Strong-Field Perspective on High-Harmonic Radiation from Bulk Solids

Mechanisms of high-harmonic generation from crystals are described by treating the electric field of a laser as a quasistatic strong field. Under the quasistatic electric field, electrons in periodic potentials form dressed states, known as Wannier-Stark states. The energy differences between the dressed states determine the frequencies of the radiation. The radiation yield is determined by the magnitudes of the interband and intraband current matrix elements between the dressed states. The generation of attosecond pulses from solids is predicted. Ramifications for strong-field physics are discussed.

Figure 1

(a) Schematic of the dynamics of electrons in the valence and conduction bands. The electron experiences both interband transition and the intraband acceleration. (b) Coordinate-space representation of the system under a static electric field. (c) Quasienergy spectra as functions of the quasistatic electric field. (d) Energy spectra of the radiation as functions of the quasistatic electric field. The color shows the intensity amplitude of the current matrix elements. (e) Numerically obtained current density spectra as functions of the peak electric field of the incident laser pulse. (f) Integrated values of the intensity amplitude of the current matrix elements in (d) over the same laser waveform as in (e).

Figure 2

Prediction of the possible generation of an attosecond pulse. The incident laser waveforms having (a) cosine and (b) sine waveforms are plotted as the red curves, while their envelopes (green curves) are identical. The blue shaded areas show the power of the HHG through high-pass filters, having cutoff energies at (a) 40 eV and (b) 38 eV. (c),(d) Numerically obtained HHG spectrograms. The window function is a Gaussian having a FWHM of 0.67 fs, i.e., 6.2 eV in energy, which broadens the spectrograms. (e),(f) Spectra of the total current matrix elements as functions of time. The color indicates the intensity amplitude of the matrix elements. (g),(h) Temporal evolution of the upper-level population. The shaded areas indicate $|\hslash {\mathrm{\Omega }}_B|>\mathrm{\Delta }$, indicating the field amplitude exceeds the last anticrossing in Fig. 1.