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Spatio-temporal coherence of free electron laser pulses in the soft x-ray regime

R. Mitzner, B. Siemer, M. Neeb, T. Noll, F. Siewert, S. Roling, M. Rutkowski, A.A. Sorokin, M. Richter, P. Juranic, K. Tiedtke, J. Feldhaus, W. Eberhardt, and H. Zacharias

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Abstract

The temporal coherence properties of soft x-ray free electron laser pulses at FLASH are measured at 23.9 nm by interfering two timedelayed partial beams directly on a CCD camera. The partial beams are obtained by wave front beam splitting in an autocorrelator operating at photon energies from hν=30 to 200 eV. At zero delay a visibility of (0.63 ± 0.04) is measured. The delay of one partial beam reveals a coherence time of 6 fs at 23.9 nm. The visibility further displays a non-monotonic decay, which can be rationalized by the presence of multiple pulse structure.

©2008 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. (a) Schematic drawing of the layout of the autocorrelator. Grazing angles of 3° and 6° for the fixed and variable delay arms, respectively, are employed to ensure a high reflectivity of the soft x-ray radiation. (b) Calculated reflectivity for amorphous carbon coated silicon mirrors for hν=30 to 200 eV. The full green line shows the reflectivity of a single mirror for a grazing angle of 6°. The beam size in x- and y- directions are 8 mm, respectively, at the position of the CCD camera.

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Fig. 2.
Fig. 2. Series of interference fringes at 23.9 nm for four different crossing angles of the partial beams from α=0.18 mrad to 0.75 mrad yielding fringe spacing of δ=130 µm to 32 µm.

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Fig. 3.
Fig. 3. Single exposure interference fringes at 23.9 nm for a crossing angle of α=0.18 mrad, (a) at zero delay and (b) at 55 fs delay between both partial beams. (c) Observed visibility (experimental data points: red dots) as a function of time delay. The green line depicts a Gaussian function with a coherence time of τcoh=6 fs, representing a single Fourier transform limited pulse. The red rectangles denote the overlap area of both partial beams.

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Fig. 4.
Fig. 4. Individual single shot spectra of the FEL pulses at about 23.9 nm.

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Fig. 5.
Fig. 5. Simulation of the time dependence of the visibility with structured pulses. Separations of pulse maxima of 10 fs (red line), 12 fs (dark blue), and 20 fs (grey) are considered. A third weak maximum with a separation of 40 fs is added to account for an increased visibility at this time delay. Inset: Schematic structure of the best fitting pulse. For this pictorial illustration a flat phase for the individual maxima at a bandwidth of Δλ=0.17 nm is chosen. A probably existing chirp of the pulses does not change the time dependence of the visibility.

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Fig. 6.
Fig. 6. Interference fringes for the fully overlapped partial beams at λ=23.9 nm. Fringe separation δ=51 µm, k=0.80.

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Tables (1)

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Table I. Operating parameters of FLASH during the experiment

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Equations (7)

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Γ ( r 1 , r 2 , τ ) = 〈 E ( r 1 , t ) E * ( r 2 , t + τ ) 〉
Γ ij ( τ ) : = 〈 E i ( t ) E j * ( t + τ ) 〉
∣ γ 12 ( τ ) ∣ = Γ 12 ( τ ) Γ 11 ( 0 ) Γ 22 ( 0 )
V = { 2 I 1 I 2 ( I 1 + I 2 ) } ∣ γ 12 ( τ ) ∣
V = ( I max − I min ) ( I max + I min ) ,
ℓ coh = ( 2 ℓ n 2 π ) ( λ 2 Δ λ ) .
L c ∼ 2 λ L g λ U ,
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