Laser Timing for Accelerators(Femtosecond Timing)

Josef Frisch

SLAC

Femtoseconds

Bryan Bandli, Scanning Electron Microscopy Laboratory, University of Minnesota

70fs

Eye blink

½ human hair at C

1 Meter of typical engineering material will change length by 30fs/°C

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5000 Years

0.1 second

70 femtoseconds

Applications of Accelerator / Laser Timing

Drive laser for RF guns Ultra-fast electron diffraction

H. Ihee et al

X-ray / laser pump probe experiments

Compton backscatter sources

LCLS

CXILLNL

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Subsystems

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General Comments

• Timing systems are typically one component of a large experiment– Reliability and low maintenance are critical!

• Timing needs to work over large timescales– It is possible to build systems that are normally stable

to femtosconds, but which can jump by nanoseconds!

• The entire accelerator / timing system / experiment needs to be consider as a whole. – Connections between subsystems may be the largest

source of problems.

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Measuring Femtoseconds - Narrow Band Clocks

Conventional electronic triggers only good to ~1ps.

Use repetitive clock to average timing measurements on millisecond timescales to allow X1000 improvement using GHz clocks

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RF SystemsTerminology

dB is a log ratio of power: dB = 10*log10(P1/P2)

dBm is a power measurement – dB relative to a 1 milli-Watt source. 0dBm = 1mW, 20dBm = 100mW

Noise figure is the ratio (in dB) of the noise of the actual device to thermal noise. Typical well designed RF systems have noise figures of <10dB, individual components can have noise figures < 1dB.

Why Use RF?

Thermal noise (at room temperature) is -174dBm in a 1Hz bandwidthSo in a 1 KHz bandwidth, thermal noise is -144dBm or 4 Attowatts

A 1 mW , 1KHz bandwidth, 10dB noise figure system would have a signal to noise of 134dBm, corresponding to an amplitude signal to noise of 2x10-7. For a 1GHz system this is a timing noise of 30 attoseconds

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RF MixersAny non-linear combination of 2 signals will produce sum and difference frequencies:

𝐴 = sin 𝑤1𝑡 + 𝜑 , 𝐵 = sin(𝑤2𝑡 + 𝜙)

𝑌 = 𝐶1𝐴 + 𝐶2𝐵 + 𝐶3𝐴2 + 𝐶4𝐵

2 + 𝐶5𝐴𝐵 +⋯

sin 𝑤1𝑡 + 𝜑 sin 𝑤2𝑡 + 𝜙 =1

2[sin 𝑤1 + 𝑤2 + 𝜑 + 𝜙 𝑡 + sin 𝑤1 − 𝑤2 + 𝜑 − 𝜙 𝑡 ]

• Contains frequency and phase difference.• Useful way to translate phase from frequency to low frequency• “Magnifies” time : 1° at 10GHz is converted to 1° at 10MHz expands time X1000

Low cost commercial units available

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RF Linearity

• Amplitude to phase conversion is a major source of timing drift and noise– Typical phase detection frequencies are ~2GHz

(ω=10GHz), so 100fs represents only 10-3 Radian

• Very difficult to measure AM-> PM due to the lack of a method to produce amplitude variation without associated phase variation.

• AM->PM is a form of nonlinearity, so it is possible to make an estimate by measuring other nonlinear terms (amplitude nonlinearity).

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Measuring Nonlinearity: IP3

Difficult to measure 1% amplitude non-linearity directly

Instead, use the beating of 2 sources to generate amplitude modulation

Nonlinearity visible in spectrum

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IP3 and Signal Levels

Input vs. output IP3 specification:manufacturers use whatever gives the higher number!

Signal level is a trade-off between linearity and noise

READ THIS!

Imagine an amplifier with:14dB noise figure (-160dBm/Hz)20dBm IP31MHz signal bandwidth

Noise level: -100dBmSignal level of -20dBm:80dB signal to noise80dB nonlinearity to noise.(If ampltude is stable, higher signal level might be better)

DO NOT USE MORE GAIN THAN YOU NEED!11

Master Clocks

The concept of an “absolute” clock is defined, but typically isn’t useful for accelerator / laser timing systems

Care about relative timing of the laser and electron (or x-ray) beam and other components.

Real clocks will gradually drift relative to each other, so clock phases are locked together at some timescale: Phase locked loop

On long timescales “physics” from the beam / laser interaction is used to set the timingAccelerator systems do not require ultra-stable clocks.

NIST

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Phase Locked Loops

• Typically design the feedback for infinite gain at DC• Gain reduced at higher frequency• For long timescale the VCO follows the phase changes of the reference oscillator• For short timescales the VCO is essentially free-running

VCO can be an electronic oscillator or a laser oscillator

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Phase Noise

Narrow band clock consisting of a phase modulated sine wave: 𝑉 = sin(𝜔𝑡 + 𝑓 𝑡 ) where 𝑓 𝑡 = a ∙ sin(𝜔𝑛𝑡)

For small a, can write as 𝑉 = sin 𝜔𝑡 + a/2 ∙ sin 𝜔 + 𝜔𝑛 𝑡 − 𝑎/2 ∙sin[(𝜔 − 𝜔𝑛𝑡)] A main line with sidebands.

Power spectrum

Noiseless

Signal with phase modulation

dB below carrier

0dBc is 1 radian RMS ,

or 1

2𝜋𝑓𝑠𝑒𝑐𝑜𝑛𝑑𝑠

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Phase noise (2)Phase noise displayed relative to carrier frequency and power.

Directly translates to timing jitter noise density (convert radians to seconds)

Convenient measurement with commercial(but expensive) instruments. Agilent E5052B

Not all commercial units give the right answer!

• Phase noise is relative to the (near ideal) reference oscillator in the instrument

• At low frequency offsets the results may not be interesting!

• At low frequency offsets it is better to directly measure phase vs reference phase15

Oscillator Phase Noise

Good quality commercial oscillators can “remember” phase to 10s of femtoseconds at 10-100Hz (Wenzel, Pascal)

Very expensive Sapphire oscillators can “remember” 10s of femtoseconds at 1-10Hz. 16

In loop / Out-of-loop Measurements

• Feedback systems (typically) have infinite gain at DC, so the “in loop” detector cannot measure drift. Low frequency noise will also be attenuated by the loop gain

• Need an independent “out of loop” detector to know how well your system is actually working

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Accelerator Timing – RF Gun

• Photo-emission typically off crest

• Energy spread produces compression

• For LCLS gun, beam time is equally controlled by laser and RF timing

RF time set by phase measurement using gun pick-off

Feedback can be pulse to pulse or continuous

Beam time is not completely determined by laser time 18

Electron Beam Compression

• Changes in input beam time are compressed to smaller changes in output time

• RF phase changes directly change output beam time.

• Input energy changes will change output time

• Beam is (typically) ultra-relativistic, so it is possible to measure the orbit in the compression chicane to determine the output beam time.

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Room Temperature LINAC

• Low repetition rate (~100Hz) limits feedbacks to below acoustic frequencies• Mechanically rigid structures with low Q are resistant to environmental noise• Shot to shot jitter ~10s of femtoseconds. 20

Superconducting LINAC

• Long RF pulses (millisecond) and high beam rate (MHz) allow intra-pulse feedback (RF and beam) which can fix a variety of noise sources

• High Q, low stiffness structures inherently sensitive to external noise• ~10 femtosecond jitter performance at FLASH with beam feedback

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Beam Arrival Time Monitors

• Rely on electromagnetic fields from beam– Generally THz bandwidths

• RF systems use GHz fields induced in cavities or other pickups

• Optical systems use beam fields to drive electro-optical modulators of fiber-coupled picosecond pulses

• Mechanics: 10fs stability implies 3 micron mechanical stability of pickoff!

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RF Beam Fields

• Accelerator beam-pipes are filled with electromagnetic radiation from upstream discontinuities.

• If the beam time pickoff is operated below the beam-pipe cutoff, upstream signals will not interfere with the measurement

• Operation above beam-pipe cutoff may be possible IF the detection system is broad-band and can detect local beam fields before the fields from upstream arrive. Extreme care must be taken with high frequency measurements.

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RF Beam Time Measurement Phase Cavity

7fs RMS compare2 cavities

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Algorithm must correct for phase shifts from temperature changes

Electro-optical beam time monitor

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Electric field

from bunch

Electro-optical

intensity modulation

6 femtosecond timing noise

published (Believe ~3 fs achieved)

F. Loehl et al

DESY/FLASH

Short pulse laser

High frequency cable

Use of RF pickoff simplifies mechanical design, but care is needed to avoid picking up signals from upstream.

Timing Transmission

• Need to transmit timing ~100M with ~100fs stability ~10-7. • Temperature coefficient of delay of RF coax and optical fibers both

~10-5/°C– Fused silica thermal expansion is very low but the index of refraction

has a significant temperature coefficient.

• Humidity effects can be as large as temperature effects. • Lower thermal coefficient specialty cables and fibers exist, but

usually not good enough to avoid the requirement for feedback• Work done at many labs around the world

– This is a favorite topic of timing research – probably because it doesn’t require a giant accelerator facility.

• Will only give a very brief overview here!• State of the art: 10s of femtoseconds stability (better in R&D

programs, worse in installed systems)

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World’s Best Timing System

LIGO: <10-28 seconds noise over 4km!Spectacular achievement!Useless for laser / accelerator timing!

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Caution on Comparing Technologies

• “Typical”, “best ever”, and “worst” performance can be very different!

• Timing systems are typically only one part of a complex accelerator / laser system.

• Need to design around “worst case” operation to guarantee performance to users.(the goal is to do science, not publish impressive numbers!)

1 day

100fs

10 Days

900fs

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Fiber timing system test

Timing Transport

Feedforward requires a very accurate measurement of timing shiftsFeedback only requires a stable measurement, but requires a bi-directional timing shift

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Fiber vs. Coax

Coax

• Limited bandwidth – GHz over 100M.

• Thermal noise - ~1/40eV

• Bulky, expensive - >1” sizes often needed

• Simple, Rugged, Common diagnostics

Fiber

• High Bandwidth – >THz with dispersion compensation

• Photon noise ~1eV

• Commercial SMF-28 inexpensive, compact

• Delicate, needs special instrumentation

Both used successfully for accelerator timing systems. Choice will depend on the design of the rest of the system

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Devil in the Details

• Unwanted reflections can prevent feedback / feedforward from operating correctly. – 1ppm reflected RF power can cause 100fs timing shifts.

• Bi-directional phase shifters are difficult to realize electronically if signal levels are different

• Directional couplers have limited directivity– Better for fiber than for coax

• Normal telecom fibers do not maintain polarization –forward and backward light sees different delays

• Real photodetectors typically have much larger than 1 photon noise - 1000 photons typical.

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Sources of Noise - Coax• RF (thermal noise), Real systems have ~10dB noise figure• Generally not a limit with normal power levels and bandwidths

Acoustic noise is significant!200M of cable94dB acoustic levels at 40Hz80fs RMS added noise

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Sources of Noise – Fibers• Photon shot noise and detector noise (at low optical

powers)• Laser wavelength variations -> dispersion -> timing

variations– Usually this is bidirectional– Can be used to advantage as a fiber delay control with a tunable

laser.

• Amplitude variations -> nonlinearity -> wavelength variations (at high optical powers)– May not be bidirectional

• Polarization mode dispersion in conventional fiber– Not bidirectional– Can be fixed with PM fiber, but very expensive and specialized

hardware.

• May be sensitive to acoustic noise33

RF Feed-Forward Link

• Average phase is first order independent of cable length• Multi-drop capability• Very simple / rugged.

• Feed forward, not feed back: in practice only see X10-X20 improvement• Reflections limit performance even in an “ideal” system

K. Jobe, SLAC

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CW RF over fiber feedback

• Fiber length feedback options: • Piezo stretcher: fast, limited range, causes polarization shifts• Fiber oven (Kilometer fiber with temperature control): long

range, slow• Wavelength tuning (use fiber dispersion)

SLAC, I-Tech and others.

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Interferometer Fiber / RF

LBNL: J. Byrd, L Doolittle, G. Huang, R. Wilcox,

• Use an (optical) frequency stabilized laser to drive an fiber optical interferometer which measures the transmission fiber length

• Laser is modulated with RF and detected by a photodiode at the far end of the fiber

• A calibrated (digital) RF phase shifter corrects the RF phase based on the interferometer measurement 36

Pulsed Fiber System

• Timing is carried by picosecond optical pulses• Timing comparison by optical techniques (nonlinear

interaction of pulses)• Work by many groups: MIT, DESY, IdestaQE, etc.

J. Kim, F. Ö. Ilday, F. X. Kärtner, O. D. Mücke, M. H. Perrott, W. H. Graves, D. E. Moncton and T. Zwart, “Large Scale Timing Distribution and RF-Synchronization for FEL-Facilities,” FEL-Conference 2004, Trieste, Italy, Aug. 26-29, 2004.

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Direct Optical Phase Transmission

reprate

comb1 linepicker

lineTX

lineRX comb2hetero-

dyne

Wilcox et al, Journal of Modern Optics 58, 1460 (2011)

• Timing carried by the OPTICAL phase – 300THz carrier!• Single cycle is 3fs, so easy to imagine <<1fs timing• Newer design does not require carrier / envelope locked lasers

(simplifies laser system).• Still a very complex system, not yet fully demonstrated in the lab.

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Laser Locking Systems

• Most rely on locking the ~100MHz mode-locked laser oscillator to a reference signal

• Commercial laser -> RF locking systems available at the ~100s fs noise level– Can to better with custom systems

• Ti:Sapphire lasers are the most commonly used, but fiber lasers are gaining popularity.

• Significant variation in the unlocked noise of different laser oscillators – directly impacts locked performance

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Laser Systems

• Mode locked laser frequency -> phase determined by optical cavity length• Optical cavity length usually controlled with piezo-electric mirror• Pulses are stretched before amplification to avoid peak power damage

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Laser Locking

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Phase Detection

• Generally the most challenging part of the laser locking system

• Laser diodes produce short (~100ps) pulses at fairly low rate (~100MHz)

– Use bandpass filters to ring the signal into a near continuous RF tone

• Use a mixer to compare the phase with the reference system

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Photodiode Phase Detection Signals

Reference Laser diode outFiltered laser diode

Mixer output LP filter output

Matlab calculation with 68MHz laser frequency and 476MHz locking frequency

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Photodiode Error Sources• Amplitude -> phase conversion

– 10GHz diodes typically biased at 5V– If peak output voltage becomes comparable to the bias, the capacitance of the

diode can change and cause a phase shift– Remember that we are looking at timing shifts on the order of <1/1000 of the

diode pulse width.

• Position sensitivity– Typical 10GHz photodiode (ET-4000) has a 40micron diameter – corresponds

to about 500fs for signals to cross the diode!

• Improved diodes: High linearity fiber coupled diodes available.– Looks like an overall improvement– Needs care to have long term stable coupling to single mode optical fiber– Available from Discovery Semiconductor. (IP3 > 40dBm!)

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Photodiode signal levels

• Need to limit the diode output voltage– ~100mV peak (on multi-GHz scope) works for

conventional diodes

• Narrow-band filter reduces signal amplitude by ratio of bandwidth to laser frequency

• SLAC system at 3.8GHz results in ~ -40dBm signal from diode

• OK – feedback bandwidth is 10KHz so (theoretical)signal to noise (with 10dB noise figure) is 3fs RMS

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Mixer LO Leakage

• A small amount (~-30dB coupling) of the high power LO reference will leak into the low power RF input

• This causes a shift in phase of the input RF signal from the diode that depends on the amplitude of the 2 signals

• Results in significant amplitude-> phase conversion.

• Can improve by using high gain amplifiers on the diode signal, BUT• IP3 limits in the mixer • High gain systems can have cross talk from other signals

• 3GHz -> τ=50ps, so need 1/1000 interference (-60dB interference) for 50fs 46

Heterodyne System

• Mix to an intermediate frequency rather than DC (frequencies from SLAC system)• Low frequency phase detection much easier:

• Can easily digitize and calculate relative phase in software• Can use low frequency mixer or analog multiplier with much better

performance than RF mixer• Signal levels small until RF mixer, then put gain at low frequency where cross talk is

less significant.• Technique used in radio receivers (R. Fessenden , 1901 (!!!))

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Multiplying the Laser Rate

M. Csatari Divall1 et al. 48

• Potential to significantly improve noise / linearity of diode detection systems

• Adds some optical system complexity

Direct Optical Pulse Locking

J.Kim, et al., Nat. Photonics 2, 733-736 (2008)

Heng Li, IdestaQE

• All-optical timing system operates with picosecond pulses -> 100GHz bandwidths

• Very low noise/ drift measurements for laser feedback

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Laser Phase Control• Laser cavity length controlled by piezo-electric driven mirror in most

commercial femtosecond lasers.• Typical resonance of 10s of KHz sets upper bandwidth limit for feedback

– feedback usually rolled-off at few-10 KHz• Need high current, low noise drive amplifier

Beware of noise sources – found that in Coherent Vitara lasers the largest noise source was the driver for the low bandwidth piezo “starter” mirror

Fixed with diode circuit to block noise:

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Laser Amplifier and Transport• In installed systems the laser amplifier / transport

chain appears to add substantial jitter:– SLAC / MEC: oscillator / FEL jitter < 100fs, but

measured optical to X-ray jitter >150fs– PSI: Oscillator jitter < 30fs, amplified pulse jitter

>150fs (Divall Marta et al)– 100s of fs increased jitter seen at Max Plank

T Mirua, et al December 15, 2000 / Vol. 25, No. 24 / OPTICS LETTERS 1795

Short term jitter relative to mode-locked laser ~10fs

Long term drift 100fs/hour 51

Compressor / Expander

Experimental and theoretical investigation of timing jitter inside a stretcher-compressor setup. Sandro Klingebiel, et al, 13 February 2012 / Vol. 20, No. 4 / OPTICS EXPRESS 3443

Steering due to air currents in compressor can cause ~100fs/microradian timing shifts.

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Amplifier / Transport Stabilization

• How to measure amplifier output timing?– Repetition rate typically too low for low noise photodiode / RF based

measurements– Can measure amplified pulse timing relative to the mode-locked

oscillator pulse using optical cross-correlators• May need a pulse fiber transmission system as well

– Direct optical phase comparison / feedback may be possible but is complex

• For low repetition rate amplified systems the noise may have too high frequency for feedback.– Even with a good measurement of the amplified laser pulse timing, a

low noise mode-locked oscillator locking system is needed.

• Offline correction– For pump / probe type experiments if is often sufficient to measure

the shot-to-shot laser timing but not correct it.– Ideally the measurement is done by comparing the beams used in

the experiment. (eg. Direct X-ray / optical cross correlation)53

“Physics” Timing

• For RF guns, the charge depends on the relative phase of the RF fields and the laser

• If QE is stable, you could feedback laser time on photocathode current!

• Can move to zero-current phase (Schottkyedge) to find “zero” time in a few seconds (done at LCLS)

• For X-ray FELS can use a separate “experiment” to measure relative X-ray and optical timing

• LCLS:• X-ray induced changes in index of

refraction in thin films• Index measured with optical laser• <10fs resolution

Solution for electron diffraction and Compton scattering not obvious 54

Timing System Architecture Guidelines• Figure out what you need to time – be specific e.g. :

– Laser pulse in gun vs. RF phase in gun– Laser pulse in experimental chamber vs. X-ray pulse in experimental

chamber

• What is the most direct signal you can measure:– Schottky edge? Cross Correlator?– Can you use this for slow drift or jitter correction?

• Create a chain of timing between the 2 signals you need to time:– Electron beam in undulator -> beam time monitor -> timing

transmission system -> laser locking system -> laser amplifier system -> laser transport system -> experimental chamber <- X-ray transport <-FEL process in undulator.

– Find the WEAKEST link and work on that. – Resist the temptation to work on the most “exciting’ part

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The most important improvement to timing stability at the LCLS was an upgrade to the laser room air conditioning system!

Timing System Engineering

• You can’t afford to buy or operate the “best possible” timing system – there is a price / performance / reliability trade-off: This is engineering , not science.

• Understand the requirements: do the experiments REALLY need <10fs jitter on a 50fs laser pulse?

• Consider the entire system design and how it interacts with your accelerator and laser systems before deciding on RF or Fiber (or both).

• This is part of a user facility, not an experiment itself. The system needs to have high reliability and be maintained by your staff.

• GET YOUR RF SIGNAL LEVELS RIGHT!

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