Semiclassical theory of terahertz multiple-harmonic generation in semiconductor superlattices

Feise, Michael W.; Citrin, D. S.

doi:10.1063/1.125380

Cited by 37 publications

(47 citation statements)

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“…In the case of solids, electrons are promoted to discrete conduction bands, where they do not evolve freely. This leads, for instance, to a different linear field dependence for the cutoff energy [6], different time-frequency characteristics of the harmonic emission between atoms and solids [8,11,16], and a different ellipticity dependence [6,17].Historically, HHG in solids was first discussed in terms of Bloch oscillations (i.e., pure intraband dynamics) [18][19][20], and more recently mainly analyzed using simplified models based on numerical solutions of the semiconductor Bloch equations [21][22][23] treating the complex, coupled interband and intraband dynamics, with the exception of the ab initio simulations of Ref. [24].…”

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“…Historically, HHG in solids was first discussed in terms of Bloch oscillations (i.e., pure intraband dynamics) [18][19][20], and more recently mainly analyzed using simplified models based on numerical solutions of the semiconductor Bloch equations [21][22][23] treating the complex, coupled interband and intraband dynamics, with the exception of the ab initio simulations of Ref. [24].…”

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

et al. 2017

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“…The processes underlying solid-state HHG have remained a matter of debate. 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].…”

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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 DL occurs immediately after the field application and becomes unobservable in the time τ due to the ac BOs dephasing. A stationary current is established in the SL after the time τ and its spectral constitution can be significantly different from that of ac BOs, especially in the presence of the static component [8,13,18]. In contrast to the DL, the SIT occurs only after time τ from the field application and can exist for a long time (mach larger than τ) [17,19] and, consequently, has more chances to be observed experimentally.…”

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confidence: 98%

Electron Bloch oscillations and electromagnetic transparency of semiconductor superlattices in multi-frequency electric fields

2009

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We examine phenomenon of electromagnetic transparency in semiconductor superlattices (having various miniband dispersion laws) in the presence of multi-frequency periodic and nonperiodic electric fields. Effects of induced transparency and spontaneous generation of static fields are discussed. We paid a special attention on a self-induced electromagnetic transparency and its correlation to dynamic electron localization. Processes and mechanisms of the transparency formation, collapse, and stabilization in the presence of external fields are studied.In particular, we present the numerical results of the time evolution of the superlattice current in an external biharmonic field showing main channels of transparency collapse and its partial stabilization in the case of low electron density superlattices.

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Semiclassical theory of terahertz multiple-harmonic generation in semiconductor superlattices

Abstract: Articles you may be interested inUltrafast optical generation and remote detection of terahertz sound using semiconductor superlattices Appl. Phys. Lett. 91, 023115 (2007);

Cited by 37 publications

References 8 publications

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

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

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

Electron Bloch oscillations and electromagnetic transparency of semiconductor superlattices in multi-frequency electric fields

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