Sincrotrone Trieste

Direct Spectro-Temporal Characterization of Femtosecond Extreme-Ultraviolet Pulses

We propose a method for a straightforward characterization of the temporal shape of femtosecond pulses in the extreme-ultraviolet/soft X-ray spectral region. The approach is based on the presence of a significant linear frequency chirp in the pulse. This allows to establish an homothetic relation between the pulse spectrum and its temporal profile. The theoretical approach is reminiscent of the one employed by Fraunhofer for describing far-field diffraction. As an application, we consider the case of a seeded free-electron laser (FEL). Theory is successfully benchmarked with numerical simulations and with experimental data collected on the FERMI@Elettra FEL. The proposed method provides FEL users with an on-line, shot-to-shot spectro-temporal diagnostic for time-resolved experiments. New light sources generating extreme-ultraviolet/soft X-ray (XUV) femtosecond pulses are among the most powerful tools for investigating the fundamental properties of matter, in gas, liquid or solid-state phases [1–3]. In fact, short wavelength (i.e., high-energy) radiation allows to achieve atomic spatial resolutions and to probe core levels of atomic and molecular bound states. Short pulses are instead required for the study of ultra-fast chemical and physical reactions, allowing separate access to electron, spin and lattice relaxation constants. A large number of these studies rely on pump-probe techniques [4], in which two light pulses with adjustable time delay and different wavelengths are used to investigate the dynamics of a given process. For the success of such experiments, a detailed knowledge and a complete control of the spectro-temporal properties of light pulses are essential. This should include the possibility for users to monitor and control the spectro-temporal features of XUV femtosecond pulses in real time (i.e., during experiments). Nowadays, measuring the spectrum of XUV pulses is not an issue, whereas getting access to the temporal information is a more challenging task. Indeed, several methods have been proposed to measure the phase and shape of femtosecond pulses in the infrared, visible and near ultraviolet spectral ranges [5, 6]. However, in the XUV domain, the strong absorption of solid-state crystals does not enable non-linear optical effects on which temporal characterizations usually rely, making them significantly more difficult. Usually, the duration of XUV pulses is determined by means of cross-correlation schemes, based on the photo-ionization of an atomic gas by the measured XUV pulse, “dressed”by a time-delayed femtosecond infrared laser [7–9]. Based on this and other approaches, several methods have been developed for the temporal characterization of ultra-short pulses generated by single-pass free-electron lasers (FEL) [10–12] and high

Vlasov equation for long-range interactions on a lattice.

We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state, and a dispersion relation, which depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turns out to depend on the mode number. When this state is unstable, the growth rates are also functions of the mode number. Explicit calculations are performed for the α-Hamiltonian mean field model with 0≤α<1, for which the mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.