Proposal for High-Energy Cutoff Extension of Optical Harmonics of Solid Materials Using the Example of a One-Dimensional ZnO Crystal.

We propose a novel approach based on the subcycle injection of carriers to extend the high-energy cutoff in solid-state high harmonics. The mechanism is first examined by employing the standard single-cell semiconductor Bloch equation (SC SBE) method for one-dimensional (1D) Mathieu potential model for ZnO subjected to the intense linearly polarized midinfrared laser field and extreme-ultraviolet pulse. Then, we use coupled solution of Maxwell propagation equation and SC SBE to propagate the fundamental laser field through the sample, and find that the high-harmonics pulse train from the entrance section of the sample can inject carriers to the conduction bands with attosecond timing, subsequently leading to a dramatic extension of high-energy cutoff in harmonics from the backside. We predict that for a peak intensity at 2×10^{11} W/cm^{2}, as a result of the self-seeding, the high-energy cutoff shifts from 20th (7.75 eV) order to around 50th (19.38 eV) order harmonics.

Solid-state harmonics beyond the atomic limit.

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.

All-Optical Probe of Three-Dimensional Topological Insulators Based on High-Harmonic Generation by Circularly Polarized Laser Fields.

We report the observation of an anomalous nonlinear optical response of the prototypical three-dimensional topological insulator bismuth selenide through the process of high-order harmonic generation. We find that the generation efficiency increases as the laser polarization is changed from linear to elliptical, and it becomes maximum for circular polarization. With the aid of a microscopic theory and a detailed analysis of the measured spectra, we reveal that such anomalous enhancement encodes the characteristic topology of the band structure that originates from the interplay of strong spin-orbit coupling and time-reversal symmetry protection. The implications are in ultrafast probing of topological phase transitions, light-field driven dissipationless electronics, and quantum computation.

Crystal orientation-dependent polarization state of high-order harmonics.

We analyze the crystal orientation-dependent polarization state of extreme ultraviolet high-order harmonics from bulk magnesium oxide crystals subjected to intense linearly polarized laser fields. We find that only along high-symmetry directions do high-order harmonics follow the polarization direction of the laser field. In general, there are strong deviations that depend on harmonic order, strength of the laser field, and crystal orientation. We use a real-space electron trajectory picture to understand the origin of polarization deviations. These results have implications in all-optical probing of electronic band structure in momentum space and valence charge distributions in real space, and in producing attosecond pulses with time-dependent polarization in compact setups.

Laser waveform control of extreme ultraviolet high harmonics from solids.

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.

Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor.

Nonlinear optical materials possess wide applications, ranging from terahertz and mid-infrared detection to energy harvesting. Recently, the correlations between nonlinear optical responses and certain topological properties, such as the Berry curvature and the quantum metric tensor, have attracted considerable interest. Here, we report giant room-temperature nonlinearities in non-centrosymmetric two-dimensional topological materials-the Janus transition metal dichalcogenides in the 1 T' phase, synthesized by an advanced atomic-layer substitution method. High harmonic generation, terahertz emission spectroscopy, and second harmonic generation measurements consistently show orders-of-the-magnitude enhancement in terahertz-frequency nonlinearities in 1 T' MoSSe (e.g., > 50 times higher than 2H MoS2 for 18th order harmonic generation; > 20 times higher than 2H MoS2 for terahertz emission). We link this giant nonlinear optical response to topological band mixing and strong inversion symmetry breaking due to the Janus structure. Our work defines general protocols for designing materials with large nonlinearities and heralds the applications of topological materials in optoelectronics down to the monolayer limit.

Redshift in the optical absorption of ZnO single crystals in the presence of an intense midinfrared laser field.

We report time-resolved electroabsorption of a weak probe in a 500 µm thick zinc-oxide crystal in the presence of a strong midinfrared pump in the tunneling limit. We observe a substantial redshift in the absorption edge that scales with the cube root of intensity up to 1 TW/cm(2) (0.38 eV cm(2/3) TW(-1/3)) after which it increases more slowly to 0.4 eV at a maximum applied intensity of 5 TW/cm(2). The maximum shift corresponds to more than 10% of the band gap. The change in scaling occurs in a regime of nonperturbative high-order harmonic generation where electrons undergo periodic Bragg scattering from the Brillouin zone boundaries. It also coincides with the limit where the electric field becomes comparable to the ratio of the band gap to the lattice spacing.

Attosecond science based on high harmonic generation from gases and solids.

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.

High-harmonic generation in amorphous solids.

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.