Alexis Chacon

Wannier-Bloch Approach to Localization in High-Harmonics Generation in Solids

Emission of high-order harmonics from solids provides a new avenue in attosecond science. On one hand, it allows to investigate fundamental processes of the non-linear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomena of HHG in an atomic gas) is the delocalization of the process, whereby an electron ionized from one site in the periodic lattice may recombine with any other. Here, we develop an analytic model, based on the localized Wannier wave functions in the valence band and delocalized Bloch functions in the conduction band. This Wannier-Bloch approach assesses the contributions of individual lattice sites to the HHG process, and hence addresses precisely the question of localization of harmonic emission in solids. We apply this model to investigate HHG in a ZnO crystal for two different orientations, corresponding to wider and narrower valence and conduction bands, respectively. Interestingly, for narrower bands, the HHG process shows significant localization, similar to harmonic generation in atoms. For all cases, the delocalized contributions to HHG emission are highest near the band-gap energy. Our results pave the way to controlling localized contributions to HHG in a solid crystal, with hard to overestimate implications for the emerging area of atto-nanoscience.

Numerical studies of light-matter interaction driven by plasmonic fields: The velocity gauge

Conventional theoretical approaches to model strong field phenomena driven by plasmonic fields are based on the length gauge formulation of the laser-matter coupling. Obviously, from the physical point of view, there exists no preferable gauge and, consequently, the predictions and outcomes should be independent of this choice. The use of the length gauge is mainly due to the fact that the quantity obtained from finite-element simulations of plasmonic fields is the plasmonic enhanced laser electric field rather than the laser vector potential. We develop, from first principles, the velocity gauge formulation of the problem and we apply it to the high-order-harmonic generation (HHG) in atoms. A comparison to the results obtained with the length gauge is made. As expected, it is analytically and numerically demonstrated that both gauges give equivalent descriptions of the emitted HHG spectra resulting from the interaction of a spatially inhomogeneous field and the single active electron model of the helium atom. We discuss, however, advantages and disadvantages of using different gauges in terms of numerical efficiency, which turns out to be very different. In order to understand it, we analyze the quantum mechanical results using time-frequency Gabor distributions. This analysis, combined with classical calculations based on solutions of the Newton equation, yields important physical insight into the electronic quantum paths underlying the dynamics of the harmonic generation process. The results obtained in this way also allow us to assess the quality of the quantum approaches in both gauges and put stringent limits on the numerical parameters required for a desired accuracy.

Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields

Above-threshold ionization (ATI) results from strong field laser-matter interaction and it is one of the fundamental processes that may be used to extract electron structural and dynamical information about the atomic or molecular target. Moreover, it can also be used to characterize the laser field itself. Here, we develop an analytical description of ATI, which extends the theoretical Strong Field Approximation (SFA), for both the direct and re-scattering transition amplitudes in atoms. From a non-local, but separable potential, the bound-free dipole and the re-scattering transition matrix elements are analytically computed. In comparison with the standard approaches to the ATI process, our analytical derivation of the re-scattering matrix elements allows us to study directly how the re-scattering process depends on the atomic target and laser pulse features -we can turn on and off contributions having different physical origins or corresponding to different physical mechanisms. We compare SFA results with the full numerical solutions of the time-dependent Schroedinger equation (TDSE) within the few-cycle pulse regime. Good agreement between our SFA and TDSE model is found for the ATI spectrum. Our model captures also the strong dependence of the photoelectron spectra on the carrier envelope phase of the laser field.

Double-electron ionization driven by inhomogeneous fields

Electron–electron correlation effects play a crucial role in our understanding of sequential (SDI) and non-sequential double ionization (NSDI) mechanisms. Here, we present a theoretical study of NSDI driven by plasmonic-enhanced spatial inhomogeneous fields. By numerically solving the time-dependent Schrödinger equation for a linear reduced model of He and a double-electron time-evolution probability analysis, we provide evidence for enhancement effects in NSDI showing that the double ionization yield at lower laser peak intensities is increased due to the spatial inhomogeneous character of plasmonic-enhanced field. The change in the emission direction of the double-ion as a function of the field inhomogeneity degree demonstrates that plasmonic-enhanced fields could configure a reliable instrument to control the ion emission. Furthermore, our quantum mechanical model, as well as classical trajectory Monte Carlo simulations, show that inhomogeneous fields are as well as a useful tool for splitting the binary and recoil processes in the rescattering scenario.

High-order harmonic generation in polyatomic systems

∗ICFO Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain §Centro de Láseres Pulsados (CLPU), Parque Científico, 37185 Villamayor, Salamanca, Spain ‡ICREA Pg. Lluís Companys 23, 08010 Barcelona, Spain †Institute of Physics of the ASCR, ELI-Beamlines project, Na Slovance 2, 182 21 Prague, Czech Republic