1. Leo Holberg et al (NIST)
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-workers
David Jones (UBC)
Jun Ye (JILA)
Steve Cundiff (JILA)
Jason Jones (JILA)
Leo Holberg et al (NIST)
Erich Ippen (MIT)
Funding
NIST, NSERC, ONR-MURI
This work has been done at JILA at the University of Colorado by Kevin Holman, David Jones, “and myself” in the lab of Jun Ye. David Jones is now with the University of British Columbia in Vancouver. We would like to acknowledge our funding sponsors …

2. Beamline endstation lasers
Why Synchronization?
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
Master clock
laser + RF
Pursuit of delta functions
Go over ultrastable & ultrafast
Historically not much communication
Over past year merging has benefited both fields
I’ll talk about benefits to ultrastable
FEL seed lasers
Beamline endstation lasers
Linac RF

3. Outline 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?
In loop vs out of loop
Allan Deviation
Timing jitter

4. Allan Deviation 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
Phase Lock Loop
Device Under Test
Master Oscillator
Frequency Counter
In loop vs out of loop

5. Timing Jitter 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
Relative timing jitter leads to amplitude jitter in SFG signal
Sum frequency generation
fs laser #1
fs laser #2
In loop vs out of loop
Single side band phase noise spectral density
Timing jitter spectral density
Spectrum analyzer

6. Methods for Synchronization
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”
In loop vs out of loop

7. Experimental Setup for RF Locking
SHG
fs Laser 2
Delay
SFG
fs Laser 1
BBO
SHG
100
MHz
14 GHz
Phase
shifter
14 GHz Loop gain
SFG
intensity
analysis
Sampling
scope
50 ps
Phase
shifter
Laser 1
repetition
rate control
100 MHz Loop gain
Basic technology for all applications

8. Timing Jitter via Sum Frequency Generation1
Top of cross-correlation curve
(two pulses maximally overlapped)
Timing jitter 1.75 fs (2 MHz BW)
30 fs
Cross-Correlation Amplitude
Timing jitter 0.58 fs (160 Hz BW)
(two pulses offset by ~ 1/2 pulse width)
Total time (1 s)
Noise spectrum (fs 2
/Hz)
Fourier Frequency (kHz) 10 -6 -4 -2
100 80 60 40 20
Mixer noise floor
Locking error signal
Ma et al., Phys. Rev. A 64, (R) (2001).
Sheldon et al. Opt. Lett (2002) .
Use cross correlation as error signal

9. Synchronization via Optical Cavity Lock
Bartels et al., Opt. Lett (2003).

10. Synchronization via Optical Cross Correlation
Output
( nm) Δt
Ti:sa
Cr:fo
3mm
Fused Silica
SFG
Rep.-Rate
Control
(1/496nm = 1/833nm+1/1225nm). 0V
Schibli et al Opt. Lett, 28, 947 (2003)

11. Balanced Cross-Correlator
Output
( nm) Δt 0V Δt
Ti:sa
Cr:fo
3mm
Fused Silica
SFG
Rep.-Rate
Control
(1/496nm = 1/833nm+1/1225nm). 0V + GD
-GD/2 + -

12. Balanced Cross-Correlator

13. 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)

14. Outline cont… Synchronization of two fs lasers Underlying technology
Pulse synchronization
Phase coherence
Applications
Coherent anti-Stokes Raman spectroscopy (CARS)
Remote optical frequency measurements/comparisons/distribution
In loop vs out of loop

15. Time/Frequency Domain Pictures of fs Pulses
Time domain
2Df
1/ frep = t t
E(t) Df
Phase accumulated in one cavity round trip
F.T.
Df = 2p fo/ frep
I(f) f fo
nn = n frep + fo
frep
Frequency domain
Derivation details:
Cundiff, J. Phys. D 35, R43 (2002)
D. Jones et. al. Science 288 (2000)

16. Requirements for Coherent Locking of fs Lasers
1/ frep1 = t1
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)
fs laser t
Pulse envelopes are locked
Evolution of carrier-envelope phases are locked
E(t)
fs laser t
fo2
I(f) f
frep
fo1
1/ frep2 = t2

17. Experimental Setup Phase lock: fo1 -fo2 = 0 (Interferometric)
Cross-Correlation
Auto-Correlation
Spectral interferometry
Delay
AOM
SHG
fs Laser 2
SFG
fs Laser 1
Delay
BBO
SHG
100
MHz
Sampling
scope
14 GHz
14 GHz
50 ps
Basic technology for all applications
Phase
shifter
14 GHz Loop gain
Laser 1
repetition
rate control
100 MHz Loop gain
Phase
shifter

18. Locking of Offset Frequencies
R.B.
100 kHz
5 MHz
60 dB
fo1 – fo2
Phase lock
activated
-1.0
-0.5
0.0
0.5
1.0
800
600
400
200
sdev = 0.15 Hz (1-s averaging time)
(fo1 – fo2) Hz
Time (s)

19. Spectral Interferometry
- Laser 1 spectrum
- Laser 2 spectrum
- Both lasers, not phase locked
- Both lasers, phase locked
Spectral Interferometry
(Linear Unit)
700
750
800
850
900
Wavelength (nm)
R. Shelton et. al. Science (2001)

20. Outline cont… Synchronization of two fs lasers Underlying technology
Pulse synchronization
Phase coherence
Applications
Coherent anti-Stokes Raman spectroscopy (CARS)
Remote optical frequency measurements/comparisons/distribution
In loop vs out of loop

21. Coherent Anti-Stokes Raman Scattering Microscopy
Four-wave mixing process with independent pump/probe and Stokes lasers (2wp-ws=was)
First demonstrated as imaging technique by Duncan et al (1982)*
Prepare coherent (resonant) molecular state
Convert molecular coherent vibrations to anti-Stokes photon wp ws wp
was
n=1
Molecular vibration levels
n=0
Capable of chemical-specific imaging of biological and chemical samples
*M.D. Duncan, J. Reinjes, and T.J. Manuccia, Opt. Lett (1982).

22. CARS Microscope Forward Detection Stokes Laser Pump/Probe Laser
Dichroic
mirror
was
wp,ws
3-D
scanner
Sample
APD
Stokes Laser
Pump/Probe Laser
NA=1.4
Objective
Filter
Forward Detection
Epi (Reverse)
Detection

23. Synchronization Performance
Stokes Laser (Master)
To CARS
microscope
Pump/Probe Laser (Slave)
14 GHz
100 MHz
Feedback Loop
FFT Spectrum Analyzer
Jitter Spectral Density
Lasers are Coherent Mira ps Ti:sapphire lasers
Noise floor of mixer/amplifiers

24. Pump/Probe Laser (Slave) Polystyrene beads in aqueous solution
Experimental Setup
Sum Frequency Generation (SFG)
used to measure relative timing jitter
SFG
BBO
Bragg Cells used
to decimate rep. rate
Stokes Laser (Master)
Bragg Cell
Pump/Probe Laser (Slave)
Bragg Cell
Polystyrene beads in aqueous solution
3-D
scanner
14 GHz
14 GHz
80 MHz
80 MHz Loop gain
14 GHz Loop gain
Phase
Shifter
Phase
Shifter
DBM
wp,ws
Dichroic
mirror
DBM
was
APD

25. Relative Timing Jitter
Pulse delay is adjusted to overlap at half-maximum point of cross-correlation
Timing jitter is converted to amplitude fluctuations
Pump/Probe
SFG
Stokes
Relative jitter via SFG
Relative jitter via CARS
With 80 MHz lock, rms jitter is ~700 fs
Switching to 14GHz lock, rms jitter is 21 fs
Bandwidth is 160 Hz

26. Images of 1mm Diameter Polystyrene Beads
Raman shift = 1600 cm-1
Pump kHz
Stokes kHz
80-MHz lock
~770 fs timing jitter
14-GHz lock
~20 fs timing jitter
2 mm
Counts
Need pump and stokes power
Counts

27. Outline cont… Synchronization of two fs lasers Underlying technology
Pulse synchronization
Phase coherence
Applications
Coherent anti-Stokes Raman spectroscopy (CARS)
Remote optical frequency measurements/comparisons/distribution
It is clear we can synchronize multiple fs lasers with low jitter and is useful we know advanced light sources will use it….so how do we do it…but need to distribute

28. 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
Increasing stability
Pursuit of delta functions
Go over ultrastable & ultrafast
Historically not much communication
Over past year merging has benefited both fields
I’ll talk about benefits to ultrastable

29. Distribution of frequency standards
Optical standard
Optical frequency
standard
fs Ti:sapphire
comb
Optical atomic clock
Noise added by fiber must be detected and minimized
1/t t
RF standard
1.5-mm transmitting
comb
Given high stability reference (optical clock = Ti:s stabilized to optical frequency standard), can transfer superior stability of optical clock to remote users over a fiber network by transferring stability of optical clock to 1.5-micron transmitting comb (also mode-locked) (references describe linking mode-locked laser diode to optical clock).
Advantages of optical clock for non-frequency metrology crowd: high frequency of optical transition allows for very low fractional instability, orders of magnitude better than that provided by microwave transitions, etc …
By using mode-locked source for transmission, can transfer simultaneously
<Animation>
Optical frequency standard
Microwave standard
Requires quality phase lock of Tx laser to optical clock
Noise added by fiber must be detected and minimized
Degradation of signal during detection must be minimized
Optical fiber network
Holman et al. Opt. Lett. 28, 2405 (2003)
Jones et al. Opt. Lett. 28, 813 (2003)
End user
End user
End user
Degradation of signal during detection minimized

30. 3.45 km fiber link between JILA and NIST
Boulder
Regional
Administrative
Network
Trapped Sr
Iodine clock
L. Hollberg
C. Oates
J. Bergquist
D. Wineland
Single Hg+ ion

31. RF transfer: modulated CW source
RF standard
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
3.5 km
1310 nm laser diode
Modulator
Focus on RF-domain transmission:
‘Simple’ method: Modulate a cw source
<Animation>
Loop back to measure transfer stability. Noise floor represents replacing 7km roundrtip link w/ short section of fiber.
FYI: single-sideband generator used to count 10 kHz.
Note 1s for 7km link & noise floor.

32. RF transfer: mode-locked laser
Pulses vs. simple sine-wave modulation?
Easier to transfer optical stability transmitting laser (all optical)
Advantages of using mode-locked laser for transfer:
1.) Simpler to link optical clock to transmitting laser

33. 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)
2.) Optical pulse cross-correlation provides more sensitive derivation of error signal, in principle allowing all harmonics of rep rate to contribute to error signal (no limitation of detector bandwidth).

34. 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)
3.) Potential for time gating detection reduces impact of broandband noise.

35. 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/t
Optical standard
RF standard
4.) As mentioned earlier, mode-locked source provides simultaneous transfer of optical & rf standards

36. 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
Mode locked fiber laser
3.5 km
Frequency / time domain analysis
8th harmonic
Local
Frequency reference
End user
Setup for analysis of jitter contribution for transfer. Mode-locked fiber laser has rep rate of 100 MHz, and around 100 fs pulses.
FYI: fiber laser is ring laser utilizing nonlinear birefringence as the mode-locking mechanism. Round trip is used, at this time there is no actual end user. For time domain analysis (Allan deviation) single side-band generator is used.

37. Transfer with mode-locked pulses
Dispersion broadens pulse (~ 1 ns) more power to maintain SNR
but …
Noise floor ( )
85 dB
30 mW
12.0 ( )
80 dB
660 mW
Spectral Width (nm)
SNR
Power
Recompress pulse
so …
Reduce bandwidth
Noise floor ( )
85 dB
30 mW
5.5 ( )
80 dB
160 mW
12.0 ( )
660 mW
Spectral Width (nm)
SNR
Power
Pulses allow reduced average power on detector while maintaining SNR, which was found to be critical to reduce noise introduced by detectors. Shown is the previously shown trace of transfer with cw modulation – point out to audience where noise floor was with this. Now, with mode-locked pulses, noise floor is 10x better (measured with short piece of fiber), and is slightly above electronic noise floor of single-sideband generator, counter, etc.
<Animation>
Dispersion causes less signal in 8th harmonic, and so must increase average power to maintain SNR (see table & animated trace).
Solution: Reduce bandwidth of pulse so not stretched as much – see table for necessary power now to maintain SNR, and not reduced instability for latest animated trace.
Could also recompress the pulse (or pre-chirp it) …
Pulses minimize instability of photodetection:
Average power ; SNR
Holman et al. Opt. Lett. 29, 1554 (2004)

38. Use dispersion shifted fiber in link
Active stabilization: free-space delay arm in-line with DSF
Not limited by receiver noise
Reduce Allan deviation to noise floor
Conditions at Receiver
Photodiode Power
SNR
Instability (1s)
40 mW
85 dB
6e-14 ( )
6e-15 ( )
To see effects of recompression, use 4 km spool of dispersion shifted fiber (DSF) which has negligible 1550 nm. Table : Now, comparable power w/ spool as opposed to noise floor to achieve same SNR, so know noise is indeed fiber noise (not detector noise). At first surprised to see it as high as 7 km of dispersive fiber, but realize any shock impacts entire 4km spool of fiber at once!
<Animate>
Employ free space delay line (mirror on a shaker / speaker) to achieve low bandwidth stabilization (10 Hz or so) – see spectral density to right (in loop). This low bandwidth stabilization is sufficient to suppress out-of-loop Allan deviation to measurement noise floor for averaging time > 1s. This would not have been possible if had been detector limited (since optically out-of-loop; 4 detectors total, 2 local, 2 return).

39. No showstoppers on synchronization (financial or technical)
Summary / Future Work…
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)

41. Compensate dispersion of installed fiber
3.5 km
81st harmonic
Local
End user
Mode locked fiber laser
Frequency reference
Dispersion compensation fiber
Eliminate low frequency noise on
installed fiber network
Dispersion compensation
Avg. power ; SNR
Now look at compensating dispersion of installed, 7 km roundtrip dispersive fiber:
Employ spool of opposite-dispersion fiber before 7 km link (pre-chirp).
Verify that indeed average power to achieve sufficient SNR is comparable with that for the noise floor measurement.
FYI: Potential problem: compensation fiber compensates roundtrip path, so at end user pulse is still chirped. Introduction of their own compensation spool would be out of the stabilization loop.
<Animate>
Also, have verified with free space delay line (shown in diagram) can eliminate low frequency noise for installed dispersive fiber as well. See jitter spectral density of in-loop jitter. Spike is due to shaker resonating (gain too high), but in data not shown here have demonstrated stabilization w/o this spike.

42. Cell Image Human Epithelial cell Image size is 50 by 50 microns
Total acquisition time: 8 seconds
Raman shift = 2845 cm-1
Pump kHz
Stokes kHz
Image taken by Dr. Eric Potma and Prof Sunney Xie at Harvard University with synchronization system commercialized by Coherent Laser Inc.
Slice
This is a human epithelial cell in phosphate buffer taken with Coherent Mira Sychrolock-AP. The lasers were tuned to the aliphatic C-H stretch band. Contrast in the image mainly results from lipids. The bright dots are presumably lipid vesicles whereas the other features are membrane structures. Also the nucleus is easily recognized.

43. Distribution over Fiber Networks
Optical Fiber Network
Master Clock
End User
Noise added by fiber must be detected and minimized
End User
Degradation of signal during detection minimized

44. Detection of Roundtrip Signal
Phase Coherent Transmission of Optical Standard
Detection of Roundtrip Signal
3.45 km fiber
+1 order
corrected
standard
at NIST
Nd:YAG
AOM 1
AOM 2
-1 order
Adjustment of AOM 1, shifts center frequency of Nd:YAG to compensate fiber perturbations
AOM 2 differentiates local and roundtrip signals
JILA I2 Atomic Clock

45. Transmission of Iodine Standard
Fiber phase noise
uncompensated
compensated
FWHM:
0.05 Hz
1 kHz
20 dB

46. Transmission of Iodine Standard
-30
-20
-10 10 20 30
Beat Frequency (Hz)
800
600
400
200
Time (s)
Fiber phase noise uncompensated
sdev (1-s) 5.4 Hz
-30
-20
-10 10 20 30
Beat Frequency (Hz)
800
600
400
200
Time (s)
Digital phase lock
sdev (1-s) 0.9 Hz

47. Techniques and technology of:
Summary/Future Work…
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)

48. Self-Referenced Locking Techniquefo
I(f) nm
frep f
nn = n frep + fo x2
n2n = 2n frep + fo fo
Need to access fo and frep
We have knobs, but we also need to generate error signals
Rep rate is simply (detector)
Comb is offset from exact harmonics fo and this is a bit harder to detect (must extract in optical domain)
Go through f to 2f
Need an optical octave in pulse spectrum
How to perform the RF to optical links
need an optical octave of bandwidth!
D. Jones et. al. Science 288 (2000)

49. Single Side Band Generator

51. 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
Will introduce the idea of remotely transferring frequency standards and discuss the motivation for high stability transfer (1.) why need high stability reference & 2.)transfer needs to be stable to reliably transfer stability of very stable optical references being developed)
In RF domain: review current method for transfer over optical fiber network
Discuss use of mode-locked laser for RF-domain transfer
Finally, discuss preliminary work on actively stabilizing transfer medium.

52. Instability of optical amplifier (EDFA)
Jitter spectral analysis (FFT)
8th harmonic
End user
Local
Frequency reference
3.5 km
Mode locked fiber laser
EDFA
One final comment: what is jitter introduced by erbium-doped fiber amplifier (EDFA)? This will be necessary for long-distance frequency transfer.
See from jitter spectral density adds low frequency noise (well with bandwidth of current servo), but due to gain dynamics of amplifier reduced high frequencies.

53. 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
10x improvement with mode-locked pulses due to enhanced modulation depth provided by pulses, allowing lower avg. power while maintaining SNR, which was found to be important.
Due to importance to reduce optical power while maintaining SNR, important to reduce temporal stretching of pulse. This has been done in 2 ways:
1.) Reduce pulse bandwidth
2.) Pre-chirp pulse with dispersion compensation fiber
With compressed pulse, have demonstrated active stabilization both for lab spool of DSF, and for installed fiber in conjunction with dispersion compensation fiber. Bandwidth of stabilization has been sufficient to reduce Allan deviation to measurement noise floor for averaging times > 1 s.
Finally, seen than noise introduced by amplifier is well within stabilization loop bandwidth – important for long-distance transfer.