Shaping FEL radiation: from multipulse/multicolor emission to generation of twisted light PRIMO Ž REBERNIK RIBI Č School on Synchrotron and Free-Electron-Laser Based Methods, ICTP , April 2016
SOME OF THE PROPERTIES USERS EXPECT FROM A LIGHT SOURCE • High peak brilliance and full tunability in the spectral region of interest • Possibility of controlling pulse duration • Full transverse and longitudinal coherence (diffraction imaging, coherent control) • Variable polarization (circular dichroism, surface science) • Ultimate feature: the ability to arbitrarily shape the radiation pulse in the temporal and spatial (longitudinal and transverse) domains
YOU CAN‘T ALWAYS GET WHAT YOU WANT? • In the IR to UV spectral region, the majority of previously mentioned requirements are met by conventional table-top lasers. • In the VUV to X-ray spectral domain, different approaches must be used in order to achieve laser-like properties of light. Seeded FELs are currently the most promising candidates for reaching this goal.
OUTLINE • quick recap of bending magnet and undulator radiation • basic principles of FEL operation • self-amplified spontaneous emission (SASE) vs. seeded FELs • advanced FEL concepts: longitudinal (temporal) and transverse (spatial) shaping of FEL pulses
Bending Magnet Radiation (continued) From Heisenberg’s Uncertainty Principle for rms pulse duration and photon energy thus (5.4b) 2 �� ��� � ��� � m / 2e �� 2 BENDING MAGNET RADIATION Thus the single-sided rms photon energy width (uncertainty) is (5.4c) A more detailed description of bending magnet radius finds the critical photon energy (5.7a) In practical units the critical photon energy is (5.7b) Professor David Attwood Univ. California, Berkeley Bending Magnet Critical Photon Energy and Undulator Central Radiation Cone, EE290F, 13 Feb 2007 Ch05_BendMagRad2_April04.ai http://photon-science.desy.de
UNDULATOR RADIATION dI & # $ ! 2 c π d / ω ω ω = % " n 1 λ n ≈ 1 Δ ω nN ω n figure by Bastian Holst ( ) N 1 / ω π ω − ω 1 N = number of undulator periods Resonant wavelength: λ = undulator period u ! $ 2 n γ 2 1 + K 2 λ n = λ u γ = electron energy 2 + γ 2 θ 2 & , # " % K B ∝ λ = undulator parameter u 0 (only odd harmonics on-axis, B = peak undulator field 0 i.e., θ = 0) n = harmonic number
UNDULATOR RADIATION „EXPLAINED“ Resonant wavelength: Pulse properties: D detector ! $ 2 γ 2 1 + K 2 λ = L 2 + γ 2 θ 2 # & " %
TIME STRUCTURE OF SYNCHROTRON RADIATION Streak-camera image 110 section Time (ps) 6.7 0 Time ( µ s) Time structure of synchrotron radiation is a replica of that of the electron bunch, and is FWHM ≈ 30 ps invariant over the entire spectrum.
DECREASING THE PULSE DURATION A femtosecond laser is used to imprint an energy modulation onto a long electron bunch (femtoslicing). R E P O R T S of meth- fem- synchrotron in- elec- reso- wiggler. sepa- ALS – Berkeley modulated dispersive storage of synchro- Drawback: strong reduction of photon flux (by a factor of 1000). R.#W.#Schoenlien#et#al.,#Science,#2000 !
SYNCHROTRON RADIATION: TYPICAL PERFORMANCE Tunability : Full (between IR and X-rays) Shot-to-shot reproducibility : Very good Polarization : Fully adjustable Repetition rate : hundreds of MHz Peak brilliance : ≈ 10 21 ph/s/0.1%BW/mm 2 /mrad 2 (at 10 keV) Pulse duration : tens of picoseconds Natural spectral resolution : ≈ few percent Coherence : good transverse, poor longitudinal
INCREASING THE BRILLIANCE photon flux brilliance (or brightness ) ∝ unit area unit solid angle × Limited!by! wake#field# 10!KeV!!! instabili8es# Limited!by! brilliance ∝ I beam diffrac4on! ε x ε y Future!upgrades! Present!situa4on! Low Emittance Rings Workshop, Crete, 2011
INCREASING THE BRILLIANCE, TRY NO. 2 Is this a brute force approach? Yes and no...
WHAT IS A FEL ? • electrons are accelerated in a high-energy linear accelerator to a speed close to c (speed of light) P. Emma et al. , Nat. Photonics (2010) 4 , 641 • electron bunch enters the undulator � (uncorrelated) emission of radiation by individual electrons • interaction of electrons with previously emitted waves leads to microbunching � partly correlated emission • complete microbunching � the emission is fully correlated
FEL GAIN Exponential optical gain, ! $ x I ( x ) = I o exp # & " % 2 γ 2 1 + K 2 λ ≠ L electrons lose energy L G " % $ ' and “fall out” of 2 # & resonance with the wave The electron beam and the emitted electromagnetic wave co-propagate in a long undulator. Electrons couple with spontaneous emission, resulting in exponential amplification (gain) of the intensity until saturation is reached.
A QUESTION OF COHERENCE Incoherent Coherent FEL synchrotron emission emission B.W.J. McNeil, N. R. brilliance ∝ I 2 brilliance ∝ I beam Thompson, Nature beam Photonics , 2010
WHY MORE BRILLIANCE? AREN’T SYNCHROTRONS POWERFUL ENOUGH? protein nanocrystallography coherent X-ray diffraction imaging (CXDI) non-periodic objects � continuous diffraction pattern � oversampling � phase retrieval � image reconstruction CXDI of single mimivirus particles λ = 6.9 Å measurements on photosystem I H. N. Chapman et al. , Nature, 2011 M. M. Seibert et al. , Nature , 2011
SELF-AMPLIFIED SPONTANEOUS EMISSION (SASE) FEL 100 x 10 z y E rad ( µ J) 1 0.1 0.01 0 5 10 15 20 25 30 z (m) Initial emission that is being amplified originates from electron shot-noise: 2 N 1 ! ! π j eK cos( z ) [ x x ( z )] [ t t ( z )] ∑ = δ − δ − e j j L γ j 1 j =
SASE SPECTRAL AND TEMPORAL CHARACTERISTICS (FLASH) Spectral!profile!! Intensity (a.u.) Temporal!profile!(simula4on)!! E rad = 40 µ J 12 10 8 13.5 13.6 13.7 13.8 13.9 14.0 P (GW) λ (nm) 6 4 2 0 10 20 30 40 50 W.!Ackermann! et#al.,#Nature,#2007 ! t (fs)
SASE PULSE ENERGY STABILITY (FLASH) Probability!distribu4on!for!the!energy!of!FLASH!radia4on!pulses! End!of!exponen4al!growth! Satura4on! σ = 72% σ = 18% 0.8 M = 1.9 2 0.6 p ( E rad ) p ( E rad ) 0.4 1 0.2 0.0 0 0 1 2 3 4 5 0 1 2 3 4 5 E rad / E rad E rad / E rad W.!Ackermann #et#al.,#Nature,#2007 !
OVERCOMING SASE LIMITS 1 – SELF SEEDING E photon !=!930!eV! 4 5 x 10 Fraction of energy 1 Avg seeding 0.8 Sim. seeding • improved!central! 4 0.6 Intensity (arb. units) Avg SASE 0.4 wavelength!stability! 4 x 10 0.2 Average seeded 12 • narrower!bandwidth! Average SASE 3 0 Single − shot seeded 0 200 400 600 800 1000 Intensity (arb. units) 10 Single − shot SASE Bandwidth (meV) (increased!brightness)! 8 2 • limited!ability!to!shape!the! 6 4 radia4on!pulse! 2 1 0 − 1000 − 500 0 500 1000 Relative photon energy (meV) 0 − 3000 − 2000 − 1000 0 1000 2000 3000 Relative photon energy (meV) D.!Ratner! et#al.,# PRL,!2015!
OVERCOMING SASE LIMITS 2 – SEEDING BY AN EXTERNAL COHERENT SIGNAL (HIGH GAIN HARMONIC GENERATION - HGHG) dispersive section radiation at λ seed / n (4 bending magnets) λ seed modulator radiator seed pulse electron bunch E. Hemsing et al., Rev. Mod. Phys, 2014 b n ~exp[ − n 2 B 2 / 2]J n [ − nAB ] A = energy modulation normalized to the initial energy spread max : AB ≈ 1 ⇒ b n ~exp[ − n 2 / 2 A 2 ] B = (dimensionless) dispersive strength FEL radiation properties are governed by the seed laser => PULSE SHAPING!
FERMI SEEDED FEL FEL1: 100 nm – 20 nm FEL2: 20 nm – 4 nm a 1 FEL intensity (a.u.) 0.5 0 5 4 2 0 g 0 4.0 − 2 a 1.0 − 4 3 Horizontal size (mm) − 5 Vertical size (mm) 3.5 Spectrum intensity (a.u.) Vertical dimension (mm) 2 Spectrum intensity (a.u.) 3.0 0.8 b 2.5 1 0.6 1.2 2.0 0 1.0 0.4 1.5 FEL intensity (a.u.) 0.8 − 1 1.0 0.6 0.2 − 2 0.5 0.4 0.2 − 3 0.0 0.0 0.0 10.7 10.75 10.8 10.85 10.9 10.74 10.76 10.78 10.80 10.82 10.84 10.86 38.35 38.30 Wavelength (nm) FEL λ (nm) 500 38.25 400 Photon energy (eV) 38.20 300 38.15 200 Allaria! et#al.,#Nature#Photonics ,!2012!and!2013! FEL shot (no.) 38.10 100 38.05 0
FERMI SEEDED FEL Adriatic sea Linear accelerator ~130 m Undulator gallery ~100 m Experimental hall ~50 m
SHAPING FEL LIGHT: TWO COLOR FEL SCHEMES (FOR X-RAY PUMP-X-RAY PROBE EXPERIMENTS)
TWO COLOR FEL SCHEMES How can we generate two FEL pulses with different wavelengths? 2 1 + K 1,2 λ 1,2 = λ u split undulator scheme 2 γ 2 1 + K 2 λ = λ u 2 γ 2 1 + K 2 twin-bunch scheme λ 1,2 = λ u 2 γ 2 1,2 probe pump two colors + delay = τ##
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