High harmonic generation (HHG) from gas-phase atoms (or molecules) has opened up a new frontier in ultrafast optics, where attosecond time resolution and angstrom spatial resolution are accessible. The fundamental physical pictures of HHG are always explained by the laser-induced recollision of particle-like electron motion, which lay the foundation of attosecond spectroscopy. In recent years, HHG has also been observed in solids. One can expect the extension of attosecond spectroscopy to the condensed matter if a description capable of resolving the ultrafast dynamics is provided. Thus, a large number of theoretical studies have been proposed to understand the underlying physics of solid HHG. Here, we revisit the recollision picture in solid HHG and show some challenges of current particle-perspective methods, and present the recently developed wave-perspective Huygens–Fresnel picture for understanding dynamical systems within the ambit of strong-field physics.

We investigate the orientation dependence of high-order harmonic generation (HHG) in graphene by solving the semiconductor Bloch equations. The tight-binding approximation including up to the third-nearest-neighbor atoms is used to model the graphene. Our simulations show that the orientation dependence of HHG shows different patterns for different harmonics. With increasing the laser intensity, these patterns become similar except for a double-peak structure shown in lower-order harmonics. The double-peak structure appears at high laser intensity due to the contribution of the harmonic perpendicular to the laser polarization direction. The harmonic yield is decomposed as the contributions of the nearest-neighbor interaction, the second-nearest-neighbor interaction, and the third-nearest-neighbor interaction. Our results show that the harmonic yields are mainly contributed by the nearest-neighbor interaction, but the third-nearest-neighbor interaction also plays an important role and modifies the orientation dependence.

We propose an all-optical method to reconstruct the transition dipole moment of solid materials. Our method is realized by high-order harmonic generation driving by a multicycle laser pulse. The relations between the transition dipole moment and the harmonic yield are established. It is found that the transition dipole phase is related to the intensity ratio of the neighboring odd and even harmonics, and the modulus of the transition dipole moment is related to the odd harmonics. We investigate the high-order harmonic generation in symmetric crystals and asymmetric crystals by solving the semiconductor Bloch equations and use these relations to successfully reconstruct their relative transition dipole moments.

There has been a longstanding doubt that the conversion efficiency of high harmonics in solids is much lower than expected at such a high level of electron density. To address this issue, we revisit the dynamical process of high harmonic generation (HHG) in solids in terms of wavelet interference. We find that the constructive interference among the wavelets has intrinsic consistency with the phase matching of coupled waves in nonlinear optics, which we call Bloch-wave phase matching. Our analysis indicates that most of the wavelets are out of phase and coherently canceled out during the solid HHG process, leading to only a small fraction of excited electrons effectively contributing to HHG. Consequently, the conversion from the excited electron to HHG is fairly low. Moreover, a Bloch-wave phase-matching scheme is proposed and a nearly 3 orders of magnitude enhancement of solid HHG can be achieved by engineering the crystal structures. Our Letter addresses a longstanding doubt and provides a novel idea and theoretical guidance for realizing efficient all-solid-state tabletop ultraviolet light sources.

We experimentally explore the fingerprint of the microscopic electron dynamics in second-order harmonic generation (SHG). It is shown that the interbond electron hopping induces a novel source of nonlinear polarization and plays an important role even when the driving laser intensity is 2 orders of magnitude lower than the characteristic atomic field. Our model predicts anomalous anisotropic structures of the SHG yield contributed by the interbond electron hopping, which is identified in our experiments with ZnO crystals. Moreover, a generalized second-order susceptibility with an explicit form is proposed, which provides a unified description in both the weak and strong field regimes. Our work reveals the nonlinear responses of materials at the electron scale and extends the nonlinear optics to a previously unexplored regime, where the nonlinearity related to the interbond electron hopping becomes dominant. It paves the way for realizing controllable nonlinearity on an ultrafast time scale.