Harmonics In Solids Research Articles

Bloch-Wave Phase Matching of High Harmonic Generation in Solids.

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.

Non-linear propagation effects of intense femtosecond pulses on below bandgap harmonics in solids

The non-linear propagation of the intense near-infrared (NIR) driving field in crystals poses a challenge and can offer an opportunity to control the spectral properties of harmonics in solids. Here, we have investigated the non-linear propagation effects in wide bandgap dielectrics such as Magnesium Oxide (MgO), Chromium (Cr) doped MgO (Cr: MgO), Sapphire (Sa) crystals, and fused silica (FS). Furthermore, we have generated second and third harmonics (TH) and measured the linear polarization dependence of harmonics in these thin solids to explore the non-linear response at a strong field. We observe spectral shifts and broadening of the driving field spectrum which is imprinted on the harmonics. We attribute these effects to the strong photoionization, generation of free-carrier density, and self-phase modulation effects. This work shows the sensitivity to control the spectral profile of harmonics by manipulating the driving field, showing the possibility of new tailored solid-state ultraviolet sources for optical diagnostics.

Electron-electron interactions and high-order harmonics in solids

The generation of high-order harmonics in bulk systems is a young and fast-growing area of research. Beginning in 2011 with the pioneering studies of high-order harmonic generation in bulk dielectrics, significant progress has already been made in understanding the details of the microscopic mechanisms behind this phenomenon, such as the role of intra- and interband polarization, the contribution of the electronic band structure and dipole moments to the harmonic spectrum, and the effects of structural and electronic symmetry. However, the role of electron-electron correlations in the excited system is much less understood. In this work, we study the role of these effects in the high-order harmonic spectrum by using the Time-Dependent Density Functional Theory (TDDFT) approach with the Dynamical Mean-Field Theory (DMFT) exchange-correlation kernel. In this approximation, one takes into account the time-resolved on-site electron-electron interactions. As we demonstrate, the correlation effects significantly affect the high-harmonic spectrum, most importantly through ultrafast modification of the interband polarization of the system.

Angle-resolved high-order harmonics in wurtzite-type ZnO

High-order harmonics in solids provide a method of analyzing the intraband and interband dynamics of a solid driven by an ultrafast laser. This study analyzed the contributions of intraband and interband dynamics based on angle-resolved high-order harmonics. According to the simulations and experiments, we found that the angular divergences of the harmonics have an evident boundary at the bandgap when the laser is polarized along the asymmetric direction, which is primarily invoked by the interplay of an interband transition and an intraband electron movement, and the intraband and interband dynamics have different sensitivities of the spatial phase of driving laser.

Generation, manipulation, and application of high-order harmonics in solids

The generation of high-order harmonics based on the interaction between ultrafast intense laser and matter provides a platform for studying the light-matter interaction in the non-perturbative region. It is also the main route to generating desktop extreme ultraviolet light source and attosecond pulse. The non-perturbative solid high-order harmonic involves the core content of ultrafast strong field physics, condensed matter physics, materials science, information science and other fields. Since it was first experimentally observed in 2011, it has rapidly become the research frontier of strong field physics and attosecond science. This review summarizes the research progress and important applications of solid high-order harmonics from the perspective of an experimentalist. Firstly, distinct characteristics are shown for solid high-order harmonic by comparing the dependence of harmonic yield and cut-off energy on driving laser parameters with gas high-order harmonic. Then, the progress of manipulation and application are highlighted for solid high-order harmonic, including the precise control of harmonic yield, polarization, space-time distribution through the design of target structure or laser field, as well as the application of solid high-order harmonic spectroscopy in the fields of material structure characterization and ultrafast electron dynamics. Finally, the future is prospected for the study of solid high-order harmonics.

Spectral caustics of high-order harmonics in one-dimensional periodic crystals.

We theoretically investigate the spectral caustics of high-order harmonics in solids. We analyze the one-dimensional model of high-order harmonic generation (HHG) in solids and find that apart from the caustics originating from the van Hove singularities in the energy band structure, another kind of catastrophe enhancement also emerges in solids when the different branches of electron-hole trajectories generating high-order harmonics coalesce into a single branch. We solve the time-dependent Schrödinger equation in terms of the periodic potential and demonstrate the control of this kind of singularity in HHG with the aid of two-color laser fields. The diffraction patterns of the harmonic spectrum near the caustics agree well with the interband electron-hole recombination trajectories predicted by the semiconductor semiclassical equation. This work is expected to improve our understanding of the HHG dynamics in solids and enable us to manipulate the harmonic spectrum by adjusting the driving field parameters.

Ultrafast intraband electron dynamics of preexcited SiO2.

Intraband high-order harmonics in solids reflect the nonlinear motion of carriers in the energy bands and have important applications. In general, multiple energy bands contribute to the intraband harmonics. We reveal the interference mechanism of intraband harmonics between electrons and holes by using the k-resolved semiclassical intraband model. The model gives a quantitative relationship between the intraband radiation yield, the energy band dispersion, and the laser parameters. Based on a preexcitation scheme, we present a method to reconstruct energy bands by using the intraband harmonics. We simulate the intraband harmonics of photo-carriers polarized by a bias field. The variation of harmonic yields as a function of a delay time results from the k-resolved energy band dispersion and reflects the Bloch oscillation of photo-carriers driven by the bias field.

Generation of high harmonics in solids

SynopsisWe have developed an ab-initio multi-scale simulation to model light synthesis and propagation through transparent media accounting for the non-linear response of the solid. Using this approach we are able to investigate the build-up of high harmonics induced by strong and short laser pulses along the propagation direction inside a large band-gap dielectric, diamond. Detailed analysis of the results allows to identify minimum requirements necessary to realistically model laser-solid interactions.

Multi-Frequency Piezoelectric Micromachined Ultrasonic Transducers

In this paper multi-frequency piezoelectric MEMS ultrasonic transducers (pMUTs) are designed, characterized and tested for nondestructive evaluation (NDE) of solids. The transducers operate in flexural mode, and are tuned to three different frequencies namely 1 MHz, 1.5 MHz and 2 MHz. The microstructural layers consist of aluminum nitride (AlN) as an active sensing layer sandwiched between metal and doped silicon electrodes. pMUTs are designed with octagonal and circular membranes. The vibration of silicon membrane assists piezoelectric element to convert energies. The transducers are modeled numerically to obtain their dynamic characteristics. Piezoelectric Multi-User MEMS Processes (PiezoMUMPs) are utilized to manufacture pMUTs. The electromechanical characterization shows that the circular design has higher figure of merit as compared to the octagonal design due to more uniform stress distribution transferred between silicon and AlN layers. It is demonstrated that the piezeoelectric layer should be deposited up to the inflection point of diaphragm deformation. This avoids the signal cancellation due to opposite polarization. The performance of pMUTs as receiver is evaluated to detect the creep damage by implementing nonlinear ultrasonic testing (NLUT). NLUT is based on detecting higher harmonics in solids due to heterogeneity in materials. Significant amplification in the second harmonics is obtained due to highly narrowband and low damping characteristics of pMUTs that improves the resolution of NLUT to detect subwavelength damage. Higher harmonics can be detected using small footprint pMUT device, which is not possible with conventional piezoelectric transducers. This allows better spatial resolution of nonlinear measurement.

Orientation dependence of temporal and spectral properties of high-order harmonics in solids

We investigate the connection between crystal symmetry and temporal and spectral properties of high-order harmonics in solids. We calculate the orientation-dependent harmonic spectrum driven by an intense, linearly polarized infrared laser field, using a momentum-space description of the generation process in terms of strong-field-driven electron dynamics on the band structure. We show that the orientation dependence of both the spectral yield and the subcycle time profile of the harmonic radiation can be understood in terms of the coupling strengths and relative curvatures of the valence band and the low-lying conduction bands. In particular, we show that in some systems this gives rise to a rapid shift of a quarter optical cycle in the timing of harmonics in the secondary plateau as the crystal is rotated relative to the laser polarization. We address recent experimental results in MgO [Y. S. You et al., Nat. Phys. 13, 345 (2017).] and show that the observed change in orientation dependence for the highest harmonics can be interpreted in the momentum space picture in terms of the contributions of several different conduction bands.

Detection of acoustic second harmonics in solids using a heterodyne laser interferometer

Acoustic second harmonic generation in solids is difficult to measure and often requires careful sample preparation. In this paper, a heterodyne interferometer modified to measure acoustic fundamental and second harmonics is presented. It requires relatively little sample preparation and it provides noncontact, wideband, absolute, and pointlike measurements. It is shown that the output of an ideal heterodyne interferometer does not contain any even harmonics of a single-frequency acoustic signal. Odd harmonics, however, are produced in calculable amounts. A detailed model of the interferometer is introduced to account for various sources of spurious second harmonics and the model is experimentally verified. Three methods of calibration for the absolute measurement of surface displacement are presented. Measurements of the nonlinearity parameter, β, of a fused quartz sample are shown to agree with literature values.