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

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Abstract
The temporal structure of the polarization and carrier-envelope phase slip of high-harmonic waveforms generated in bulk gallium selenide within the duration of a single multi-terahertz driving pulse can be controlled by the crystal symmetry. High-harmonic (HH) generation in crystalline solids1,2,3,4,5,6 marks an exciting development, with potential applications in high-efficiency attosecond sources7, all-optical bandstructure reconstruction8,9 and quasiparticle collisions10,11. Although the spectral1,2,3,4 and temporal shape5 of the HH intensity has been described microscopically1,2,3,4,5,6,12, 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 combs13,14,15 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 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.

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