Stabilizing the Stabilizing the Carrier-Envelope Carrier-Envelope Phase of the Kansas Phase of the Kansas Light SourceLight Source Eric Moon

Zuoliang Duan11-9-2005

Outline Theoretical Description of the CE phase Why do we care about the CE phase? Can we control it? Yes! Here’s how it’s done

for the KLS and why it works. Single-Shot CE Phase Measurement Setup Results Future Plans

Why do we care about controlling the change of the carrier-envelope phase? Important for experiments utilizing few-cycle

laser pulses, e.g. High Harmonic Generation Can use a stabilized frequency comb to

perform spectroscopy. Related to this year’s Nobel prize! More applications to come!

Results from Others

• Fortier et al1, have reported phase coherence times of 326 s.

• Witte et al2, have observed coherence times of 500 s.

• Our group has observed coherence times of 85 s.

• The main goal is to achieve long term, on the order of hours, for running experiments.

[1] Fortier et al, IEEE Journal Topics Quantum Electron, Vol. 9, 1002-1010, 2003

[2] Witte et al, App. Physics B, 78, 5-12, 2004

Theory1

)(ˆ tE

)](exp[)(ˆ)( CEctitEtE

CE

c

For a single laser pulse:

Carrier-frequency

Carrier-envelope phase

Envelope-function

Mode-locked lasers emit a regular train of pulses.

[1] Fortier et al, IEEE J. Select. Topics Quantum Electron., vol. 9, pp.1002-1010,2003.

Theory1Time-Domain Description of the Mode-Locked Pulse Train

[1] Fortier et al, IEEE J. Select. Topics Quantum Electron., vol. 9, pp.1002-1010,2003.

Theory1

0L

Due to material dispersion inside the laser cavity, the CE phase changes.

The laser cavity length:

ddnLCE 02)

1()( 0

0

cn

vLnn

cL

ggCE

[1] Fortier et al, IEEE J. Select. Topics Quantum Electron., vol. 9, pp.1002-1010,2003.

Theory1

)])((exp[)(ˆ)( 0 cCEc ntintEtE

m

CEc mEiE )2()(ˆ)exp()( 0

Mode-Locked Pulse Train in the Time Domain:

Mode-Locked Pulse Train in the Frequency Domain:

0 CECE n

20CErepf

f

0fmff repm

[1] Fortier et al, IEEE J. Select. Topics Quantum Electron., vol. 9, pp.1002-1010,2003.

Frequency Comb and Laser Spectrum1

[1] Fortier et al, IEEE J. Select. Topics Quantum Electron., vol. 9, pp.1002-1010,2003.

TheoryThe regular spacing of the frequency comb allows access to the change of the carrier-envelope phase.

How?

Can use a self-referencing technique!

Theory1

The self-referencing technique requires an octave-spanning spectrum of the laser.

Beating the second harmonic and fundamental frequency combs of the laser yields a frequency proportional to the change of the carrier-envelope phase.

)2()(22 0020 fnffnffff reprepnn

20CErepf

f

[1] Fortier et al, IEEE J. Select. Topics Quantum Electron., vol. 9, pp.1002-1010,2003.

Theory

The CE phase change can be controlled by locking the offset frequency, f0, to a known frequency.

In the case of the KLS, f0 is set equal to one-quarter of the repetition rate of the oscillator.

420repCErep ff

f

2

CE

Experiment

The KLS utilizes a Kerr-Lens Mode locked Ti:Sapphire Oscillator emitting a ~77 million pulses per second.

The pulses are roughly 12 fs at the output of the laser and carry nJ energy per pulse.

The oscillator is the starting point for the self-referencing technique.

Why not use the amplifier output?

600 700 800 900 10000.0

0.2

0.4

0.6

0.8

1.0

FWHM=35.8 nm

10-10-05

KLS Amplifier Output

Nor

mal

ized

Inte

nsity

(arb

. uni

ts)

Wavelength (nm)

One reason: Spectrum too narrow!

Ti:S

Pump

M0

A1Lens

M1

M2

M3

M4M4E

M5

M6M7

M8

CPOC

M9

M10UltrashortPulseOutput

ECDC-Module

KLS Oscillator Cavity

500 600 700 800 900 1000 1100 12000.0

0.2

0.4

0.6

0.8

1.0

9-7-2005

Spectrum of Ti:Sapphire Oscillator Beam Measured at input to PCF

Norm

alize

d In

tens

ity (a

rb. u

nits)

Wavelength (nm)

From fs Laser

half wave plate 800nmλ/2

IR mirror

out-couplingobjectivef=8.55mm

in-couplingobjectivef=7.5mm

Silvermirror

dichroic beam splitter HR 532nm,HT1064nm

HR532nm mirror

HR532nm mirror

HR1064nm mirror

λ/2half wave plate

532nm

λ/2 half wave plate 1064nm

filter RG715

focusing Lensf=30mm

collimating Lensf=30mm

BBO crystal

HR532nm mirror

polarizingbeam-splitter532nm

polarizingbeam-splitter532nm

λ/2half wave plate

532nm

grating900lines/mm

focusing Lensf=30mm

offset frequencyphotodiode

APD

Stabilization Experimental Setup

PCF

Chirped mirror

Chirped mirror

500 600 700 800 900 1000 1100 12000.0

0.2

0.4

0.6

0.8

1.0

9-7-2005

PCF Output Spectrum yielding Phase Lock2nd Order Spectrometer Diffractions Included

Norm

alize

d In

tens

ity (a

rb. u

nits)

Wavelength (nm)

1064 nm

532 nm

500 600 700 800 900 1000 1100 12000.0

0.2

0.4

0.6

0.8

1.0

9-7-2005

Infrared Spectrum of PCF Output yielding Phase Lock

Norm

alize

d In

tens

ity (a

rb. u

nits)

Wavelenth (nm)

~1064 nm, Doubled in BBO Crystal

Offset Frequency while Phase Locked

Observation of Beat Note and Frequency Comb

f0=19.375MHz frep-f0

CE Phase Stability After Pulse Amplification2

A second f-2f interferometer after the KLS amplifier provides a means for quantifying the CE phase stabilization stability.

10% of the KLS amplifier output is sent to the experimental setup.

White-light is generated in a sapphire plate and a BBO crystal provides second-harmonic generation.

[2] Baltuska et al.,IEEE J. Select. Topics Quantum Electron., vol. 9, pp. 972-989, 2003.

Theory2

Interference between the white light and second harmonic pulses:

))()(cos(*)()()1(2)()()1()( 0 wwwwIwIaawaIwIawS WLSHGSHGWLSHGWL

0)()( www WLSHGPhase of the Interference Signal:

The shot-to-shot change of this phase can be monitored by the second f-2f setup.

[2] Baltuska et al.,IEEE J. Select. Topics Quantum Electron., vol. 9, pp. 972-989, 2003.

Experiment

M2

BS50:50

Ti:S

Pump

M0

A1Lens

M1

M3

M4M4E

M5

M6M7

M8

CPOC

AO modulator 

spectralbroadening

nonlinearinterferometer

lockingelectronics

HR IR mirror

HR

IR m

irror

HR IR mirror

BS 9:1stretcheramplifiercompressor

1kHz fs laser

Single-shot phase measurement

f-2f Interferometer after KLS Amplifier

half wave plate

VNA

silver mirrorf=70mm

half wave plate

sapphire d=2.3mm

BBO

f=75mm

spectrometer

1kHz fs laser

SHG

two silver mirrors

concave silver Mirrors: f=100mm

silver mirrorsFCWL: fundamental Continuum white light

FCWL

FCWL

SHG

polarizer

532nm HR mirror532nm HR mirror

VNA

∆T=0.265ps

Spectrum of the Second Harmonic generated in the BBO Crystal

Single-Shot: Not Locked

Line-Out of the Interference Pattern

1 pulse

Phase-Locked

Not Phase-Locked

Phase-Locked

Not Phase-Locked

51 pulses

Phase-Locked

Not Phase-Locked

101 pulses

Phase-Locked

Not Phase-Locked

200 pulses

1000 pulsesPhase-Locked

10000 pulsesphase-locked

103000 pulsesPhase-locked

Summary

The change of the carrier-envelope phase of the KLS has been stabilized.

A technique for observing the carrier-envelope phase change shot-to-shot has been utilized.

CE phase coherence times of up to 85 seconds have been observed.

Future

Send a slow CE phase drift signal from the second f-2f interferometer back to the locking electronics to achieve longer locking times.

Thanks!

Dr. Zenghu Chang Al Rankin KLS Members: Mahendra Shakya, Shambhu

Ghimire, Chris Nakamura, Chengquan Li, and Steve Gilbertson

Zuoliang Duan for being a great partner on this project.

Dr. Corwin and Dr. Washburn