High-harmonic generation from Bloch electrons in solids

Wu, Mengxi; Ghimire, Shambhu; Reis, David A.; Schafer, Kenneth J.; Gaarde, Mette B.

doi:10.1103/physreva.91.043839

Cited by 336 publications

(372 citation statements)

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“…S1) and a fine k-grid (∆k 0.01) have been found to be crucial prerequisites for convergence to the ab-initio TDDFT simulation. Another important convergence parameter is the number of VBs and CBs [27,28]. The present results (Fig.…”

supporting

confidence: 53%

“…Several simplifying models have been proposed accounting for Bloch oscillations within a single band ("intraband harmonics") [22,23] and non-linear interband polarization ("interband harmonics") [15,24,25] as sources of HHG. Most descriptions involve the semiconductor Bloch equations (SBE, [26]) using input parameters on various levels of sophistication and a varying number of energy bands [27,28]. Recently, first simulations employing time-dependent density functional theory (TDDFT, [29]) have become available [30,31].…”

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confidence: 99%

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Ab initio multiscale simulation of high-order harmonic generation in solids

et al. 2018

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High-harmonic generation by a highly non-linear interaction of infrared laser fields with matter allows for the generation of attosecond pulses in the XUV spectral regime. This process, well established for atoms, has been recently extended to the condensed phase. Remarkably well pronounced harmonics up to order ∼ 30 have been observed for dielectrics. We present the first ab-initio multiscale simulation of solid-state high-harmonic generation. We find that mesoscopic effects of the extended system, in particular the realistic sampling of the entire Brillouin zone, the pulse propagation in the dense medium, and the inhomogeneous illumination of the crystal have a strong effect on the formation of clean harmonic spectra. Our results provide a novel explanation for the formation of clean harmonics and have implications for a wide range of non-linear optical processes in dense media.PACS numbers: 42.65. Ky, 42.50.Hz, 72.20.Ht The generation of high harmonics (HHG) in the nonlinear interaction of intense ultrashort infrared (IR) laser pulses with matter has turned out to be a highly successful route towards the generation of attosecond pulses in the EUV and XUV spectral regimes [1][2][3][4]. It has become the workhorse of investigation of a vast array of electronic processes on the attosecond time scale [5]. Expanding the range of accessible photon energies and intensities faces, however, fundamental limitations. Experimental and theoretical investigations have established a scaling of the cut-off energy E cut ∝ λ 2 for HHG from atoms in the gas phase raising hopes to reach ever higher photon energies by increasing the wavelength λ of the driving laser pulse. However, the intensity in the cut-off region was found to scale unfavorably I cut ∝ λ −5.3 due to the large spatial dispersion of the electron wave packet upon return to its parent atom [6][7][8][9][10]. Propagation effects in gas filled capillaries have been found to partially offset this suppression at high λ [11].Extending HHG to the condensed phase promises to overcome some of these limitations to enable compact and brighter light sources and to open up the novel field of solid-state photonics on the attosecond scale. The recent observation of HHG in solids for intensities below the damage threshold [12][13][14][15][16][17][18] suggests opportunities for controlling electronic dynamics [16,17] and for an alloptical reconstruction of the band structure [19].The observed solid-state HHG substantially differs from the corresponding atomic spectra. For example, while for atoms the cut-off frequency ω HHG cut scales linearly with the (peak) intensity I 0 of the driving pulse [20,21] One major puzzle has remained so far unresolved: while many experiments display remarkably "clean" harmonic spectra with pronounced peaks near multiples of the driving frequency (odd multiples when inversion symmetry is preserved) all the way up to the cutoff frequency, corresponding simulations display a noisy spectrum lacking any clear harmonic structure over a wide range of fre...

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confidence: 99%

Ab initio multiscale simulation of high-order harmonic generation in solids

et al. 2018

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“…In the interband picture 6,27 , the harmonic signal is proportional to the dipole moment 30 , q unit cell U * CB,k (r)rU VB,k (r)d 3 r, where q is the electronic charge, r is the position, and U * CB,k and U VB,k are the periodic part of the conduction band (CB) and valence band (VB) Bloch functions, respectively. Therefore, the VB Bloch function could be evaluated in principle with the knowledge of the CB Bloch function and vice versa.…”

Section: Methodsmentioning

confidence: 99%

“…We find that harmonic e ciency 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.High-harmonic generation (HHG) in bulk crystal is attributed to the sub-cycle electronic motion driven by an intense laser field [2][3][4][5][6][7][8][9][10][11] . There has been a growing interest in utilizing HHG to probe the electronic structure of solids 8,9,11 .…”

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Anisotropic high-harmonic generation in bulk crystals

2016

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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 di raction 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 3-11 . Here, using single-crystal MgO, we demonstrate that high-harmonic generation in solids is sensitive to interatomic bonding. We find that harmonic e ciency 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.High-harmonic generation (HHG) in bulk crystal is attributed to the sub-cycle electronic motion driven by an intense laser field [2][3][4][5][6][7][8][9][10][11] . There has been a growing interest in utilizing HHG to probe the electronic structure of solids 8,9,11 . Vampa et al. reconstructed the momentum-dependent bandgap of ZnO along the -M direction using HHG from a two-colour driving field 11 . Luu et al. retrieved the energy dispersion of the lowest conduction band of SiO 2 assuming that the harmonics are produced by the intraband currents 8 . The dependence of solid-state HHG on the coupling of multiple electronic bands has also been identified with the production of even harmonics in GaSe 9 and the emergence of a second plateau in rare-gas solids 12 . These findings show the possibility of using solidstate HHG to probe the electronic band structures in solids, but the analyses are so far limited to one dimension. For a complete electronic structure, it is desirable to exploit the microscopic process to measure the periodic potential in three dimensions (real space). This is analogous to tomographic imaging of a molecule, where the three-dimensional spatial information (that is, orbital wavefunction) of the target molecule is extracted [13][14][15] . Those measurement techniques are based critically on the dependence of HHG efficiency on molecular alignment with respect to the laser field 16 .In this letter, we demonstrate the strong sensitivity of HHG to the atomic-scale structure in the cubic wide-bandgap crystal MgO. First, using a linearly polarized field, we measure a highly anisotropic angular distribution in high-harmonic signal-despite the isotropic linear and weakly anisotropic nonlinear optical properties of the cubic crystal in the perturbative regime 17 . Second, we observe a strong ellipticity dependence of the HHG yield similar to the gas-phase HHG 18 for small elliptic...

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Plasmon‐Enhanced Circular Polarization High‐Harmonic Generation from Silicon

Ren,

Chen,

Wang

et al. 2024

Advanced Optical Materials

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High harmonics of circular polarization can be directly generated by monochromatic circularly polarized incident light owing to the high density and stable structure of crystal media. If the arrangement of multiple coplanar atoms in the unit structure of the crystal exhibits rotational symmetry, the polarization state of the high harmonics generated from the crystal follows specific selection rules that have been observed in the 2D crystal medium. In addition, the geometric symmetry of the coplanar atom distribution is related to the orientation of cubic crystals. This implies that only the polarization along a specific crystal orientation can achieve a selection of high‐harmonic polarization states. However, this is a very weak process in cubic crystals owing to the attenuation of crystal anisotropy to circularly polarized light and the dependence of the electron transition rate on the crystal orientation. In this study, plasmonic nanoantennas are designed on silicon crystal films to enhance this process. The harmonic emission is more than ten times brighter than that without nanoantennas and conformed to the selection rules for high harmonics. The research results offer a new approach for deepultraviolet space filtering, carrier control, and the development of compact extremeultraviolet light sources.

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High-harmonic generation from Bloch electrons in solids

Cited by 336 publications

References 65 publications

Ab initio multiscale simulation of high-order harmonic generation in solids

Ab initio multiscale simulation of high-order harmonic generation in solids

Anisotropic high-harmonic generation in bulk crystals

Plasmon‐Enhanced Circular Polarization High‐Harmonic Generation from Silicon

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