We present an inversion method called pBasex aimed at reconstructing the original Newton sphere of expanding charged particles from its two-dimensional projection by fitting a set of basis functions with a known inverse Abel integral. The basis functions have been adapted to the polar symmetry of the photoionization process to optimize the energy and angular resolution while minimizing the CPU time and the response to the cartesian noise that could be given by the detection system. The method presented here only applies to systems with a unique axis of symmetry although it can be adapted to overcome this restriction. It has been tested on both simulated and experimental noisy images and compared to the Fourier-Hankel algorithm and the original Cartesian basis set used by [Dribinski et al.Rev. Sci. Instrum. 73, 2634 (2002)], and appears to give a better performance where odd Legendre polynomials are involved, while in the images where only even terms are present the method has been shown to be faster and simpler without compromising its accuracy.

manyChirality is ubiquitous in nature and fundamental in science, from particle physics to metamaterials. The most established technique of chiral discrimination -photoabsorption circular dichroism -relies on the magnetic properties of a chiral medium and yields an extremely weak chiral response. We propose and demonstrate a new, orders of magnitude more sensitive type of circular dichroism in neutral molecules: photoexitation circular dichroism. It does not rely on weak magnetic effects, but takes advantage of the coherent helical motion of bound electrons excited by ultrashort circularly polarized light. It results in an ultrafast chiral response and the efficient excitation of a macroscopic chiral density in an initially isotropic ensemble of randomly oriented chiral molecules. We probe this excitation without 1 arXiv:1612.08764v1 [physics.atm-clus] 27 Dec 2016 Here d 01 , d 02 and d 12 are the dipole transition vectors connecting the ground |0 and the two excited states |1 , |2 (Fig. 1b), ∆E 21 is the energy spacing between the excited states. For more than two states, Eq.(1) will contain the sum over all pairs of excited states n, m, leading to oscillations at all relevant frequencies ∆E nm . As a function of time the induced dipole vector maps out a helix (Fig. 3 1b) and the z-component of the helical current is j P XCD z ∝ σ[ d 01 × d 02 ] d 12 ∆E 21 cos(∆E 21 t). (2) Both d P XCD z and j P XCD z are quintessential chiral observables (see e.g. 19, 20 ). Indeed, both are proportional to the light helicity σ = ±1 and to the triple product of three vectors [ d 01 × d 02 ] d 12 . This product presents a fundamental measure of chirality: it changes sign upon reflection and thus has an opposite sign for left and right enantiomers. For randomly oriented non-chiral molecules d P XCD z = j P XCD z = 0. Eqs.(1,2) lead to the following conclusions. First, the coherent excitation of electronic states leads to a charge displacement in the light propagation direction. Hence, a macroscopic dipole d P XCD z and the corresponding chiral density are created in the excited states, with a chiral current oscillating out of phase for the two enantiomers. Second, PXCD requires no magnetic or quadrupole effects. Hence, it is orders of magnitude stronger than standard photoabsorption CD. While photoabsorption CD exploits the helical pitch of the laser field in space, PXCD takes advantage of the sub-cycle rotation of the light field in time and is inherently ultrafast. Indeed, PXCD arises only if the excitation dipoles d 01 , d 02 are non-collinear: for the angle φ between the two transition dipoles, the PXCD (Eqs. (1,2)) is proportional to σ sin(φ). Since σ = ±1, σ sin(φ) = sin(σφ) = sin(σωτ ), where ω is light frequency and τ = φ/ω is the required time for the light field to rotate by the angle φ. PXCD vanishes if the coherence between excited states |1 and |2 is lost and reflects dynamical symmetry breaking in an isotropic medium.The oscillations of the PXCD signal Eqs.(1,2) appear to suggest that probing it requires the

International audienceCircular dichroism in the extreme ultraviolet range is broadly used as a sensitive structural probe of matter, from the molecular photoionization of chiral species1, 2, 3 to the magnetic properties of solids4. Extending such techniques to the dynamical regime has been a long-standing quest of solid-state physics and physical chemistry, and was only achieved very recently5 thanks to the development of femtosecond circular extreme ultraviolet sources. Only a few large facilities, such as femtosliced synchrotrons6, 7 or free-electron lasers8, are currently able to produce such pulses. Here, we propose a new compact and accessible alternative solution: resonant high-order harmonic generation of an elliptical laser pulse. We show that this process, based on a simple optical set-up, delivers bright, coherent, ultrashort, quasi-circular pulses in the extreme ultraviolet. We use this source to measure photoelectron circular dichroism on chiral molecules, opening the route to table-top time-resolved femtosecond and attosecond chiroptical experiments

We studied the photoionization of 2-pyridone and its tautomer, 2-hydroxypyridine by means of VUV synchrotron radiation coupled to a velocity map imaging electron/ion coincidence spectrometer. The photoionization efficiency (PIE) spectrum is composed of steps. The state energies of the [2-pyridone](+) cation in the X[combining tilde] ground and A excited electronic states, as well as of the [2-hydroxypyridine](+) cation in the electronic ground state, are determined. The slow photoelectron spectra (SPES) are dominated by the 0(0)(0) transitions to the corresponding electronic states together with several weaker bands corresponding to the population of the pure or combination vibrational bands of the cations. These vibrationally-resolved spectra compare very well with state-of-the-art calculations. Close to the ionization thresholds, the photoionization of these molecules is found to be mainly dominated by a direct process whereas the indirect route (autoionization) may contribute at higher energies.

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