Generation and Application of Carrier Envelope Phase Controlled Single-Cycle Optical Pulse Train

Wei-Jan Chen 陳蔚然

Department of Physics, National Tsing Hua University

Sep. 22, 2009

Generation of sub-single-cycle pulses in the optical region

• Introduction• Review of basic concepts• Modeling molecular modulation• Present status of experiments• How to determine pulse duration• Advance concepts

Prefix for small and large numbers:

micro 10-6 mega 106

nano 10-9 giga 109

pico 10-12 tera 1012

femto 10-15 peta 1015

atto 10-18 exa 1018

zepto 10-21 zetta 1021

yotta 10-24 yocto 1024

shortest time -- about 100 as

most intense light -- 1023 W/cm2Man made today:

Courtesy C. D. Lin, Kansa State U

Attoworld

www.attoworld.de/attoworld.html

Attosecond: 10-18 second

C x 10-18 sec = 0.3 nm

Time scales

300 nm optical cycle

Short pulses can be used to monitor and controlmolecular and electronic motion

Characteristic length and time scales for structure and dynamics in the microcosm

F. Krausz & M. Ivanov, Rev. Mod. Phys. 81 163 (2009)

Laser pulses got shorterover the years

Peak intensityincreased

100

Sho

rtest

opt

ical

pul

se m

easu

red,

fs

102

101

104

103

1970 1980 1990 2000 20101960 1970 1990 2010

1010

1020

1015

1025

Focu

sed

inte

nsity

, W/c

m2

Mode-locked Dye andTi:Sapphire lasers;

HHG pulses . Chirped PulseAmplification

Ultrafast science High field physics

Molecular modulation

)()( 00 ωω Xettx tjFT −⎯→←−

Correlation between time and frequency

Fourier transform: ωω ω detxX ti∫∞

∞−

−= )()(

In phase Random phase

Effect of random phasePrinciple of optical interference of coherent light fields

What is a single cycle optical pulse

(a) Monochromatic light: sinusoidal wave propagation(b) Beating of two waves, ω1 and ω2

(a)

(b)

(c) Many waves propagating to form a wave packet (left)(d) Ultimate wavepacket is a single-cycle and sub-cycle pulse pulse (right)

What is a single cycle optical pulse

(c) (d)

Optical cycle

..)(~)( cctEtE += )( 0)()(~ φω += tietAtE

∫∫

∞

∞

=

0

20

2

0)(

)(

ωω

ωωωω

dE

dECarrier frequency

: Fourier transform of E(t))(ωE

T. Brabec and F. Krausz, Phys. Rev. Lett. 78, 3282 (1997)

cosine pulseφn = 0

Inverted cosineφn = π

Single cycle waveforms

2.6 fs

684 as

12,820 cm-1

50,000 cm-1

780 nm

200 nm

sine pulseφn = π/2

Carrier envelope phase)cos()()( 00 φω += ttEtE

commensurate

ω

incommensurate

ω

ω m

Constant CEP requires that the frequencies are commensurate and the relative phases form an arithmetic series

mq nωω =

ωn = nωm + ωceo

Constant carrier envelope phase

E(t) = An (t)cos(nωm (t + φm /ωm ) + φCEP )n

∑

φn = φCEP + nφm

∑ +=n

nnn ttEtE )cos()()( φω Φn = carrier envelope phase

φn = ωceot + φn'

Ingredients of an attosecond single-cycle optical pulse:

1. Broad spectrum – 2 or more octaves2. In phase condition3. Constant carrier envelope phase:

• Commensurate frequencies• Constant phase difference between adjacent

spectral components4. Stable and controllable carrier envelope phase

Methods of generating attosecond pulses

A

Advantages: single pulse100 attosecond

Disadvantages: 30-100 eV photonsvery low powerconstitutes a few cyclesKrauze et.al., Nature 421, 611 (2003)

R. Lopez-Martens et. al., PRL 94, 033001 (2005)

High-order harmonic generation of phase-stabilized femtosecond pulse

B

Methods of generating attosecond pulses

High-order stimulated Raman scattering using molecular modulation

q= -2

δω

-1 0 1

43

2 Etc.

i

ba

Advantages: IR-UV regiongood powersingle-cycle

Disadvantages: complex setup8-50 fs pulse spacinglimited to ~ 300-500 as

M.Y. Shverdin et.al., PRL 94, 033904 (2005)

Three-step model

P. Corkum, Phys. Rev. Lett. 71, 1994 (1993)

Isolated Attosecond-pulse production

M. Hentschel et al, Nature 414, 509 (2001)

PHYSICS TODAY October 2004Search and Discovery

Attosecond Bursts Trace the Electric Field of Optical Laser PulsesThe familiar textbook sketch of light's oscillating electric field can now

be drawn directly from measurements.

A. Baltuska et al., Nature 421, 611 (2003)E. Goulielmakis et al., Science 305, 1267 (2004)

http://www.physicstoday.org/

Nature 449, 1029 (2007)

Common theme

Photon energies 30 eV to 100 eV (EUV to soft x-ray region)

Traditional pump-probe measurements

Photoelectron or photoion detection

Weak pulses - long signal acquisition time

inter-nucleardistance

time

ω m

n = n0 + δ cosωmtRefractive Index

Molecular modulation is analogous to electro-optic modulation

Molecular Modulation

infraredinput

multi-color

output

molecular

modulator

ωq=ω0+qωm q= -2,-1,0,1,2,3….Alexei SokolovSteve Harris

Two strong laser fields adiabatically drive the molecules into a maximally coherent state.

ab

i

Δ ω

δ ω

Ω 0Ω − 1

Coherent Molecular Excitation

( )

( )

( ) ( )aabbababbbaaab

bbbabbabaabbb

bbabbabaabaa

iii

i

i

ρρργδτ

ρ

ργρρτ

ρ

ργρρτ

ρ

−Ω+++Ω−Ω=∂

∂

−Ω−Ω−=∂

∂

+Ω−Ω=∂

∂

⊥

||

∑

∑

∑

+=Ω=Ω

=Ω

=Ω

qqqqbaab

qqqbb

qqqaa

EEd

Eb

Ea

*1

*

2

2

21

2121

Maximal coherence, ρab = 0.5

Coherent Molecular Excitation

⎥⎦

⎤⎢⎣

⎡−ΩΩ

ΩΩ−=

δbbbaabaa

effH h

∑

∑

∑

+=Ω=Ω

=Ω

=Ω

qqqqbaab

qqqbb

qqqaa

EEd

Eb

Ea

*1

*

2

2

21

2121

∑

∑

∑

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−+

−−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−+

−−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−+

−−=

j qaj

jbaj

qbj

jbajq

j qbj

jb

qbj

jbq

j qaj

ja

qaj

jaq

d

b

a

ωωωμμ

ωωωμμ

ωωωμ

ωωωμ

ωωωμ

ωωωμ

2

22

2

22

2

21

21

21

h

h

h

ϕiabab eΩ=Ω

Solution to the Hamiltonion:

( ) ( ) ( ) 22 422 abbbaabbaaeff

E Ω++Ω−Ω±−Ω+Ω=−= ± δδλ hhh

( ) ( ) bea iϕθθ −±± +=± sincos

( )

( ) 22 42

tanabbbaabbaa

ab

Ω++Ω−Ω±+Ω−Ω

Ω=±

δδθ

ρab±( ) =

12

eiϕ sin2θ ±( ) = ± ΩabΩaa − Ωbb + δ( )

2 + 4 Ωab2

Ωab >> Ωaa − Ωbb + δ5.0=abρ

Eigenfunctions

Eigenvalues:

Coherence:

Coherent Molecular Excitation

Adiabatically prepared molecules modulate the driving fields producing a wide comb

∂Eq∂z

= − jηhω q N aqρ aa Eq + dq ρbb Eq + bq*ρ ab Eq−1 + cq

* ρab* Eq+1( )

dispersion coupling

E1E0E−1E−2

P=0.1 atm

E0E−1 H2

At maximum coherence, ρab = 0.5 the dispersion and coupling terms become comparable. Phase-matching is then not important, and generation is collinear.

Sideband Generation and Propagation

Propagation equation for the qth sideband: ωq = ωq-1 + ω0 – ω-1

|b>|a>

|i>

E0 E1 E2 E3E−2 E−1

Courtesy M. Shverdin

Stimulated Raman Scattering

Traditional SRS:

Generation occurs at high gas pressureMolecular excitation occurs on-resonanceAnti-Stokes generation occurs off-axisFew Stokes and anti-Stokes orders are observed.

Courtesy M. Shverdin

Why low temperature1. Put all molecules into one ro-vibrational state

make all molecules contribute to the process

μλλνν )(

)(110285.1212

0

11

0

0 KTnmm

kTmkT

cD×===Δ

T = 300K ΔνD, D2 = 778 MHzT = 77K ΔνD, D2 = 389 MHz

T = 300K ΔνD, H2 = 1100 MHz ∑

∑

∑

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−+

−−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−+

−−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−+

−−=

j qaj

jbaj

qbj

jbajq

j qbj

jb

qbj

jbq

j qaj

ja

qaj

jaq

d

b

a

ωωωμμ

ωωωμμ

ωωωμ

ωωωμ

ωωωμ

ωωωμ

2

22

2

22

2

21

21

21

h

h

h

2. Reduce Doppler width to increase the coherencemolecules with equal detuning but opposite in sign will off-set their contribution to the coherence build up

( )1*110

+−− +++=∂

∂qabqqbaqqbbqqaaq

qq EdEdEbEac

iNEρρρρ

εω

ξh

All Three Spectra

VisibleIR UV1.56 μm 195 nm

10 μJ1 mJ10 mJ 100 μJ

H2 Rotation Spectra: 29 sidebands, spaced by 587 cm-1

D2 Vibration Spectra: 16 sidebands, spaced by 2994 cm-1

395 nm

195 nm

1 μ m

1.06 μm

Multiplicative Spectra: ~ 200 sidebands, spaced by < 587 cm-1

Phys. Rev. A (R)(1997)Phys. Rev. Lett. 81 (1998)Opt. Lett. 24 (1999)Phys. Rev. Lett. 84 (2000)Phys. Rev. Lett. 85 (2000)Phys. Rev. A 63 (2001)Phys. Rev. Lett. 91 (2003)Phys. Rev. Lett. 93 (2005)

Motivation• form subfemtosecond pulses• produce THz pulse train • generate tunable high power vacuum uv pulses• arbitrary waveform synthesis

Use gas phase hydrogen at room temperature

Cons:large Doppler widthrequires two tunable high-

power high- resolution lasers spaced 4155 cm-1 apart

smaller pulse train pulse-to-pulse spacing

Pros:large Raman transition of 4155

cm-1 for Q(1)2/3 population in single

quantum state (v=0, j=1) at room temperature

many parameters are knownnondestructibleroom temperature is easy to

operate

δ

0ω1−ω

a

b

j⎥⎦

⎤⎢⎣

⎡−ΩΩ

ΩΩ−=

δbbbaabaa

effH h∑

∑

∑

+=Ω=Ω

=Ω

=Ω

qqqqbaab

qqqbb

qqqaa

EEd

Eb

Ea

*1

*

2

2

21

2121

∑

∑

∑

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−+

−−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−+

−−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−+

−−=

j qaj

jbaj

qbj

jbajq

j qbj

jb

qbj

jbq

j qaj

ja

qaj

jaq

d

b

a

ωωωμμ

ωωωμμ

ωωωμ

ωωωμ

ωωωμ

ωωωμ

2

22

2

22

2

21

21

21

h

h

h

( )

( )

( ) ( )aabbababbbaaab

bbbabbabaabbb

bbabbabaabaa

iii

i

i

ρρργδτ

ρ

ργρρτ

ρ

ργρρτ

ρ

−Ω+++Ω−Ω=∂

∂

−Ω−Ω−=∂

∂

+Ω−Ω=∂

∂

⊥

||

Simulation

Thanks to Prof. Fam Le Kien for the full set of matrix element data

∂Eq∂z

= − jηhωq N(aqρaa Eq + dqρbb Eq ) + 0.666N(bq*ρab Eq−1 + bq +1ρab

* Eq +1)[ ]

Experimental Arrangement

δωlaser ~ 100 MHzΔtlaser ~5 nsλ0=589 nmλ-1=780 nm

H2 pressure ~1 atm.H2 Doppler width 250-750 MHz

Intensity ~ 12 GW/cm2Ωab,z=0~2 GHzρab ~0.4tdelay~0-1 ns

H2

MgF2

Telescope

Beam combiner

589 nm

780 nm

q=-2 to 8

q=8 and higher

Raman sidebands generated

15th order at 126 nm observed 124 126 128 130 132 134 136

0.0

0.1

0.2

0.3

0.4

0.5

0.6

arb.

uni

ts

nm

15

14

q= -2

δω

-1 0 1

43

2 Etc.

i

ba

q = 3, λ = 339.6 nm6 238.6 nm9 183.9 nm

12 149.6 nm14 133.0 nm

Total spectral span >70,000 cm-1(~500 as)

-4 -2 0 2 4

0.00

0.02

0.04

0.06

0.08

0.10

puls

e en

ergy

(mJ)

detuning (GHz)

3 4 5 6 7 8 9

-4 -2 0 2 4

0

10

20

30

40

50

puls

e en

ergy

(mJ)

detuning (GHz)

total -2 -1 0 1 2

Note:

589 nm ↔ 16978 cm-1 ( 4 x 4155.2 = 16621 cm -1)

780 nm ↔ 12822.8 cm-1 (3 x 4155.2 cm-1 = 12465.6 cm-1)

The sidebands are not commensurate.

New input wavelengths:

ω0 = 16621 cm-1 (602 nm)ω-1 = 12465.6 cm-1 (802 nm)

These wavelengths produce a commensurate set of sidebands, as shown on the right:

Raman Order

nm cm-1 4 wave-mixing order

∞ 0

-3 2407 4155

-2 1203 8310 1

-1 802 12465 2

0 602 16620 3

1 481 20775 4

2 401 24930 5

3 344 29085 6

4 301 33240 7

5 267 37395 8

6 241 41550 9

7 219 45705 10

8 201 49860 11

9 185 54015

mq nωω =

Phase adjustment Setup

Dye Laser

Ti:Sapphier Laser

Xe

602nm

802nm

PMT

Phase Modulator

n

a

b

0E1−E

2−E3−E

2E3E

+ + +

Four Wave Mixing

Raman Sidebands Generation

f=50cm f=20cm

(filter)

(achromatic lens f=25cm for IR to UV)

(achromatic lens f=8cm for IR to UV)

E1

M. Y. Shverdin et al. PRL 94, 033904 (2005)

LC phase modulator

λcutoff430 nm --> 380 nm

6 sidebands 7 sidebands

UV sidebands are generated at efficiencies 10-8 to 10-12 by a four-wavemixing process in a xenon cell at ~100 torr. Phasematching allows onlythe two photons up one photon down type of conversion. A total of n-1 different UV sidebands, beginning at the next short wavelength sideband, are generated.

Xe

generated UV

Raman

Raman sidebands

f=15cm

PMT

filter

Four-wave Mixing

3ω

5ω

4ω

8ω

7ω

6ω6ω

5ω

8ω

7ω 5ω

8ω

8475 ωωωω =−+

8356 ωωωω =−+

8576 ωωωω =−+

Four wave mixing:

q= -2

δω

-1 0 1

43

2 Etc.

i

ba

Multiple quantum paths interference

Four Wave Mixing in Xe

+ + +

*kji EEEE χα =

⇒

144135245355

−+−+−+−+:7

⇒⎩⎨⎧

=−=−=−=−=−

ts

32

1425

132435

φφφφφφφφφφ

s415 += φφ)− t325 += φφ

st 4321 −=− φφts

32

14

24

+=+=

φφφφ

)−

ts 3221 −=− φφ

⇒st

tsst=

−=− 3243

⇒

⎪⎪⎩

⎪⎪⎨

⎧

+=+=+=+=

4Δφφ

3Δφφ

2Δφφ

Δφφ

15

14

13

12

kji φφφφα −+=

In phase condition

7=6+6-5, 6+5-4, 6+4-3, 6+3-2, 6+2-1.

5+5-3, 5+4-2, 5+3-1.

4+4-1

6, 5, 4 : 6+6-5, 6+5-4 Φ65=Φ54+3 : 6+4-3, 5+5-3 Φ65=Φ54=Φ43+2 : 6+3-2, 5+4-2 Φ65=Φ54=Φ43=Φ32+1 : 6+2-1, 5+3-1, 4+4-1 Φ65=Φ54=Φ43=Φ32=Φ21

1: 1203nm

2: 802nm

3: 602nm

4: 481nm

5: 401nm

6: 344nm

7: 301nm

Searching in phase condition

-2 -1 0 1 20.00

0.01

0.02

0.03

(a) 481 nm

-2 -1 0 1 20.00

0.04

0.08

(b) 602 nm

-1 0 10.0

0.1

0.2

301

nm s

igna

l int

ensi

ty(a

. u.)

Relative phase shift (π radian)

(c) 802 nm

-1 0 10.0

0.1

0.2

0.3

(d) 1203 nm

How to measure the pulse width?

Solution: Correlation using pulses formed by the sidebands themselves.

Synthesize two pulses from the subsets of sidebands and electronically delay one pulse with respect to the other. Measure the resulting four-wave signal with a photomultiplier.

Autocorrelation is standard way to measure ultrafast pulsewidth.However it could not be done here because of the wide bandwidth.

pulse 2

pulse 1

simulation

0 . 0 2 . 5 5 . 0 7 . 5 1 0 . 0 1 2 . 5 1 5 . 0 1 7 . 5 2 0 . 0

e r r o r b a r = 1 5 %

Cross Correlation of Single Cycle Pulse Train

(1,2,3)

(4,5,6)

Sideband Orders

Simulation

Experiment

- 1 6 - 8 0 8 1 60 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

Pow

er (a

rb. u

nits

)

- 1 6 - 8 0 8 1 60 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

Pow

er (a

rb. u

nits

)

T i m e d e l a y ( f e m t o s e c o n d )

Cross correlation signal of incommensurate pulses

CEO frequency ~ 349 cm-1Waveform repeats every 96 fs

Pulse train

-16 -8 0 8 16-1

0

1 (b)

E fi

eld

ampl

itude

(a. u

.)

Time (fs)

-16 -8 0 8 16-1

0

1

(a)

Commensurate

Incommensurate

Carrier envelope phase is constant to ~2.5 part in 106

Total phase slip of

Status of sub-cycle optical pulse generation by molecular modulation

0.833 cycle per pulse1.4 fs envelope440 as cycle widthconstant carrier envelope phase 2 ns pulse train duration8.0 fs pulse spacing~1 MW peak power

IAMS sub-cycle source

Total spectral span >70,000 cm-1

Phys. Rev. Lett. 100, 163906 (2008)

Ingredients of an attosecond single-cycle optical pulse:

1. Broad spectrum – 2 or more octaves2. In phase condition3. Constant carrier envelope phase:

• Commensurate frequencies• Constant phase difference between adjacent

spectral components4.Stable and controllable carrier envelope phase

CEP control

Phys. Rev. Lett. 102, 213902 (2009)

Summary and Outlook

• Generated commensurate pulse train • Single pulse duration 1.4fs• Sub-single-cycle pulse: 0.8 cycles• CEP (carrier-envelope phase) control

• Sub-femtosecond pulse generation• Arbitrary waveform• Application for ultra-fast dynamics

Harmonics1203

802

602

481

401

344

301

~25,000cm-1

1064

532

355

266

213

~37,600cm-1

0.833 cycle per pulse1.4 fs envelope440 as cycle widthconstant carrier

envelope phase 2 ns pulse train

duration8.0 fs pulse spacing~1 MW peak power

-4 -2 0 2 4-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

Ele

ctric

Fie

ld A

mpl

itude

(arb

. uni

ts)

Time (fs)

ElectricField

WaveEnvelope

CEP = 0

-4 -2 0 2 4-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.0

CEP = π/2

Ele

ctric

Fie

ld A

mpl

itude

(arb

. uni

ts)

Time (fs)

Attosecond pulse train

Raman Order

nm cm-1

1 2407 4155

2 1203 8310

3 802 12465

4 602 16620

5 481 20775

6 401 24930

7 344 29085

8 301 33240

9 267 37395

10 241 41550

11 219 45705

12 201 49860

13 185 54015

Nd:YAGHarmonics

nm cm-1

1 1064 9398

2 532 18796

3 355 28194

4 266 37592

5 213 46990

We can control the CEP and shape the pulse waveform.We can synthesize a waveform which like the XUV-IR combination.

Advance Concepts

• Generate subfemtosecondpulses: add more sidebands and improve sideband power

• Increase pulse-to-pulse spacing

• Develop control of carrier envelope phase

• Modulate in photonic crystal fiber

• Arbitrary waveform synthesis

• Optical-deep uv attosecond pump-probe• Tracing molecular vibrational wavepacket• Low energy electron dynamics in atoms• Electron dynamics in semiconductors: direct bandgap vs indirect bandgap

Technology Science

GroupIAMS Andy Kung(孔慶昌) Wei-Jan Chen(陳蔚然)

Zhi-Ming Hsieh(謝智明) Shu Wei Huang(黃書偉)Hao-Yu Su(蘇皓瑜) Chien-Jen Lai(賴建任) Sih-Ying Wu(吳思螢)

National Chiao Tung University: Ci-Ling Pan(潘犀靈) Ru-Pin Pan(趙如蘋) Tsung-Ta Tang(湯宗達)Han-Sung Chan(詹翰松)

National Sun-Yat-Sen UniversityChao-Kuei Lee(李晁逵)

National Tsing Hua University

Acknowledgement

Stanford: Steve Harris and his students

TAMU: Alexei Sokolov

Berkeley: Ron Shen

Research supported by Academia Sinica and the NSC

Thanks for your attention

Generation and Application of Carrier Envelope Phase Controlled Single-Cycle Optical Pulse TrainGeneration of sub-single-cycle pulses in the optical region投影片編號 3Attoworld投影片編號 5Time scalesCharacteristic length and time scales for structure and dynamics in the microcosmLaser pulses got shorter�over the years投影片編號 9投影片編號 10Effect of random phase�Principle of optical interference of coherent light fields�投影片編號 12投影片編號 13Optical cycle投影片編號 15Carrier envelope phase投影片編號 17投影片編號 18投影片編號 19投影片編號 20Three-step modelIsolated Attosecond-pulse production投影片編號 23投影片編號 24投影片編號 25Molecular ModulationCoherent Molecular ExcitationCoherent Molecular Excitation投影片編號 29Sideband Generation and PropagationStimulated Raman Scattering投影片編號 32All Three SpectraMotivation投影片編號 35投影片編號 36投影片編號 37投影片編號 38Phase adjustment Setup投影片編號 40Four-wave Mixing投影片編號 42Four Wave Mixing in XeIn phase conditionSearching in phase conditionHow to measure the pulse width?投影片編號 47投影片編號 48Pulse train投影片編號 50投影片編號 51投影片編號 52投影片編號 53投影片編號 54投影片編號 55Summary and OutlookHarmonicsAttosecond pulse trainAdvance Concepts投影片編號 60Thanks for your attention