Structure- and laser-gauges for the semiconductor Bloch equations in high-harmonic generation in solids

The semiconductor Bloch equations (SBEs) are routinely used for simulations of strong-field laser-matter interactions in condensed matter. In systems without inversion or time-reversal symmetries, the Berry connections and transition dipole phases (TDPs) must be included in the SBEs, which in turn requires the construction of a smooth and periodic structure gauge for the Bloch states. Here, we illustrate a general approach for such a structure-gauge construction for topologically trivial systems. Furthermore, we investigate the SBEs in the length and velocity gauges, and discuss their respective advantages and shortcomings for the high-harmonic generation (HHG) process. We find that in cases where we require dephasing or separation of the currents into interband and intraband contributions, the length gauge SBEs are computationally more efficient. In calculations without dephasing and where only the total current is needed, the velocity gauge SBEs are structure-gauge independent and are computationally more efficient. We employ two systems as numerical examples to highlight our findings: an 1D model of ZnO and the 2D monolayer hexagonal boron nitride (h-BN). The omittance of Berry connections or TDPs in the SBEs for h-BN results in nonphysical HHG spectra. The structure- and laser-gauge considerations in the current work are not restricted to the HHG process, and are applicable to all strong-field matter simulations with SBEs

HHG in solids: Multi-band couplings leading to multiple plateaus

We discuss the theory of HHG in solids, relevant to recent experimental observations of multiple plateaus in HHG from solid argon. A multi-band model explains the cutoffenergies and relative strengths of the different plateaus

Time-frequency representations of high order harmonics

We calculate time-frequency representations (TFRs) of high-order short pulse harmonics generated in the interaction between neon atoms and an intense laser field, including macroscopic effects of propagation and phase matching in the non-linear medium. The phase structure of the harmonics is often complicated and the TFR can help to resolve the different components of this structure. The harmonic pulses exhibit an overall negative chirp, which can be attributed in part to the intensity dependence of the harmonic dipole phase. In some cases, the harmonic field separates in the time-frequency domain and clearly exhibits two different chirps. We also compute an experimental realization of a TFR (using Frequency Resolved Optical Gating, FROG) for a high harmonic. Due to the complicated time structure of the harmonics, the FROG trace is visually complex. © 2001 Optical Society of America

Imperfect Recollisions in High-Harmonic Generation in Solids

We theoretically investigate high-harmonic generation in hexagonal boron nitride with linearly polarized laser pulses. We show that imperfect recollisions between electron-hole pairs in the crystal give rise to an electron-hole-pair polarization energy that leads to a double-peak structure in the subcycle emission profiles. An extended recollision model (ERM) is developed that allows for such imperfect recollisions, as well as effects related to Berry connections, Berry curvatures, and transition-dipole phases. The ERM illuminates the distinct spectrotemporal characteristics of harmonics emitted parallel and perpendicularly to the laser polarization direction. Imperfect recollisions are a general phenomenon and a manifestation of the spatially delocalized nature of the real-space wave packet, they arise naturally in systems with large Berry curvatures, or in any system driven by elliptically polarized light

Space-time considerations in the phase locking of high harmonics

The combination of several high order harmonics can produce an attosecond pulse train, provided that the harmonics are locked in phase to each other. We present calculations that evaluate the degree of phase locking that is achieved in argon and neon gases interacting with an intense, 50 fs laser pulse, for a range of macroscopic conditions. We find that phase locking depends on both the temporal and the spatial phase behavior of the harmonics, as determined by the interplay between the intrinsic dipole phase and the phase matching in the nonlinear medium. We show that, as a consequence of this, it is not possible to compensate for a lack of phase locking by purely temporal phase manipulation

Laser-induced bound-state phases in high-order harmonic generation

We present single-molecule and macroscopic calculations showing that laser-induced Stark shifts contribute significantly to the phase of high-order harmonics from polar molecules. This is important for orbital tomography, where phases of field-free dipole matrix elements are needed in order to reconstruct molecular orbitals. We derive an analytical expression that allows the first-order Stark phase to be subtracted from experimental measurements

Quantum path distributions for high-order harmonics in rare gas atoms

We present quantum path distributions of high-order harmonics produced by rare gas atoms interacting with an intense 810 nm laser field, obtained by numerical integration of the time-dependent Schrodinger equation within the single active electron approximation. We find that the distributions are sensitive to the atomic potentials, and differ from the distributions predicted by the strong field approximation. We demonstrate that these differences can lead to significant differences in the time-frequency behavior of the harmonics produced in a macroscopic nonlinear medium

Characterizing Anomalous High-Harmonic Generation in Solids

Anomalous high-harmonic generation (HHG) arises in certain solids when irradiated by an intense laser field, as the result of a nonlinear perpendicular current akin to a Hall current. Here, we theoretically characterize the anomalous HHG mechanism, via development of an ab-initio methodology for strong-field laser-solid interaction that allows a rigorous decomposition of the total current. We identify two key characteristics of the anomalous harmonic yields: an overall increase with laser wavelength; and pronounced minima at certain intensities or wavelengths around which the emission time profiles drastically change. Such signatures can be exploited to disentangle the anomalous harmonics from the competing interband harmonics, and thus pave way for the experimental identification and time-domain control of pure anomalous harmonics.Comment: 7 pages, 4 figure