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Reconstructing attosecond pulses

November 4, 2015

A new attosecond pulse reconstruction modality uses an algorithm derived from ptychography.

Extracting information from experiments on the dynamics of atoms, molecules or solids, i.e. on the dynamics of their nuclei and electronic charge distribution, is essential for a physical understanding and the verification of theoretical models. The fastest electronic processes, e.g. photo-ionization, Auger decay, tunneling ionization, or shake-up, happen on attosecond time scales. However, before probing of attosecond phenomena became feasible, a number of technical challenges had to be addressed. One of the most pressing challenges was to develop techniques to characterize the electric field of an isolated attosecond pulse or a train of such pulses as they are generated in the process of high-order harmonic generation.
Here, Thomas Feurer, Ursula Keller and co-workers present a new modality for attosecond pulse characterization which is derived from a phase retrieval scheme widely used in lensless imaging, namely ptychography. It is related to the solution of the phase problem in crystallography as proposed by Hoppe and was first demonstrated experimentally at visible wavelengths. In ptychography a real space object, in particular its amplitude and phase, is reconstructed iteratively from a series of far-field diffraction measurements.

Applying ptychography to the reconstruction of temporal rather than spatial objects requires operating in one dimension with the conjugated variables time and frequency. The unknown temporal object is to be reconstructed iteratively from a series of far-field diffraction measurements, i.e. spectra. Each of those is recorded after delaying the coherent illumination pulse with respect to the temporal object with the time delay being smaller than the temporal support of the illumination pulse. The temporal resolution is primarily limited by the range of spectral amplitudes which can be recorded with a sufficiently high signal-to-noise ratio (SNR). Recently, the authors have shown that ptychography can indeed be applied to reconstruct temporal objects if the illumination pulse is fully characterized. They have subsequently shown that ptychography is a very powerful technique for ultrafast pulse characterization. Here, the authors show that the concept can be extended to attosecond pulse characterization or photo-electron streaking experiments in general.
Fig. 1. Spectrogram of attosecond pulses. First row: Isolated bandwidth-limited attosecond pulse of 0.24 fs duration. Second row: Same attosecond pulse with a quartic phase of 2 · 10−4 fs4. Third row: Pulse train consisting of nine unchirped pulses each 0.24 fs long. Fourth row: Same pulse train with a quadratic phase of 2 · 10−2 fs2.

In the context of this publication, the authors offer a minimal example MATLAB code that demonstrates the capabilities of this method based on four example data sets. Use of this software is free under the condition, that you include a reference to the original publication (below) whenever you make use of it.
Download software (10.56 MB).

The paper was choosen for inclusion in OSA Spotlight on Optics.


Lucchini, M., Brügmann, M.H., Ludwig, A., Gallmann, L., Keller, U., and Feurer, T. (2015) Ptychographic reconstruction of attosecond pulses. Optics Express  23,  29502-29513 (10.1364/OE.23.029502) Lucchini-2015 (2.31 MB).

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