We investigate theoretically high-harmonic generation (HHG) in bulk crystals exposed to intense midinfrared lasers with photon energies smaller than the band gap. The two main mechanisms, interband ...and intraband HHG, are explored. Our analysis indicates that the interband current neglected so far is the dominant mechanism for HHG. Saddle point analysis in the Keldysh limit yields an intuitive picture of interband HHG in solids similar to atomic HHG. Interband and intraband HHG exhibit a fundamentally different wavelength dependence. This signature can be used to experimentally distinguish between the two mechanisms in order to verify their importance.
Plasmonic antennas can enhance the intensity of a nanojoule laser pulse by localizing the electric field in their proximity. It has been proposed that the field can become strong enough to convert ...the fundamental laser frequency into high-order harmonics through an extremely nonlinear interaction with gas atoms that occupy the nanoscopic volume surrounding the antennas. However, the small number of gas atoms that can occupy this volume limits the generation of high harmonics. Here we use an array of monopole nano-antennas to demonstrate plasmon-assisted high-harmonic generation directly from the supporting crystalline silicon substrate. The high density of the substrate compared with a gas allows macroscopic buildup of harmonic emission. Despite the sparse coverage of antennas on the surface, harmonic emission is ten times brighter than without antennas. Imaging the high-harmonic radiation will allow nanometre and attosecond measurement of the plasmonic field thereby enabling more sensitive plasmon sensors while opening a new path to extreme-ultraviolet-frequency combs.
We experimentally demonstrate backward emission of high-harmonics of a near-infrared laser from MgO and Si crystals in the direction of specular reflection. We show that the variation of the ...high-harmonic power with the angle of incidence can be predicted with nonlinear reflection coefficients derived originally for perturbative nonlinearities. A comparison of transmission and reflection geometries suggests that backward-propagating high-harmonics are an excellent reference to study nonlinear propagation of intense light in solids. Backward emission will enable phase matching of the high-harmonic beam and the integration of the functionalities of extended gas-phase high-harmonic beamlines into a single optical element. The potential to achieve phase matching paves the way to solid-state based high-harmonic sources with higher flux than the best transmission-based sources, where high-harmonics are strongly absorbed by the crystal itself.
When intense light interacts with an atomic gas, recollision between an ionizing electron and its parent ion creates high-order harmonics of the fundamental laser frequency. This sub-cycle effect ...generates coherent soft X-rays and attosecond pulses, and provides a means to image molecular orbitals. Recently, high harmonics have been generated from bulk crystals, but what mechanism dominates the emission remains uncertain. To resolve this issue, we adapt measurement methods from gas-phase research to solid zinc oxide driven by mid-infrared laser fields of 0.25 volts per ångström. We find that when we alter the generation process with a second-harmonic beam, the modified harmonic spectrum bears the signature of a generalized recollision between an electron and its associated hole. In addition, we find that solid-state high harmonics are perturbed by fields so weak that they are present in conventional electronic circuits, thus opening a route to integrate electronics with attosecond and high-harmonic technology. Future experiments will permit the band structure of a solid to be tomographically reconstructed.
The band structure of matter determines its properties. In solids, it is typically mapped with angle-resolved photoemission spectroscopy, in which the momentum and the energy of incoherent electrons ...are independently measured. Sometimes, however, photoelectrons are difficult or impossible to detect. Here we demonstrate an all-optical technique to reconstruct momentum-dependent band gaps by exploiting the coherent motion of electron-hole pairs driven by intense midinfrared femtosecond laser pulses. Applying the method to experimental data for a semiconductor ZnO crystal, we identify the split-off valence band as making the greatest contribution to tunneling to the conduction band. Our new band structure measurement technique is intrinsically bulk sensitive, does not require a vacuum, and has high temporal resolution, making it suitable to study reactions at ambient conditions, matter under extreme pressures, and ultrafast transient modifications to band structures.
Perturbative optical nonlinearities induced by static electric fields1 have proven useful in visualizing dynamical function in systems including operating circuits2,3, electric and magnetic domain ...walls4, and biological matter5, and in controlling light for applications in silicon photonics6. Here, we extend field-induced second-harmonic generation to the non-perturbative regime. We demonstrate that static or transient fields up to terahertz (THz) frequencies applied to silicon and ZnO crystals generate even-order high harmonics. Images of the even harmonics confirm that static fields delivered with conventional electronics control the spatial properties of the high-harmonic emission. Extending our methodology to higher-harmonic photon energies7,8 paves the way for realizing active optics in the extreme ultraviolet and will allow imaging of operating electronic circuits9, of Si-photonic devices10 and of other functional materials11,12, with higher spatio-temporal resolution than perturbative methods. For THz spectroscopy, our method has the bandwidth to allow measurement of attosecond transients imprinted on THz waveforms.
Experiments on intense laser driven dielectrics have revealed population transfer to the conduction band to be oscillatory in time. This is in stark contrast to ionization in semiconductors and is ...currently unexplained. Current ionization theories neglect coupling between the valence and conduction band and therewith, the dynamic Stark shift. Our single-particle analysis identifies this as a potential reason for the different ionization behavior. The dynamic Stark shift increases the band gap with increasing laser intensities, thus suppressing ionization to an extent where virtual population oscillations become dominant. The dynamic Stark shift plays a role dominantly in dielectrics which, due to the larger band gap, can be exposed to significantly higher laser intensities.
High harmonic generation (HHG) in solids is investigated. We find that interband emission is dominant for the midinfrared laser driver frequencies, whereas intraband emission dominates the ...far-infrared range. Interband HHG is similar to atomic HHG and therewith opens the possibility to apply atomic attosecond technology to the condensed matter phase. Interband emission is investigated with a quasiclassical method, by which HHG can be modeled based on the classical trajectory analysis of electron-hole pairs. This analysis yields a simple approximate cutoff law for HHG in solids. Differences between HHG in atoms and solids are identified that are important for adapting atomic attosecond technology to make it applicable to condensed matter.
Short wavelength high-harmonic sources are undergoing intense development for applications in spectroscopy and microscopy. Despite recent progress in peak and average power, spatial control over ...coherent extreme ultraviolet (XUV) beams remains a formidable challenge due to the lack of suitable optical elements for beam shaping and control. Here we demonstrate a robust and precise approach that structures XUV high-order harmonics in space as they are emitted from a nanostructured MgO crystal. Our demonstration paves the way for bridging the numerous applications of shaped light beams from the visible to the short wavelengths, with potential uses for applications in microscopy and nanoscale machining.
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