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

qq

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.