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Attosecond Pulse Trains from FEL Amplifiers. Brian McNeil, Neil Thompson, David Dunning & Brian Sheehy. Workshop on X-Ray FEL R&D LBNL October 23 - 25, 2008. Outline. Brief summary of ‘conventional’ cavity mode locked lasers Mode formation & locking in a SASE FEL amplifier

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Attosecond Pulse Trains from FEL Amplifiers

Brian McNeil, Neil Thompson, David Dunning & Brian Sheehy

Workshop on X-Ray FEL R&D LBNL October 23 - 25, 2008

  • Brief summary of ‘conventional’ cavity mode locked lasers
  • Mode formation & locking in a SASE FEL amplifier
  • 3D & 1D simulations in XUV & VUV
  • Application to High Harmonic attosecond structure
  • Improved models
  • Conclusions
ultra short pulse generation
Ultra-short pulse generation

This history of short pulse generation in ‘conventional’ lasers has developed from the first mode-locked lasers, through dye-lasers, Ti:Sapphire and now to High Harmonic Generation in gas jets. Since 1964, pulse durations have been reduced by ~ 5 orders of magnitude to ~130 as and very recently* to ~80 as.

*E. Goulielmakis et al., Science 320,1614 (2008)

cavity modes
n = 1



n = 2



n >> 2


Cavity modes*

perimeter = s


A repeated waveform generates a spectral comb

  • Envelope is atomic linewidth: gain bandwidth of lasing medium
  • Mode spacing ∆ωs=2πc/s
  • No of modes q = bandwidth/mode spacing
Cavity mode-locking


  • Mode-locking occurs when a fixed phase relationship develops between the axial modes.
    • Application of e.g. cavity length modulation causes axial modes to develop sidebands.
    • Cavity modulation at round trip frequency causes sidebands at mode spacing Δωs . Neighbouring modes couple and phase lock.
    • The the output consists of a one dominant repeated short pulse.
axial modes from an amplifier fel
Eg: s =10m, λ=10 nm,

Nw = 50 q =107

Electron delayδ

s= δ + Nwλ

Nw period



n = 2

n =1

n = 3




Example: λ=12.4nm, N = 12, δ= 551nm s = 700nm# of modes: q = 2.35

Axial Modes from an amplifier FEL
  • For cavity FEL, gain bandwidth ~ 1/2Nw
  • No of modes within bandwidth q = s/2Nwλ
  • Too many modes to resolve & needs optics
  • Alternative: synthesise axial mode spectrum without cavity

The spectrum is the same as a ring cavity of length s.

Have synthesized a ring cavity of length equal to the total slippage between modules

axial mode analysis
Axial mode analysis

The analysis demonstrates that the axial modes generated are formally identical to those of a cavity.

The ‘cavity’, however, is significantly shorter, so that only a few modes may fall under the gain bandwidth.

This now allows coupling via a modulation introduced at a relatively large frequency.

Similarities to DOK: V. N. Litvinenko, Nucl. Instrum. Methods Phys. Res., Sect. A 304, 463 (1991).

modelocking simulations in genesis 1 3
Modelocking Simulations in Genesis 1.3

Interaction of e-beam and laser in modulator simulated

Modulated e-beam propagated in undulator, including SHOTNOISE.

Energy Modulation converted into BEAMFILE






Chicane dispersion applied with 4-dipole chicane (IBFIELD, IMAGL, IDRIL)


Radiation delayed using OFFSETRADF and ALIGNRADF parameters


Repeat Until Saturation

xuv output comparison
XUV Output Comparison

SASESpike FWHM ~ 10fs

Mode-CoupledSpike FWHM ~ 1 fs

Mode-LockedSpike FWHM ~ 400 as

1D Simulation:

Mode locking mechanism


Typical FEL amplifier schematic: (4GLS XUV-FEL)

FEL amplifiers are broken into a series of undulator sections. Between these sections it is necessary to accommodate phase-shifters, electron focussing elements and beam positioning monitors. Inclusion of electron bunch delay chicanes should not significantly affect this generic design. Note, typically the electron delay chicane will be independent of energy and of total length ~12-15cm. The chicanes are therefore easy to incorporate into an undulator lattice.


Chicane Magnet stability:

Path length change:





Energy stability:

E.g. in XUV case 2nd term is factor 10-5 smaller

Energy spread:



amplified hhg no modes
Amplified HHG – no modes*


*B W J McNeil, J A Clarke, D J Dunning, G J Hirst,

H L Owen, N R Thompson, B Sheehyand P H Williams,

Proceedings FEL 2006

Also - New Journal of Physics 9, 82 (2007)

Amplified HHG – with modes

P. M. Paul, et al. Science 292, 1689 (2001)

and his the resonant harmonic of the HHG seed

E.g. for operation at the h=65th harmonic of a Ti:Sapphire drive laser with :

amplified hhg retaining structure


Drive λ=805.22nm, h =65, σt=10fs

Amplified HHG – retaining structure
1D Simulation:

HHG amplification mechanism

1D Simulation:

HHG amplification mechanism with energy modulated beam at multiple of mode spacing

simulated spectrum
39th harmonic

Cannot modelfor


Cannot modelfor


Current computational codes e.g. Genesis

Simulated spectrum

For averaged FEL codes the minimum sample rate is:

Nyquist freq.

Freq. range for non-aliasing:

=> Freq. range that e.g. Genesis can simulate properly without aliasing is:

Pulse lengths able to be modelled are limited!

1d enhanced frequency range model @ 12 4nm
1D enhanced frequency range model @ 12.4nm

Spike width FWHM = 57as !(~1.4 optical cycles)

450 as: same as Genesis @12.4nm

More modes now, therefore shorter spikes:

  • Application of mode-locking techniques, stolen from ‘conventional’ cavity lasers, indicate possibility of generating attosecond pulse trains from FEL amplifiers
  • Method tested using full 3D simulation code used in design of e.g. XFEL and LCLS: predicts attosecond pulse trains in good agreement with analysis.
  • Method can be employed to amplify HHG pulses while retaining their attosecond structure
  • Evidence that mode-locking may be better than 3D models suggested when a numerical model accessing wider frequency space is used.

“Potential advantages”: relatively easy to implement – modulator undulator and chicane inserts between undulator modules. Shorter pulses (~23as @ 1.5Å) in a train with variable time structure.

“Practical difficulties”: more difficult to identify at this stage – more modelling required.

Opens up possibility of stroboscopic interrogation of matter using light with the spatiotemporal resolution of the atom.