High-harmonic generation (HHG) in bulk solids permits the exploration of materials in a new regime of strong fields and attosecond timescales [1][2][3][4][5][6] . The generation process has been discussed in the context of strongly driven electron dynamics in single-particle bands [7][8][9][10][11][12][13][14] . Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the HHG process The recent observation of HHG in bulk solids provides a new approach to attosecond photonics and has opened up exciting opportunities for the study of strong-field and ultrafast electron dynamics in the condensed phase [1][2][3][4][5][6]

The microscopic valence electron density determines the optical, electronic, structural and thermal properties of materials. However, current techniques for measuring this electron charge density are limited: for example, scanning tunnelling microscopy is confined to investigations at the surface, and electron di raction requires very thin samples to avoid multiple scattering 1 . Therefore, an optical method is desirable for measuring the valence charge density of bulk materials. Since the discovery of high-harmonic generation (HHG) in solids 2 , there has been growing interest in using HHG to probe the electronic structure of solids 3-11 . Here, using single-crystal MgO, we demonstrate that high-harmonic generation in solids is sensitive to interatomic bonding. We find that harmonic e ciency is enhanced (diminished) for semi-classical electron trajectories that connect (avoid) neighbouring atomic sites in the crystal. These results indicate the possibility of using materials' own electrons for retrieving the interatomic potential and thus the valence electron density, and perhaps even wavefunctions, in an all-optical setting.High-harmonic generation (HHG) in bulk crystal is attributed to the sub-cycle electronic motion driven by an intense laser field [2][3][4][5][6][7][8][9][10][11] . There has been a growing interest in utilizing HHG to probe the electronic structure of solids 8,9,11 . Vampa et al. reconstructed the momentum-dependent bandgap of ZnO along the -M direction using HHG from a two-colour driving field 11 . Luu et al. retrieved the energy dispersion of the lowest conduction band of SiO 2 assuming that the harmonics are produced by the intraband currents 8 . The dependence of solid-state HHG on the coupling of multiple electronic bands has also been identified with the production of even harmonics in GaSe 9 and the emergence of a second plateau in rare-gas solids 12 . These findings show the possibility of using solidstate HHG to probe the electronic band structures in solids, but the analyses are so far limited to one dimension. For a complete electronic structure, it is desirable to exploit the microscopic process to measure the periodic potential in three dimensions (real space). This is analogous to tomographic imaging of a molecule, where the three-dimensional spatial information (that is, orbital wavefunction) of the target molecule is extracted [13][14][15] . Those measurement techniques are based critically on the dependence of HHG efficiency on molecular alignment with respect to the laser field 16 .In this letter, we demonstrate the strong sensitivity of HHG to the atomic-scale structure in the cubic wide-bandgap crystal MgO. First, using a linearly polarized field, we measure a highly anisotropic angular distribution in high-harmonic signal-despite the isotropic linear and weakly anisotropic nonlinear optical properties of the cubic crystal in the perturbative regime 17 . Second, we observe a strong ellipticity dependence of the HHG yield similar to the gas-phase HHG 18 for small elliptic...

We observe off-axis phase-matched terahertz generation in long air-plasma filaments produced by femtosecond two-color laser focusing. Here, phase matching naturally occurs due to off-axis constructive interference between locally generated terahertz waves, and this determines the far-field terahertz radiation profiles and yields. For a filament longer than the characteristic two-color dephasing length, it emits conical terahertz radiation in the off-axis direction, peaked at 4-7° depending on the radiation frequencies. The total terahertz yield continuously increases with the filament length, well beyond the dephasing length. The phase-matching condition observed here provides a simple method for scalable terahertz generation in elongated plasmas.

We investigate high-power terahertz (THz) generation in two-color laser filamentation using terawatt (TW) lasers including a 0.5 TW, 1 kHz system, as well as 2 and 30 TW systems both operating at 10 Hz. With these lasers, we study the macroscopic effect in filamentation that governs THz output energy yields and radiation profiles in the far field. We also characterize the radiation spectra at a broad range of frequencies covering radio-micro-waves to infrared frequencies. In particular, our 1 kHz THz source can provide high-energy (>1 µJ), high average power (>1 mW), intense (>1 MV cm −1 ) and broadband (0.01-60 THz) THz radiation via two-color filamentation in air. Based on our scaling law, an ∼30 TW laser can produce >0.1 mJ of THz radiation with multigigawatt peak power in ∼1.5 m long filamentation.

Solid-state high-harmonic sources offer the possibility of compact, high-repetition-rate attosecond light emitters. However, the time structure of high harmonics must be characterized at the sub-cycle level. We use strong two-cycle laser pulses to directly control the time-dependent nonlinear current in single-crystal MgO, leading to the generation of extreme ultraviolet harmonics. We find that harmonics are delayed with respect to each other, yielding an atto-chirp, the value of which depends on the laser field strength. Our results provide the foundation for attosecond pulse metrology based on solid-state harmonics and a new approach to studying sub-cycle dynamics in solids.

We demonstrate high-field (>8 MV/cm) terahertz generation at a high-repetition-rate (1 kHz) via two-color laser filamentation. Here, we use a cryogenically cooled femtosecond laser amplifier capable of producing 30 fs, 15 mJ pulses at 1 kHz as a driver, along with a combination of a thin dual-wavelength half-waveplate and a Brewster-angled silicon window to enhance terahertz generation and transmission. We also introduce a cost-effective, uncooled microbolometer camera for real-time terahertz beam profiling with two different modes.

We investigate the mechanism of elliptically polarized terahertz (THz) pulse generation in femtosecond two-color laser-produced plasma. In the case of in-line laser focusing, we observe the THz polarization evolves from linear to elliptical with increasing plasma length. This ellipticity arises from two combined effects--successive polarization rotation of local THz plasma sources, caused by laser phase and polarization modulations, and the velocity mismatch between laser and THz, which produces an elliptical THz pulse from a series of time-delayed, polarization-rotating local THz fields.

Two-dimensional (2-D) transverse photocurrent generation is studied and applied to control and optimize terahertz energy and polarization in two-color, laser-produced air filaments. A full control of terahertz output is demonstrated and explained in the context of 2-D photocurrent model.