High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations

Golde, D.; Meier, Torsten; Koch, S. W.

doi:10.1103/physrevb.77.075330

Cited by 338 publications

(289 citation statements)

References 28 publications

Supporting

Mentioning

280

Contrasting

Order By: Relevance

“…For oscillations in a single cosine band, the harmonics of the drive frequency are expected to extend on the order of ω B /ω (ref. 12), where ω B = eEd/h is the corresponding Bloch frequency for Bragg scattering of an electron of charge e from a lattice of periodicity d for a peak electric field, E. However, in our experiments, we detect harmonics up to the 25th order for conditions when ω B /ω ∼ 5. A more realistic LETTERS description for the mechanism would include the dressed band structure with both intra-and inter-band transitions as well as propagation effects.…”

mentioning

confidence: 48%

Observation of high-order harmonic generation in a bulk crystal

et al. 2010

View full text Add to dashboard Cite

Harmonic generation is a general feature of driven nonlinear systems. In particular high-order harmonic generation (HHG) in atomic gases 1 is the basis for producing attosecond pulses 2,3 . In molecules and clusters, the existence of multiple ionization and recombination sites makes for richer dynamics allowing imaging of molecular orbitals 4,5 , higher conversion efficiency 6 and the possibility of extending the high-energy cutoff 7 . In the strong-field limit, HHG in bulk crystals is fundamentally different from that in the atomic case owing to the high density and periodic structure. Here we present the first observation of HHG in a bulk crystalline solid using a long-wavelength few-cycle laser. The harmonics spectra extend well beyond the band edge of the ZnO crystal, show a clear non-perturbative character and exhibit a cutoff that scales linearly with the electric field of the drive laser. Our results have important implications for the understanding of attosecond electron dynamics and other non-equilibrium band-structure-related phenomena in strongly driven bulk solids.The HHG spectrum from a gas typically comprises a region of rapidly decreasing low orders that scale perturbatively followed by a slowly varying succession of higher orders that scale nonperturbatively with the strength of the drive laser 1 . At the tunnelling limit of strong-field ionization 8 , the non-perturbative harmonic generation process has been described semiclassically in a recollision model 9,10 consisting of three steps: tunnel ionization of an electron, its acceleration in the laser field, and its recombination to the parent ion with an energy release in the form of higher-energy photons-a coherent process that occurs on successive half-cycles of the laser pulse, leading to emission of odd harmonics. The single-atom maximum photon energy is 9,11h ω max = I p + 3.2U p , where I p is the ionization potential and U p = e 2 E 2 λ 2 /16π 2 mc 2 is the ponderomotive energy of the electron in the laser field. The amplitude of the maximum excursion of a recolliding electron is r max = eEλ 2 /4π 2 mc 2 . For the conditions of our experiments, E = 0.6 V Å −1 at λ = 3.25 µm, the atomic case would be U p = 5 eV and r max = 32 Å. The latter is many times the lattice constant of a typical crystal. Thus, we expect the possibility of ionization from one site and recombination on another; however, because of the lattice periodicity the process would still be coherent. We note that at this field strength, the potential across a lattice constant is comparable to the bandgap of a typical insulator. Therefore, the field cannot be thought of as a small perturbation to the crystal. The non-perturbative HHG from bulk crystals has been considered theoretically 12-14 but has never been observed experimentally until now.Previously, experimental observation of non-perturbative HHG in solids was only in reflection geometry [15][16][17][18] perturbative harmonics below the band edge up to the seventh order were produced by exciting semiconducting ZnSe with...

show abstract

mentioning

confidence: 48%

Observation of high-order harmonic generation in a bulk crystal

et al. 2010

View full text Add to dashboard Cite

show abstract

“…Our model based on intraband dynamics of carriers in the bulk is not able to account for the appearance of even harmonics under these circumstances. To more fully understand the experimental results for ZnO (or other semiconductors), the coupling between bands [6] and other effects such as the broken symmetry at the surface need to be further explored.…”

Section: Numerical Results For Zinc Oxidementioning

confidence: 99%

Pulsed high harmonic generation of light due to pumped Bloch oscillations in noninteracting metals

Freericks¹,

Liu²,

Kemper³

et al. 2012

Phys. Scr.

View full text Add to dashboard Cite

We derive a simple theory for high-order harmonic generation due to pumping a noninteracting metal with a large amplitude oscillating electric field. The model assumes that the radiated light field arises from the acceleration of electrons due to the time-varying current generated by the pump, and also assumes that the system has a constant density of photoexcited carriers, hence it ignores the dipole excitation between bands (which would create carriers in semiconductors). We examine the circumstances under which odd harmonic frequencies would be expected to dominate the spectrum of radiated light, and we also apply the model to real materials like ZnO, for which high-order harmonic generation has already been demonstrated in experiments.

show abstract

“…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].…”

mentioning

confidence: 99%

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

et al. 2018

View full text Add to dashboard Cite

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...

show abstract

High harmonics generated in semiconductor nanostructures by the coupled dynamics of optical inter- and intraband excitations

Cited by 338 publications

References 28 publications

Observation of high-order harmonic generation in a bulk crystal

Observation of high-order harmonic generation in a bulk crystal

Pulsed high harmonic generation of light due to pumped Bloch oscillations in noninteracting metals

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

Contact Info

Product

Resources

About