Kevin Holman

Laser synchronization and timing distribution through a fiber network using femtosecond mode-

locked lasers

Kevin Holman

JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado, USA

Co-workersDavid Jones (UBC)

Jun Ye (JILA)Steve Cundiff (JILA)Jason Jones (JILA)

Leo Holberg et al (NIST) Erich Ippen (MIT)

FundingNIST, NSERC,

ONR-MURI

Desired in next generation light sources

• Synchronize X-rays with beamline endstation lasers for pump-probe experiments

• Synchronize accelerator RF with electron bunches

• Relative timing jitter of a few fs over ~1 km

Why Synchronization?

Master clocklaser + RF

Beamline endstation lasers

Linac RF

FEL seed lasers

Synchronization of multiple fs lasers

•Underlying technology–Pulse synchronization–Phase coherence

•Applications–Coherent anti-Stokes Raman spectroscopy (CARS)–Remote optical frequency measurements/comparisons/distribution

...but first how to measure performance of frequency synchronization of two oscillators?

Outline

• Allan Deviation

• Timing jitter

Allan Deviation -typically used by metrology community as a measure of (in)stability-evaluates performance over longer time scales (> 1 sec or so)-can distinguish between various noise processes-indicates stability as a function of averaging time

Allan Deviation

4

56

10-12

2

3

4

5

All

an D

evia

tio

n

2 3 4 5 6 7 8 910

2 3 4 5

Averaging Time (s)

-20

-15

-10

-5

0

5

10

15

Fre

qu

ency

Dev

iati

on

s (H

z)

150100500 Time (sec)

Device Under Test

Master Oscillator Frequency Counter

Phase Lock Loop

Timing jitter-typically used by ultrafast community-can be measured in time domain (direct cross correlation) or frequency domain (via phase noise spectral density of error signal)-must specify frequency range

fs laser #2

Sum frequency generation

Relative timing jitter leads to amplitude jitter in SFG signal

Spectrum analyzer

fs laser #1

Single side band phase noise spectral densityTiming jitter spectral density

Timing Jitter

Radio frequency lock•Detect high harmonic of lasers’ repetition rates•Implement phase lock loop•Able to lock at arbitrary (and dynamically configurable) time delays

Optical frequency lock•Use very high harmonic (~106) for increased sensitivity•Can be more technically complex than RF lock•Can lock to high finesse cavity or CW reference laser•Similar advantages for arbitrary time delay

Optical cross correlation•Nonlinear correlation of pulse train•Use fs pulse’s (steep) rising edge for increased sensitivity•Small dynamic range…must be used with RF lock•Time delays are “fixed”

Methods for Synchronization

fs Laser 1

fs Laser 2

Laser 1repetitionrate control

100 MHz

50 ps

SHG

SHGBBO

SFG

SFGintensityanalysis

Phase shifter

14 GHz14 GHz

Phase shifter

14 GHz Loop gain

100 MHz Loop gain

Sampling scope

Delay

Experimental Setup for RF Locking

Timing jitter 0.58 fs (160 Hz BW)

Timing jitter 1.75 fs (2 MHz BW)

Top of cross-correlation curve

Total time (1 s)Cro

ss-C

orre

latio

n A

mpl

itude

30 fs

0

1(two pulses maximally overlapped)

(two pulses offset by ~ 1/2 pulse width)

Ma et al., Phys. Rev. A 64, 021802(R) (2001).Sheldon et al. Opt. Lett 27 312 (2002) .

No

ise

spec

tru

m (

fs2/H

z)

Fourier Frequency (kHz)

10-6

10-4

10-2

100

100806040200

Mixer noise floor

Locking error signal

Timing Jitter via Sum Frequency Generation

Bartels et al., Opt. Lett. 28 663 (2003).

Optical Cavity

Synchronization via Optical Cavity Lock

Output(650-1450nm)

Ti:sa

Cr:fo

3mm Fused Silica

SFG

SFG

Rep.-RateControl

(1/496nm = 1/833nm+1/1225nm).

Δt

0VSchibli et al Opt. Lett, 28, 947 (2003)

Synchronization via Optical Cross Correlation

Output(650-1450nm)

Ti:sa

Cr:fo

3mm Fused Silica

SFG

SFG

Rep.-RateControl

(1/496nm = 1/833nm+1/1225nm).

-

+

Δt

0V+GD

-GD/2

Δt

0V

Balanced Cross-Correlator

Balanced Cross-Correlator

Experimental result: Residual timing-jitter

The residual out-of-loop timing-jitter measured from 10mHz to 2.3 MHz is 0.3 fs (a tenth of an optical cycle)

1.0

0.8

0.6

0.4

0.2

0.0Cro

ss-C

orre

lati

on A

mpl

itud

e

-100 0 100

Time [fs]

100806040200Time [s]

Timing jitter 0.30 fs (2.3MHz BW)

Synchronization of two fs lasers



Outline cont…

Time domain

1/ frep =

t

E(t)

F.T. fofrep

Phase accumulated in one cavity round trip

Derivation details:Cundiff, J. Phys. D 35, R43 (2002)

D. Jones et. al. Science 288 (2000)I(f)

f

fo

n = n frep + fo

frep

Frequency domain

Time/Frequency Domain Pictures of fs Pulses

t

E(t)

For successful phase locking:

• Pulse repetition rates must be synchronized with pulse jitter << an optical cycle (at 800 nm << 2.7 fs)

• Carrier envelope phase must evolve identically (fo1=fo2)

1/ frep1 =

E(t)

fs laser

Pulse envelopes are locked

Evolution of carrier-envelope phases are locked

tfs laser

1/ frep2 =

fo2

I(f)

f

frep

fo1

Requirements for Coherent Locking of fs Lasers

fs Laser 1

fs Laser 2

Laser 1repetitionrate control

100 MHz

14 GHz14 GHz

50 ps

SHG

SHGBBO

SFG

Phase lock: fo1 -fo2 = 0

AOM

Phase shifter

Phase shifter

14 GHz Loop gain

100 MHz Loop gain

(Interferometric)Cross-CorrelationAuto-CorrelationSpectral interferometry

Sampling scope

Delay

Delay

Experimental Setup

5 MHzPhase lock activated

R.B. 100 kHz

60 d

B

fo1

– f

o2

-1.0

-0.5

0.0

0.5

1.0

8006004002000

(f o

1 –

f o2)

H

z

Time (s)

sdev = 0.15 Hz (1-s averaging time)

Locking of Offset Frequencies

900850800750700

- Laser 1 spectrum- Laser 2 spectrum- Both lasers, not phase locked- Both lasers, phase locked

Sp

ec

tra

l In

terf

ero

me

try

(L

ine

ar

Un

it)

Wavelength (nm)

(a)

R. Shelton et. al. Science 293 1286 (2001)

Spectral Interferometry

Synchronization of two fs lasers



Outline cont…

•Capable of chemical-specific imaging of biological and chemical samples

•Four-wave mixing process with independent pump/probe and Stokes lasers (2p-s=as)

•First demonstrated as imaging technique by Duncan et al (1982)*

Molecular vibration levels

Prepare coherent (resonant) molecular state

Convert molecular coherent vibrations to anti-Stokes photon

p assp

n=1

n=0

*M.D. Duncan, J. Reinjes, and T.J. Manuccia, Opt. Lett. 7 350 (1982).

Coherent Anti-Stokes Raman Scattering Microscopy

Dichroic mirror

as

p,s

3-D scanner

Sample

APD

Stokes Laser

Pump/Probe Laser

as

NA=1.4Objective

Filter

APD Forward Detection

Epi (Reverse) Detection

CARS Microscope

Stokes Laser (Master)

Pump/Probe Laser (Slave)

Feedback Loop

To CARSmicroscope

FFT Spectrum Analyzer

0.01

0.1

1

10

Am

pli

tud

e (

fs/H

z1/2

)

7 8 9

102

2 3 4 5 6 7 8 9

103

2 3 4 5 6 7 8 9

104

Frequency (Hz)

30

25

20

15

10

5

0

Jitte

r (fs)

locked unlocked total jitter

Jitter Spectral Density

Noise floor of mixer/amplifiers

100 MHz14 GHz

Lasers are Coherent Mira ps Ti:sapphire lasers

Synchronization Performance

BBO

SFG

14 GHz

Dichroic mirror

as

p,s

3-D scanner

APD

Bragg Cell

Bragg Cell

80 MHz14 GHz

Stokes Laser (Master)

Pump/Probe Laser (Slave)

PhaseShifter Phase

Shifter

14 GHz Loop gain

80 MHz Loop gain

DBM

DBM

Sum Frequency Generation (SFG)used to measure relative timing jitter

Bragg Cells usedto decimate rep. rate

Polystyrene beads in aqueous solution

Experimental Setup

1.0

0.5

0.0

-0.5

Re

lati

ve

Jit

ter

(ps

)

20151050T ime (sec)

1.2

1.0

0.8

0.6

0.4

0.2

CA

RS

In

ten

sit

y

20151050T ime (sec)

Pulse delay is adjusted to overlap at half-maximum point of cross-correlation

With 80 MHz lock, rms jitter is ~700 fs

Switching to 14GHz lock, rms jitter is 21 fs

Relative jitter via SFG

Bandwidth is 160 Hz

Relative jitter via CARS

StokesPump/Probe

SFGTiming jitter is converted to amplitude fluctuations

Relative Timing Jitter

Cou

nts

Cou

nts

100

0

100

0

80-MHz lock~770 fs timing jitter

2 m

14-GHz lock~20 fs timing jitter

Raman shift = 1600 cm-1

Pump 0.3 mW @ 250 kHzStokes 0.15 mW @ 250 kHz

Images of 1mm Diameter Polystyrene Beads

Synchronization of two fs lasers•Underlying technology

–Pulse synchronization–Phase coherence


Outline cont…

Synchronization of Remote Sources

Compare optical standards for tests of fundamental physics

Required in next generation light sources

• Synchronize X-rays with beamline endstation lasers for pump-probe experiments

• Synchronize accelerator RF with electron bunches

• Relative timing jitter of a few fs over ~1 km

Telecom network synchronization

• Low timing-jitter: dense time-division multiplexing

• Frequency reference from master clock allows dense wavelength-division multiplexing

Incr

easi

ng s

tabi

lity

Optical frequencystandard

fs Ti:sapphirecomb

Optical atomic clock

End user

Distribution of frequency standards

Optical fiber network

1.5-m transmittingcomb

End user End user

Optical standard

1/

RF standard

Holman et al. Opt. Lett. 28, 2405 (2003)Jones et al. Opt. Lett. 28, 813 (2003)

Degradation of signal during detection minimized

Noise added by fiber must be detected and minimized

JILA

NIST

Broadway

JILA

NIST

JILA

NIST

Broadway

L. HollbergC. Oates

Single Hg+ ion

J. BergquistD. Wineland

Trapped Sr

Iodine clock

BoulderRegionalAdministrativeNetwork

3.45 km fiber link between JILA and NIST

RF transfer: modulated CW source

1310 nm laser diode

RF standard

Modulator

3.5 km

Performance similar to NASA/JPL work on frequency distribution system for radio telescopes

J. Ye et al. J. Opt. Soc. Am. B 20, 1459 (2003)

Counter

10-15

10-14

10-13

10-12

All

an D

evia

tio

n

10-1

100

101

102

103

104

Averaging Time (s)

7 km transmission, no stabilization Noise floor

RF transfer: mode-locked laser

Pulses vs. simple sine-wave modulation?

• Easier to transfer optical stability transmitting laser (all optical)




• More sensitive derivation of error signal (optical pulse cross-correlation)





• Time gated transmission (immune to some noise, e.g. spurious reflections)






• Simultaneously transmit optical and microwave

1/Optical standard RF standard






• Simultaneously transmit optical and microwave

Mode locked fiber laser

3.5 km

Frequency / time domain analysis

8th harmonic

8th harmonicLocal

Frequency reference

End user

Pulses minimize instability of photodetection:• Average power ; SNR

Transfer with mode-locked pulses

Holman et al. Opt. Lett. 29, 1554 (2004)

10-16

10-15

10-14

10-13

All

an D

evia

tio

n

1 10 100 1000

Averaging Time (s)

Modulated CW over 7 kmMode-locked pulses, noise floor

• Dispersion broadens pulse (~ 1 ns) more power to maintain SNR

but …

Noise floor ( )85 dB30 W

12.0 ( )80 dB660 W

Spectral Width (nm)

SNRPower

ML pulses =12.0 nm

• Recompress pulse

so …• Reduce bandwidth Noise floor ( )85 dB30 W

5.5 ()80 dB160 W

12.0 ( )80 dB660 W

Spectral Width (nm)

SNRPower

ML pulses =5.5 nm

Use dispersion shifted fiber in link

Photodiode Power

SNR Instability (1s)

40 W 85 dB 6e-14 ( )

40 W 85 dB 6e-15 ( )

Conditions at Receiver10

-15

10-14

10-13

All

an D

evia

tio

n

1 10 100 1000

Averaging Time (s)

Modulated CW over 7 km Mode-locked pulses, noise floor =5 nm, 4 km of DSF

Active stabilization of fiber length

• Active stabilization: free-space delay arm in-line with DSF• Not limited by receiver noise• Reduce Allan deviation to noise floor

81

2

4

6

810

2

4

6

8100

2

Integ

rated Jitter (fs)

101

102

103

104

105

106

107

Fourier Frequency (Hz)

2

4

6

80.1

2

4

6

81

2

4

6

Jitt

er S

pec

tral

Den

sity

(fs

/ H

z1/2

)

4 km of DSF, unstabilized 4 km of DSF, active stabilization Noise floor

Integrated jitter

Techniques and technology of:•Synchronization of ultrafast lasers •Delivering frequency standards over fiber networks

Can be applied to synchronization efforts at next generation light sources Shorter time scales with < 10 fs jitter at multiple locations will require:

•Optical delivery of clock signal•Active stabilization of optical fiber network •Some combination of RF and all-optical error signal generation (depends on frequency range of interest)

Main message:No showstoppers on synchronization

(financial or technical)

Summary / Future Work…

Compensate dispersion of installed fiber

3.5 km

81st harmonic

Local

End userMode locked fiber laser

Frequency reference

3.5 km

Dispersion compensation fiber

•Dispersion compensationAvg. power ; SNR

6

80.1

2

4

6

81

2

4

6

810

2

Jitt

er S

pec

tral

Den

sity

(fs

/ H

z1/2

)

100

101

102

103

104

105

106

107


1

10

100

1000

Integ

rated Jitter (fs)

7 km of installed fiber, unstabilized 7 km of installed fiber, active stabilization Noise floor

Integrated jitter

•Eliminate low frequency noise on installed fiber network

0 5 10 15 20 25 30 350

20

40

60

80

100

Cou

nts

Distance [µm]

5 µm

• Human Epithelial cell

• Image size is 50 by 50 microns

•Total acquisition time: 8 seconds

• Raman shift = 2845 cm-1

Pump 0.6 mW @ 250 kHzStokes 0.2 mW @ 250 kHz

Image taken by Dr. Eric Potma and Prof. Sunney Xie at Harvard University with synchronization system commercialized by Coherent Laser Inc.

Slice

Cell Image

Distribution over Fiber Networks

Optical Fiber Network

Degradation of signal during detection minimized

End User

End User

Noise added by fiber must be detected and minimized

Master Clock

Phase Coherent Transmission of Optical Standard

Nd:YAG

3.45 km fiber

AOM 1

Detection of Roundtrip Signal

correctedstandard at NIST

JILA I2 Atomic Clock

AOM 2

-1 order

+1 order

• Adjustment of AOM 1, shifts center frequency of Nd:YAG to compensate fiber perturbations

• AOM 2 differentiates local and roundtrip signals

Transmission of Iodine Standard

Fiber phase noise uncompensated

Fiber phase noise compensated

FWHM:0.05 Hz

1 kHz

20 dB

-80

-70

-60

-50

-40

-30

-20

Bea

t Am

plitu

de (

dBV

)

100806040200Fourier Frequency (kHz)

10-16

10-15

10-14

10-13

Alla

n D

evia

tion

0.1 1 10 100Averaging Time (s)

Uncompensated Phase compensated

-30

-20

-10

0

10

20

30

Be

at F

requ

ency

(H

z)

8006004002000

Time (s)

Fiber phase noise uncompensated

sdev (1-s) 5.4 Hz

-30

-20

-10

0

10

20

30

Be

at F

requ

ency

(H

z)

8006004002000

Time (s)

Digital phase lock

sdev (1-s) 0.9 Hz

Transmission of Iodine Standard

Techniques and technology of:•Synchronization of ultrafast lasers •Delivering frequency standards over fiber networks

can be (easily) applied to synchronization efforts at next generation light sources Shorter time scales with <10 fs jitter at multiple locations will require:

•Optical delivery of clock signal•Some combination of RF and all-optical error signal generation (depends on frequency range of interest)

Summary/Future Work…

Self-Referenced Locking Technique

•need an optical octave of bandwidth!

I(f)

f0

n = n frep + fo

frep

x2 2n = 2n frep + fo

fo

fo

m

D. Jones et. al. Science 288 (2000)

Single Side Band Generator

Outline

• Why transfer highly stable frequency standards?

• Current method for transfer of RF standard

• Mode-locked laser for RF transfer

• Active stabilization of transfer network

Instability of optical amplifier (EDFA)

Mode locked fiber laser

3.5 km

8th harmonicJitter spectral analysis (FFT)

LocalFrequency reference

End user

EDFA

2

4

6

1

2

4

6

10

2

4

6

Jitt

er S

pec

tral

Den

sity

(fs

/ H

z 1

/2)

100

101

102

103

104

105

106

107


10

100

1000

Integ

rated Jitter (fs)

7 km of installed fiber, without EDFA 7 km of installed fiber, with EDFA Noise floor, without EDFA

Integrated jitter

Conclusions

• 10x improvement with mode-locked pulses for RF transfer

• Reducing temporal stretching of pulse optical power ; SNR

• Active stabilization implemented instability = measurement noise floor for frequency transfer

• EDFA jitter well within stabilization loop bandwidth

Documents

Kevin Holman