Marcello F. Ciappina

Attosecond physics at the nanoscale

Recently two emerging areas of research, attosecond and nanoscale physics, have started to come together. Attosecond physics deals with phenomena occurring when ultrashort laser pulses, with duration on the femto- and sub-femtosecond time scales, interact with atoms, molecules or solids. The laser-induced electron dynamics occurs natively on a timescale down to a few hundred or even tens of attoseconds (1 attosecond  =  1 as  =  10-18 s), which is comparable with the optical field. For comparison, the revolution of an electron on a 1s orbital of a hydrogen atom is  ∼152 as. On the other hand, the second branch involves the manipulation and engineering of mesoscopic systems, such as solids, metals and dielectrics, with nanometric precision. Although nano-engineering is a vast and well-established research field on its own, the merger with intense laser physics is relatively recent. In this report on progress we present a comprehensive experimental and theoretical overview of physics that takes place when short and intense laser pulses interact with nanosystems, such as metallic and dielectric nanostructures. In particular we elucidate how the spatially inhomogeneous laser induced fields at a nanometer scale modify the laser-driven electron dynamics. Consequently, this has important impact on pivotal processes such as above-threshold ionization and high-order harmonic generation. The deep understanding of the coupled dynamics between these spatially inhomogeneous fields and matter configures a promising way to new avenues of research and applications. Thanks to the maturity that attosecond physics has reached, together with the tremendous advance in material engineering and manipulation techniques, the age of atto-nanophysics has begun, but it is in the initial stage. We present thus some of the open questions, challenges and prospects for experimental confirmation of theoretical predictions, as well as experiments aimed at characterizing the induced fields and the unique electron dynamics initiated by them with high temporal and spatial resolution.

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.

Extending the high-order harmonic generation cutoff by means of self-phase-modulated chirped pulses

In this letter we propose a complementary approach to extend the cutoff in high-order harmonic generation (HHG) spectra beyond the well established limits. Inspired by techniques normally used in the compression of ultrashort pulses and supercontinuum generation, we show this extension can be achieved by means of a nonlinear phenomenon known as self-phase-modulation (SPM). We demonstrated that relatively long optical pulses, around 100 fs full-width half maximum (FWHM), non linearly chirped by SPM, are able to produce a considerable extension in the HHG cutoff. We have also shown it is possible control this extension by setting the length of the nonlinear medium. Our study was supported by the numerical integration of the time-dependent Schrodinger equation joint with a complete classical analysis of the electron dynamic. Our approach can be considered as an alternative to the utilization of optical parametric amplification (OPA) and it can be easily implemented in usual facilities with femtosecond laser systems. This technique also preserves the harmonic yield in the zone of the plateau delimited by I p + 3.17Up law, even when the driven pulses contain larger wavelength components.

High-order harmonic generation driven by plasmonic fields: a new route towards the generation of UV and XUV photons?

We present theoretical investigations of high-order harmonic generation (HHG) resulting from the interaction of noble gases with different kind of temporally and spatially synthesized laser fields. These fields, based on localized surface plasmons, are produced when, for instance, a metal nanoparticle or nanostructure, is illuminated by a few-cycle laser pulse. The enhanced field, which largely depends on the geometrical shape of the metallic nanostructure, has a strong spatial dependency in a scale comparable to the one where the electron dynamics takes place. We demonstrate that the spatial nonhomogeneous character of this laser field plays an important role in the HHG process and leads to a significant increase of the harmonic cutoff energy and modifications in the electron trajectories. The use of metal nanostructures appears to be an alternative way of generating coherent XUV light with a laser field whose characteristics can be spatially synthesized locally.

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.

Carrier-Wave Rabi-Flopping Signatures in High-Order Harmonic Generation for Alkali Atoms

We present a theoretical investigation of carrier-wave Rabi flopping in real atoms by employing numerical simulations of high-order harmonic generation (HHG) in alkali species. Given the short HHG cutoff, related to the low saturation intensity, we concentrate on the features of the third harmonic of sodium (Na) and potassium (K) atoms. For pulse areas of 2π and Na atoms, a characteristic unique peak appears, which, after analyzing the ground state population, we correlate with the conventional Rabi flopping. On the other hand, for larger pulse areas, carrier-wave Rabi flopping occurs, and is associated with a more complex structure in the third harmonic. These characteristics observed in K atoms indicate the breakdown of the area theorem, as was already demonstrated under similar circumstances in narrow band gap semiconductors.