Uncovering extreme nonlinear dynamics in solids through time-domain field analysis

P. D. Keathley, S. V. B. Jensen, M. Yeung, M. R. Bionta, and L. B. Madsen

Phys. Rev. B 107, 054302 – Published 3 February 2023

Abstract

We show that time-domain analysis of high harmonic generation from solids with subcycle resolution and broad, continuous spectral coverage is now experimentally viable due to the emergence of sensitive, solid-state optical-field-sampling techniques. With this experimental opportunity in mind, we use time-dependent density functional theory to explore what insights such a time-domain, field-resolved analysis might uncover about the extreme nonlinear electron dynamics responsible for high-harmonic generation (HHG) within solids. We illustrate how simple, visual analysis of the time-domain fields provides clear insight into the interplay between intra- and interband dynamical processes underlying nonlinear light generation when spectral signatures do not. Importantly, we observe conditions where the dominant emission mechanism suddenly switches from intra- to interband over a subcycle region of time within the pulse envelope of the driving wave form. This complex field response means that phase-resolved techniques requiring a certain level of periodicity are, in general, inadequate for the study of HHG from solids. We find that field-resolved measurements having both subcycle time resolution and broad, nearly continuous spectral coverage are required for a general understanding of solid-state HHG.

Received 21 October 2022
Revised 23 January 2023
Accepted 24 January 2023

DOI:https://doi.org/10.1103/PhysRevB.107.054302

Physics Subject Headings (PhySH)

Nonlinear DynamicsAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

P. D. Keathley ^1,*,†, S. V. B. Jensen ^2,*, M. Yeung¹, M. R. Bionta ^1,‡, and L. B. Madsen ^2,§

¹Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark

^*These authors contributed equally to this work.
^†pdkeat2@mit.edu
^‡Present address: Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA.
^§bojer@phys.au.dk

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 107, Iss. 5 — 1 February 2023

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Simulating harmonic field sampling using solid-state TIPTOE. (a) Notional schematic of the field-sampling experiment using TIPTOE. Abbreviations: BS, beam-splitter; CM, curved mirror; DM, dichroic mirror; HCM, holey curved mirror. (b) Calculation of $Γ (E_{G} (t))$ representing the instantaneous electron tunneling response from the metal surface. (c) Magnitude of the sampling transfer function $| {\tilde{H}}_{Det} (ω) |$ . (d)–(f) Comparison of direct TDDFT field output and the result of our simulation of the sampling response. (d) TDDFT output $| E_{sig} {(t) |}^{2}$ (shaded green line) and sampled field response $| E_{sampled} {(t) |}^{2}$ (solid red line) as a function of time. The insets denote temporal regions dominated by intra- or interband generation, which is described in detail in Sec. 3. Gabor transform spectrograms of (e) the TDDFT fields and (f) sampled fields showing results up to the ninth harmonic. Here the white vertical line is inserted to illustrate the band gap energy of the HHG emitter.
Reuse & Permissions
Figure 2
Normalized high-harmonic spectra for each condition simulated: driving wavelength of $2 µ m$ with a peak intensity of $4 \times 10^{10} W {cm}^{- 2}$ (bottom, blue curve), driving wavelength of $2 µ m$ with a peak intensity of $5 \times 10^{10} W {cm}^{- 2}$ (middle, orange curve), and driving wavelength of $2.3 µ m$ with a peak intensity of $4 \times 10^{10} W {cm}^{- 2}$ (top, green curve). Each curve is normalized differently for visual clarity. For each case the same system was used as a generation medium, with a band gap of roughly 3.3 $e V$ .
Reuse & Permissions
Figure 3
Time-domain fields generated by various harmonic contributions for a driving wavelength of $2 µ m$ and peak intensity of $4 \times 10^{10} W {cm}^{- 2}$ . (a) All HOs $\geq 2$ , (b) HOs from 3 to 7, and (c) HOs from 7 to 11.
Reuse & Permissions
Figure 4
Comparison between the semiclassical and TDDFT models. All driving conditions are the same as for Fig. 3. (a) Time-domain fields for all generated HOs $\geq 2$ for the semiclassical model (green) and HOs 3–7 for the TDDFT model. Note that just like for the lower HO of the TDDFT model, the semiclassical model predicts high-order harmonic fields that are concentrated under peaks of the square of the driving electric field. (b) A comparison of the spectra of the two models. The semiclassical model is dominated by the lower-order harmonics and drops off rapidly with increasing HO. On the other hand, due to the presence of interband processes and richer accounting of electron-electron interactions, an extended plateau forms in the TDDFT response. The TDDFT harmonics have rich structuring and a broader bandwidth in comparison with the harmonics predicted by the simple semiclassical response.
Reuse & Permissions
Figure 5
Time-domain fields generated by various harmonic contributions for a driving wavelength of $2.3 µ m$ and peak intensity of $4 \times 10^{10} W {cm}^{- 2}$ . (a) All HOs $\geq 2$ , (b) HOs from 3 to 7, and (c) HOs from 7 to 11.
Reuse & Permissions
Figure 6
Time-domain fields generated by various harmonic contributions for a driving wavelength of $2 µ m$ and peak intensity of $5 \times 10^{10} W {cm}^{- 2}$ . (a) All HO $\geq 2$ . Note the sudden transition from intraband- to interband-type radiation at $t \approx 95 f s$ . (b) HO from 3 to 7 and (c) HO from 7 to 11.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics