Generalized molecular orbital tomography

Vozzi, C.; Negro, Matteo; Calegari, Francesca; Sansone, G.; Nisoli, M.; Silvestri, S. De; Stagira, S.

doi:10.1038/nphys2029

Cited by 399 publications

(401 citation statements)

References 24 publications

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“…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 .…”

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confidence: 99%

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%

Anisotropic high-harmonic generation in bulk crystals

2016

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“…This error is also observed in the previous works especially for the σ orbital. Besides the limited spectrum range, the imaging errors may also result from several other reasons, such as the discrete sampling in the frequency domain with the interval of 2ω L , and the SFA and singleactive-electron approximation used in the theoretical model [7][8][9][10]12]. In the MOT process, when the Stark phase is approximately subtracted by using the analytical expression derived in [18], the main structure of the target orbital is also successfully reproduced in both the length and velocity forms.…”

Section: Tomographic Reconstructionmentioning

confidence: 94%

“…By applying this method to a series of aligned molecules, they accomplished a tomographic reconstruction of the highest occupied molecular orbital (HOMO) of N 2 . Since then, the MOT has attracted a great deal of attention for its great significance in uncovering the basic properties of molecules and chemical reactions [7][8][9][10][11][12][13]. In most of the works, the target molecular orbitals are symmetric with either gerade or ungerade symmetry, while the MOT of nonsymmetric orbitals is more difficult.…”

Section: Introductionmentioning

confidence: 99%

“…Ref. [12,26]. Therefore, in this work we suggest a method to solve this problem by using a tailored laser pulse with the relatively high intensity.…”

Section: Simulating and Controlling The Hhgmentioning

confidence: 99%

“…The intensity and wavelength of the laser pulse we use are 1 × 10 14 W/cm 2 and 1.5 µm respectively. Employing the 1.5 µm mid-IR laser source allows us to extend the harmonic spectrum considerably with a low laser intensity below the barrier suppression intensity [12,31], which ensures the validity of the used MO-ADK model and strong-field approximation (SFA) in our theoretical description. Another benefit of keeping the intensity low is that it will reduce the effect of the Stark shift.…”

Section: Simulating and Controlling The Hhgmentioning

confidence: 99%

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Influence of large permanent dipoles on molecular orbital tomography

Zhu¹,

Qin²,

Zhang³

et al. 2013

Opt. Express

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The influence of large permanent dipoles on molecular orbital tomography via high-order harmonic generation (HHG) is investigated in this work. It is found that, owing to the modification of the angle-dependent ionization rate resulting from the Stark shift, the one-side-recollision condition for the tomographic imaging can not be satisfied even with the few-cycle driving pulses. To overcome this problem, we employ a tailored driving pulse by adding a weak low-frequency pulse to the few-cycle laser pulse to control the HHG process and the recollision of the continuum electrons are effectively restricted to only one side of the core. Then we carried out the orbital reconstruction in both the length and velocity forms. The results show that, the orbital structure can only be successfully reproduced by using the dipole matrix elements projected perpendicular to the permanent dipole in both forms.

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2024

Physics of Solar Energy and Energy Storage

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Generalized molecular orbital tomography

Cited by 399 publications

References 24 publications

Anisotropic high-harmonic generation in bulk crystals

Anisotropic high-harmonic generation in bulk crystals

Influence of large permanent dipoles on molecular orbital tomography

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