Strong-field laser excitation of solids can produce extremely nonlinear electronic and optical behaviour. As recently demonstrated, this includes the generation of high harmonics extending into the vacuum-ultraviolet and extreme-ultraviolet regions of the electromagnetic spectrum. High harmonic generation is shown to occur fundamentally differently in solids and in dilute atomic gases. How the microscopic mechanisms in the solid and the gas differ remains a topic of intense debate. Here we report a direct comparison of high harmonic generation in the solid and gas phases of argon and krypton. Owing to the weak van der Waals interaction, rare (noble)-gas solids are a near-ideal medium in which to study the role of high density and periodicity in the generation process. We find that the high harmonic generation spectra from the rare-gas solids exhibit multiple plateaus extending well beyond the atomic limit of the corresponding gas-phase harmonics measured under similar conditions. The appearance of multiple plateaus indicates strong interband couplings involving multiple single-particle bands. We also compare the dependence of the solid and gas harmonic yield on laser ellipticity and find that they are similar, suggesting the importance of electron-hole recollision in these solids. This implies that gas-phase methods such as polarization gating for attosecond pulse generation and orbital tomography could be realized in solids.

We study the generation of high harmonic radiation by Bloch electrons in a model transparent solid driven by a strong mid-infrared laser field. We solve the single-electron time-dependent Schrödinger equation (TDSE) using a velocity-gauge method [New J. Phys. 15, 013006 (2013)] that is numerically stable as the laser intensity and number of energy bands are increased. The resulting harmonic spectrum exhibits a primary plateau due to the coupling of the valence band to the first conduction band, with a cutoff energy that scales linearly with field strength and laser wavelength. We also find a weaker second plateau due to coupling to higher-lying conduction bands, with a cutoff that is also approximately linear in the field strength. To facilitate the analysis of the time-frequency characteristics of the emitted harmonics, we also solve the TDSE in a time-dependent basis set, the Houston states [Phys. Rev. B 33, 5494 (1986)], which allows us to separate inter-band and intra-band contributions to the time-dependent current. We find that the inter-band and intraband contributions display very different time-frequency characteristics. We show that solutions in these two bases are equivalent under an unitary transformation but that, unlike the velocity gauge method, the Houston state treatment is numerically unstable when more than a few low lying energy bands are used.

Attosecond pulses are generated by a macroscopic number of ionizing atoms interacting with a focused laser pulse, via the process of high harmonic generation. The physics of their generation consists of an interplay between the microscopic laser–atom interaction and macroscopic effects due to ionization and phase matching in the nonlinear medium. In this review, we focus on a complete understanding of the way in which attosecond pulses arrive at a target where they can be characterized and used in an experiment. We discuss a number of results from calculations of attosecond pulse generation obtained by simultaneous solution of the time-dependent Schrödinger equation and the Maxwell wave equation. These results, which allow for a clean separation of microscopic and macroscopic factors, illustrate how macroscopic effects are used to select attosecond pulses from the radiation that is emitted by atoms interacting with a strong laser field.

We report the generation, compression, and delivery on target of ultrashort extreme-ultraviolet light pulses using external amplitude and phase control. Broadband harmonic radiation is first generated by focusing an infrared laser with a carefully chosen intensity into a gas cell containing argon atoms. The emitted light then goes through a hard aperture and a thin aluminum filter that selects a 30-eV bandwidth around a 30-eV photon energy and synchronizes all of the components, thereby enabling the formation of a train of almost Fourier-transform-limited single-cycle 170 attosecond pulses. Our experiment demonstrates a practical method for synthesizing and controlling attosecond waveforms.

We investigate the spectral and temporal structure of high harmonic emission from argon exposed to an infrared laser field and its second harmonic. For a wide range of generating conditions, trains of attosecond pulses with only one pulse per infrared cycle are generated. The synchronization necessary for producing such trains ensures that they have a stable pulse-to-pulse carrier envelope phase, unlike trains generated from one color fields, which have two pulses per cycle and a pi phase shift between consecutive pulses. Our experiment extends the generation of phase stabilized few cycle pulses to the extreme ultraviolet regime.