High-harmonic (HH) generation in crystalline solids1–6 marks an exciting development, with potential applications in high-efficiency attosecond sources7, all-optical bandstructure reconstruction8,9, and quasiparticle collisions10,11. Although the spectral1–4 and temporal shape5 of the HH intensity has been described microscopically1–6,12, the properties of the underlying HH carrier wave have remained elusive. Here we analyse the train of HH waveforms generated in a crystalline solid by consecutive half cycles of the same driving pulse. Extending the concept of frequency combs13–15 to optical clock rates, we show how the polarization and carrier-envelope phase (CEP) of HH pulses can be controlled by crystal symmetry. For some crystal directions, we can separate two orthogonally polarized HH combs mutually offset by the driving frequency to form a comb of even and odd harmonic orders. The corresponding CEP of successive pulses is constant or offset by π, depending on the polarization. In the context of a quantum description of solids, we identify novel capabilities for polarization- and phase-shaping of HH waveforms that cannot be accessed with gaseous sources.

We have observed four-wave mixing in a semiconductor laser configured to emit on two wavelengths simultaneously. The four-wave mixing sidebands exist up to 4 THz stemming from a modulation of the carrier plasma at the difference frequency of the two laser modes. In addition, we were able to generate and detect tunable THz radiation at this difference frequency from the laser device itself suggesting a scheme for a tunable THz source.

Direct emission of terahertz (THz) radiation out of a two-colour semiconductor laser is reported and analysed. The geometry of the tunable two-colour laser is described together with the physical mechanisms responsible for the emission at the THz difference frequency of the two pump colours used. On the basis of this analysis, different possibilities are suggested to increase the emitted THz intensity towards application relevant levels.

A density-matrix many-body theory for the description of the interacting electron-hole system in direct-gap semiconductors is presented. The Coulomb interaction between all electrons, the coupling to a quantized light field, and a reservoir of phonons are included. The theory is evaluated to compute the electron-hole and electron-electron correlation functions after initialization of the system as uncorrelated plasma. The dynamical development of pair correlations is discussed.