All-Optical Reconstruction of Crystal Band Structure

Vampa, Giulio; Hammond, T. J.; Thiré, Nicolas; Schmidt, Bruno E.; Légaré, François; McDonald, Chris; Brabec, Thomas; Klug, D. D.; Corkum, P. B.

doi:10.1103/physrevlett.115.193603

Cited by 506 publications

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“…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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confidence: 99%

“…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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confidence: 99%

Anisotropic high-harmonic generation in bulk crystals

2016

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“…Because of a higher electronic density, solids are one promising route towards compact, brighter HHG sources. The recent observation of nonperturbative HHG in solids without damage [6][7][8][9][10], extending even beyond the atomic limit [10], has opened the door to the observation and control of attosecond electron dynamics in solids [8,9,11], all-optical band-structure reconstruction [12], and solid-state sources of isolated extreme-ultraviolet pulses [9,11]. However, in contrast to HHG from gases, the microscopic mechanism underlying HHG from solids is still controversially debated in the attoscience community, in some cases casting doubts on the validity of the proposed microscopic model and resulting in confusion about the correct interpretation of experimental data.…”

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Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids

et al. 2017

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An accurate analytic model describing the microscopic mechanism of high-harmonic generation (HHG) in solids is derived. Extensive first-principles simulations within a time-dependent density-functional framework corroborate the conclusions of the model. Our results reveal that (i) the emitted HHG spectra are highly anisotropic and laser-polarization dependent even for cubic crystals; (ii) the harmonic emission is enhanced by the inhomogeneity of the electron-nuclei potential; the yield is increased for heavier atoms; and (iii) the cutoff photon energy is driver-wavelength independent. Moreover, we show that it is possible to predict the laser polarization for optimal HHG in bulk crystals solely from the knowledge of their electronic band structure. Our results pave the way to better control and optimize HHG in solids by engineering their band structure. DOI: 10.1103/PhysRevLett.118.087403 Atoms and molecules interacting with strong laser pulses emit high-order harmonics of the fundamental driving laser field. The high-harmonic generation (HHG) in gases is routinely used nowadays to produce isolated attosecond pulses [1][2][3][4] and coherent radiation ranging from the visible to soft x rays [5]. Because of a higher electronic density, solids are one promising route towards compact, brighter HHG sources. The recent observation of nonperturbative HHG in solids without damage [6][7][8][9][10], extending even beyond the atomic limit [10], has opened the door to the observation and control of attosecond electron dynamics in solids [8,9,11], all-optical band-structure reconstruction [12], and solid-state sources of isolated extreme-ultraviolet pulses [9,11]. However, in contrast to HHG from gases, the microscopic mechanism underlying HHG from solids is still controversially debated in the attoscience community, in some cases casting doubts on the validity of the proposed microscopic model and resulting in confusion about the correct interpretation of experimental data. Various competing simplified models have been proposed but they often are based on strong approximations and a priori assumptions, often stating that there is a strong similarity with the processes underlying atomic-gas HHG emission. However, it is clear that many-body effects due to the crystalline structure of solids and the fermionic nature of interaction electrons play a decisive role that fundamentally distinguishes the solid from the gas case. It is the scope of the present work to unravel within an ab initio approach what the impact is of the underlying electronic band structure of the solids in the observed HHG emission.The process of HHG from gases is by now well understood in terms of the three-step model [13][14][15] in which electrons are first promoted from the ground state of the atom (or molecule) to the continuum, then accelerated by the electric field, and finally recombine with the parent ion. With this simple, intuitive model most of the observed effects are well described, in particular, the dependence of the harmonic cutoff energ...

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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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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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All-Optical Reconstruction of Crystal Band Structure

Cited by 506 publications

References 37 publications

Anisotropic high-harmonic generation in bulk crystals

Anisotropic high-harmonic generation in bulk crystals

Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids

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

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