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

The emitted radiation from semiconductor nanostructures due to the excitation with intense ultrashort optical laser pulses is analyzed. Semiconductor Bloch equations that consistently describe the coupled light-field-induced interband and intraband dynamics are solved numerically. It is demonstrated that the intraband dynamics considerably influences the light emission in the regime of extreme nonlinear optics. In particular, the intraband acceleration significantly modifies the dynamics of the interband polarization which results in a strong enhancement of high-harmonic generation.

Figure 1

(Color online) Excitation dependent emission of a GaAs quantum wire with a tight-binding band structure. $\omega$ is the spectrometer frequency, ${\omega }_R$ the peak Rabi frequency, and ${\omega }_0$ the excitation frequency. The logarithmic color encoding covers seven orders of magnitude, see (a). In (a), the emission for pure interband dynamics is shown, i.e., $I_{\mathrm{rad}}\left(\omega \right)=I_{\mathrm{rad}}^{\mathrm{pol}}\left(\omega \right)$. (b), (c), and (d) show the spectra for coupled interband and intraband dynamics due to the polarization $I_{\mathrm{rad}}^{\mathrm{pol}}\left(\omega \right)$, the current $I_{\mathrm{rad}}^{\mathrm{curr}}\left(\omega \right)$, and the total emission $I_{\mathrm{rad}}\left(\omega \right)$, respectively.

Figure 2

Cross section through Fig. 1 at ${\omega }_R=3{\omega }_0$ for pure interband dynamics (dashed curve) and the coupled interband and intraband dynamics showing $I_{\mathrm{rad}}^{\mathrm{pol}}\left(\omega \right)$ (light gray curve), $I_{\mathrm{rad}}^{\mathrm{curr}}\left(\omega \right)$ (dark gray curve), and $I_{\mathrm{rad}}\left(\omega \right)$ (solid black curve). (a) The emission spectra on a logarithmic scale for a wide $\omega$ range, whereas in (b) the emission in the transition region, where $I_{\mathrm{rad}}^{\mathrm{pol}}\left(\omega \right)$ and $I_{\mathrm{rad}}^{\mathrm{curr}}\left(\omega \right)$ are comparable, is shown on a linear scale.

Figure 3

(Color online) Total emission spectra $I_{\mathrm{rad}}\left(\omega \right)$ for coupled interband and intraband dynamics. In (a) a tight-binding model with a bandwidth of ${\Delta }_e=2.5\mathrm{eV}$ and an effective mass of $m_e=0.19m_0$ is used. (b) is for a dispersion that includes also second-nearest neighbor interactions with ${\Delta }_e=2.5\mathrm{eV}$ and $m_e=0.069m_0$.