Coherence:from Undulators
to Free Electron Lasers
David Attwood
University of California, Berkeley

Cheiron School
September 2015
SPring-8
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Coherence

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2Coherence

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Born and Wolf, Chapter 10

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Coherence, partial coherence, and incoherence

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Spatial and temporal coherence

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Marching band and coherence lengths

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Spectral bandwidth and longitudinal coherence length

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A practical interpretation of spatial coherence

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Partially coherent radiation approaches uncertainty
principle limits

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X-rays from relativistic electrons

Courtesy of John Madey

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Undulator radiation from a small electron beam
radiating into a narrow forward cone is very brightAttwood_Cheiron_Sept2015_2.ppt

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Undulator radiation

Following Albert Hoffman
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Calculating Power in the Central Radiation Cone: Using the well known“dipole radiation” formula by transforming to the frame of reference
moving with the electrons

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Power in the central cone

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Power in the central radiation cone
for three soft x-ray undulators

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Power in the central radiation cone
for three hard x-ray undulators

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Ordinary light and laser light
Ordinary thermal light source, atoms
radiate independently.

A pinhole can be used to obtain spatiallycoherent light, but at a great loss of power.

A color filter (or monochromator) can beused to obtain temporally coherent light,
also at a great loss of power.
Pinhole and spectral filtering can be used toobtain light which is both spatially andtemporally coherent but the power will bevery small (tiny).
All of the laser light is both spatially andtemporally coherent*.
Arthur Schawlow, “Laser Light”, Sci. Amer. 219, 120 (Sept. 1968)
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Spatially coherent undulator radiation

Courtesy of Kris Rosfjord, UCBAttwood_Cheiron_Sept2015_2.ppt

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Spatially and spectrally filtered undulator radiation

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A soft x-ray coherence beamline at the ALS

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A hard x-ray coherence beamline at the APS

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Coherent power at SPring-8

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Measuring spatial coherence with Young’s double slit
interferometer

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Spatial coherence measurements of undulator
radiation using Young’s 2-pinhole technique

Courtesy of Chang Chang, UC Berkeley and LBNL.
λ = 13.4 nm, 450 nm diameter pinholes, 1024 x 1024 EUV/CCD at 26 cm ALS, 1.9 GeV, λu = 8 cm, N = 55
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Spatial coherence measurements of undulator
radiation using Young’s 2-pinhole technique

Courtesy of Chang Chang, UC Berkeley and LBNL.
λ = 13.4 nm, 450 nm diameter pinholes, 1024 x 1024 EUV/CCD at 26 cm ALS, 1.9 GeV, λu = 8 cm, N = 55
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Ordinary light and laser light
Ordinary thermal light source, atoms
radiate independently.

A pinhole can be used to obtain spatiallycoherent light, but at a great loss of power.

A color filter (or monochromator) can beused to obtain temporally coherent light,
also at a great loss of power.
Pinhole and spectral filtering can be used toobtain light which is both spatially andtemporally coherent but the power will bevery small (tiny).
All of the laser light is both spatially andtemporally coherent*.
Arthur Schawlow, “Laser Light”, Sci. Amer. 219, 120 (Sept. 1968)
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Coherence: laser, undulator, free electron laser

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Undulators, FELs and coherence

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Spatial and temporal coherenceof undulators and FELs

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The evolution of incoherent clapping
to coherent clapping

Suggested by Hideo Kitamura,(RIKEN)
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The bunching advantage of FELs
In an undulator with random, uncorrelated electron positions within
the bunch, only the radiated self-fields E add constructively.
• Coherence is somewhat limited• Power radiated is proportional to Ne (total # electrons)
For FEL lasing the radiated fields are strong enough to form
“microbunches” within which the electron positions are wellcorrelated. Radiated fields from these correlated electrons are inphase. The net electric field scales with Nej, the # of electrons in the
microbunch, and power scales with Nej2 times the number ofmicrobunches, nj.
• Essentially full spatial coherence• Power radiated is proportional to ΣnjNej2; Gain ~ 3 × 106

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FEL Physics

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Equations of motion for the stronger electric field FEL

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Undulators and FELs

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Seeded FEL

Seeded FEL. Initial bunching driven
by phase coherent seed laser pulse. Improved pulse structure and spectrum.
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Spatial and temporal coherencewith undulators and FELs

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Electron energies and subsequent axis crossings are affected by
the amplitude and relative phase of the co-propagating field

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FEL Microbunching

Courtesy of Sven Reiche, UCLA, now SLS

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Gain and saturation in an FEL

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FEL lasing and the parameter ρFEL

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Measuring FEL spatial coherence

LCLS, 780 eV, 300 fsec, ¼ nC,1mJ/pulse
78% energy in TEM00 mode

Courtesy of I. Vartanyants (DESY) and A. Sakdinawat (SLAC); PRL 107, 144801 (30Sept2011)
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The coherence properties of Free Electron LasersAttwood_Cheiron_Sept2015_2.ppt

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Measuring the FEL SASE spectrum

Courtesy of D. Zhu, J. Hastings, W. Feng, (SLAC); APL 101, 034103 (July 2012)
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Reduced FEL SASE spectra, thus longer coherence
length, with “self-seeding”

20 eV
0.4 eV = 50:1 reduction
8 keV
Δλ4
==2×
10
0.4 eV
λ2 × 104
× 1.5 Å=2

1.5 µmJ. Amann, et al.,Nature Photonics 6, 693 (Oct 2012)
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Pump-probe capabilities at SACLA

Courtesy of H. Tanaka, SACLA
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FEL pumped, narrow line, Cu Kα atomic laser at 1.54 ÅCourtesy of M. Yabashin, SACLA
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Typical FEL parameters

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Probing matter on the scale of nanometersand femtoseconds

Science and Technology of Future Light Sources (Argonne, Brookhaven, LBNL and SLAC: Four lab report toDOE/Office of Science, Dec. 2008)
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2nd Edition in progress: new FEL, HHG, Coherence,and X-ray Imaging chapters

UC Berkeley
www.coe.AST.berkeley.edu/sxr2009
www.coe.AST.berkeley.edu/srms
www.youtube.com

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