
0.045
0.005
Laser
J. Zheng 2005J. Zheng 2005
Summary
1. Plasma Bragg gratings can be a novel tool for light control and fast compression in the high intensity regime, because of their ultrahigh damage threshold >1000J/cm2.
2. The radiations result from the excited large-amplitude plasma waves at the plasma boundary and through mode conversion from electrostatic to electromagnetic waves, where the plasma inhomogeneity plays a crucial role. The emission can both serve as a high intensity THz source and an easy diagnostic tool for the wakefield amplitude.