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A sub-cycle modulation in reflectivity is observed in bulk crystals subjected to intense laser fields. The effect provides a new way to probe attosecond dynamics in materials.

Recent progress in high power ultrafast short-wave and mid-wave infrared lasers has enabled gas-phase high harmonic generation (HHG) in the water window and beyond, as well as the demonstration of HHG in condensed matter. In this Perspective, we discuss the recent advancements and future trends in generating and characterizing soft X-ray pulses from gas-phase HHG and extreme ultraviolet (XUV) pulses from solid-state HHG. Then, we discuss their current and potential usage in time-resolved study of electron and nuclear dynamics in atomic, molecular and condensed matters. Different methods are demonstrated in recent years to produce attosecond pulses. Here, the authors discuss recent development and future prospects of the generation of such pulses from gases and solids and their potential applications in spectroscopy and ultrafast dynamics in atoms, molecules and other complex systems.

High-harmonic generation in a solid turns out to be sensitive to the interatomic bonding — a very useful feature that could enable the all-optical imaging of the interatomic potential. 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 diffraction 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 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 . Here, using single-crystal MgO, we demonstrate that high-harmonic generation in solids is sensitive to interatomic bonding. We find that harmonic efficiency 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.

Observations of high-harmonic generation from a single layer of a transition metal dichalcogenide opens the door to studying strong-field and attosecond phenomena in two-dimensional materials. 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 15 , 16 , including different symmetries 17 , 18 , 19 , access to individual valleys 20 , 21 and enhanced many-body interactions 22 , 23 , 24 , 25 . Here we demonstrate non-perturbative HHG from a monolayer MoS 2 crystal, with even and odd harmonics extending to the 13th order. The even orders are predominantly polarized perpendicular to the pump and are compatible with the anomalous transverse intraband current arising from the material’s Berry curvature, while the weak parallel component suggests the importance of interband transitions. The odd harmonics exhibit a significant enhancement in efficiency per layer compared to the bulk, which is attributed to correlation effects. The combination of strong many-body Coulomb interactions and widely tunable electronic properties in two-dimensional materials offers a new platform for attosecond physics.

High-harmonic spectroscopy, an ultrafast all-optical technique initially conceptualized in atomic and molecular systems, has now emerged as a powerful platform for studying the structure and dynamics of condensed matter. Unlike that in the gas phase, solid-state high-harmonic generation relies on the fundamental response from high atomic density and periodicity, leading to interband transitions and coherent driving of electrons and holes in their respective bands. These mechanisms make high-harmonic spectroscopy particularly sensitive to the electronic band structure, topological properties and many-body correlations in condensed media. An advantage of high-harmonic spectroscopy over other spectroscopic methods is its ability to probe ultrafast phenomena, capturing femto- to attosecond dynamics of multi-band and strongly correlated electron interactions in solids. In this Review, we discuss the latest experimental and theoretical advances in ultrafast high-harmonic spectroscopy of solids and provide perspectives for future research in this field. High-harmonic spectroscopy on solids is an ultrafast all-optical technique to study the structure and dynamics of materials. This Review discusses areas of condensed-matter physics where this technique can provide particular insight.

The prediction and realization of topological insulators have sparked great interest in experimental approaches to the classification of materials1–3. The phase transition between non-trivial and trivial topological states is important, not only for basic materials science but also for next-generation technology, such as dissipation-free electronics4. It is therefore crucial to develop advanced probes that are suitable for a wide range of samples and environments. Here we demonstrate that circularly polarized laser-field-driven high-harmonic generation is distinctly sensitive to the non-trivial and trivial topological phases in the prototypical three-dimensional topological insulator bismuth selenide5. The phase transition is chemically initiated by reducing the spin–orbit interaction strength through the substitution of bismuth with indium atoms6,7. We find strikingly different high-harmonic responses of trivial and non-trivial topological surface states that manifest themselves as a conversion efficiency and elliptical dichroism that depend both on the driving laser ellipticity and the crystal orientation. The origins of the anomalous high-harmonic response are corroborated by calculations using the semiconductor optical Bloch equations with pairs of surface and bulk bands. As a purely optical approach, this method offers sensitivity to the electronic structure of the material, including its nonlinear response, and is compatible with a wide range of samples and sample environments.Researchers demonstrate a method based on circularly polarized laser-field-driven high-harmonic generation for probing non-trivial and trivial topological phases in a three-dimensional topological insulator.

A direct comparison of high harmonic generation in the solid and gas phases of Ar and Kr reveals higher harmonics in these rare-gas solids caused by strong interband couplings; evidence of recollisions implies that gas-phase techniques for attosecond pulse generation and orbital tomography could be adapted for solids. Harmonics in solid- and gas-phase Ar and Kr In recent years the technique of high harmonic generation of light, known for decades for gases, has been be translated to solids, opening up a range of possible applications in table-top short-wavelength light sources and in exploring matter at ultrafast timescales. However, the underlying physical mechanisms are still under debate. Here Georges Ndabashimiye et al . report on high harmonic generation experiments in single-element systems, where modelling is not complicated by covalent bonding, as it has been for solids such as ZnSe and GaSe in previous studies. They study argon and krypton in both solid and gas form and observe high harmonic spectra for the solid phases that extend much further than for the gas form. This effect could be explained by strong interband couplings. 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 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . High harmonic generation is shown to occur fundamentally differently in solids and in dilute atomic gases 1 , 2 , 3 , 4 , 5 , 6 , 9 , 10 , 11 , 12 , 13 . How the microscopic mechanisms in the solid and the gas differ remains a topic of intense debate 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 14 , 15 , 16 , 17 , 18 . 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.

High-order harmonic generation is a nonlinear optical process that enables the creation of light pulses at frequencies much higher than that from a seed laser. The host medium for this interaction is typically a gas. Now, the process has been observed in a bulk crystalline solid with important implications for attosecond science. Harmonic generation is a general feature of driven nonlinear systems. In particular high-order harmonic generation (HHG) in atomic gases 1 is the basis for producing attosecond pulses 2 , 3 . In molecules and clusters, the existence of multiple ionization and recombination sites makes for richer dynamics allowing imaging of molecular orbitals 4 , 5 , higher conversion efficiency 6 and the possibility of extending the high-energy cutoff 7 . In the strong-field limit, HHG in bulk crystals is fundamentally different from that in the atomic case owing to the high density and periodic structure. Here we present the first observation of HHG in a bulk crystalline solid using a long-wavelength few-cycle laser. The harmonics spectra extend well beyond the band edge of the ZnO crystal, show a clear non-perturbative character and exhibit a cutoff that scales linearly with the electric field of the drive laser. Our results have important implications for the understanding of attosecond electron dynamics and other non-equilibrium band-structure-related phenomena in strongly driven bulk solids.

High-harmonic generation (HHG) is a signature optical phenomenon of strongly driven, nonlinear optical systems. Specifically, the understanding of the HHG process in rare gases has played a key role in the development of attosecond science1. Recently, HHG has also been reported in solids, providing novel opportunities such as controlling strong-field and attosecond processes in dense optical media down to the nanoscale2. Here, we report HHG from a low-loss, indium-doped cadmium oxide thin film by leveraging the epsilon-near-zero (ENZ) effect3–8, whereby the real part of the material’s permittivity in certain spectral ranges vanishes, as well as the associated large resonant enhancement of the driving laser field. We find that ENZ-assisted harmonics exhibit a pronounced spectral redshift as well as linewidth broadening, resulting from the photo induced electron heating and the consequent time-dependent ENZ wavelength of the material. Our results provide a new platform to study strong-field and ultrafast electron dynamics in ENZ materials, reveal new degrees of freedom for spectral and temporal control of HHG, and open up the possibilities of compact solid-state attosecond light sources.

High-harmonic generation in isolated atoms and molecules has been widely utilized in extreme ultraviolet photonics and attosecond pulse metrology. Recently, high-harmonic generation has been observed in solids, which could lead to important applications such as all-optical methods to image valance charge density and reconstruct electronic band structures, as well as compact extreme ultraviolet light sources. So far these studies are confined to crystalline solids; therefore, decoupling the respective roles of long-range periodicity and high density has been challenging. Here we report the observation of high-harmonic generation from amorphous fused silica. We decouple the role of long-range periodicity by comparing harmonics generated from fused silica and crystalline quartz, which contain the same atomic constituents but differ in long-range periodicity. Our results advance current understanding of the strong-field processes leading to high-harmonic generation in solids with implications for the development of robust and compact extreme ultraviolet light sources. Although higher harmonic generation from solids has become of interest in many fields, its observation is typically limited to crystalline solids. Here, the authors demonstrate that higher harmonics can be generated from amorphous solids.