Solid-state harmonics beyond the atomic limit

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

doi:10.1038/nature17660

Cited by 440 publications

(386 citation statements)

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“…2) is at variance with a large number of solid-state HHG experiments finding a clean harmonic spectrum [12,15,17,18]. A recently employed phenomenological approach to "purify" the spectrum has invoked including very short dephasing times of the order of a fraction of an optical cycle (T 2 ≈ T 0 /4 [32]) or of about 1 fs [17,33] into the microscopic description.…”

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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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“…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].…”

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

et al. 2018

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“…The ellipticity dependence in solids is also material-dependent; for example, it is relatively weak in ZnO (ref. 2), but fairly strong in rare-gas solids 12 . As these crystals exhibit different bonding character, the nature of the bonding in solids seems to play an important role in defining the solid-state strongfield response.…”

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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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“…[3] a wide bandgap ZnO target (3.2 eV) was excited by a pulse with central wavelength of 3.25 µm, meaning that at least 9 photons are required for an excitation from the valance to the conduction band [see also [4] for more details]. Recently, a direct comparison of high-order harmonic generation in the solid and gas phases of argon and krypton has been reported [5].…”

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confidence: 99%

“…Recently, a direct comparison of high-order harmonic generation in the solid and gas phases of argon and krypton has been reported [5].…”

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Gauge invariance and interpretation of interband and intraband processes in high-order harmonic generation from bulk solids

Földi¹

2017

Phys. Rev. B

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A theoretical model for high-order harmonic generation (HHG) in bulk solids is considered. Our approach treats laser-induced inter-and intraband currents on an equal footing. The sum of these currents is the source of the high-order harmonic radiation, and does not depend on the particular electromagnetic gauge we choose to describe the process. On the other hand, as it is shown using analytic and numerical calculations, the distinction between intra-and interband dynamics is gauge dependent, implying that the interpretation of the process of HHG using these terms requires carefulness.Introduction The idea that solid state targets illuminated by strong, short near infrared pulses can produce coherent X-ray radiation [1] or even attosecond electromagnetic bursts [2] preceded the first experiments that demonstrated the appearance of high-order harmonics (up to order of 25) in the spectra of strongly driven solid state samples. In Ref.[3] a wide bandgap ZnO target (3.2 eV) was excited by a pulse with central wavelength of 3.25 µm, meaning that at least 9 photons are required for an excitation from the valance to the conduction band [see also [4] for more details]. Recently, a direct comparison of high-order harmonic generation in the solid and gas phases of argon and krypton has been reported [5].Theoretically, semiconductor Bloch-equations were applied to describe the problem [6], a closed-form expression were given to the subcycle-resolved transition rate of electrons between bands [7], appearance of attosecond pulses were predicted [8], semiclassical [9] and a saddlepoint [10] analysis were performed and the role of an indirect bandgap was also investigated [11].

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Solid-state harmonics beyond the atomic limit

Cited by 440 publications

References 27 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

Gauge invariance and interpretation of interband and intraband processes in high-order harmonic generation from bulk solids

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