Symmetry-controlled temporal structure of high-harmonic carrier fields from a bulk crystal

High-harmonic (HH) generation in crystalline solids(1-6) marks an exciting development, with potential applications in high-efficiency attosecond sources(7), all-optical bandstructure reconstruction(8,9) and quasiparticle collisions(10,11). Although the spectral(1-4) and temporal shape(5) of the HH intensity has been described microscopically(1-6,12), 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 combs(13-15) to optical clock rates, we show how the polarization and carrier-envelope phase (CEP) of HH pulses can be controlled by the crystal symmetry. For certain 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 p, 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.