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


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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Figure 1: High-harmonic intensity and polarization for different crystal orientations of gallium selenide.
Figure 2: Crystal-angle dependence of HH generation and comparison between experiment and theory.
Figure 3: Subcycle HH pulse trains generated for different crystal directions.
Figure 4: Temporal structure of the HH carrier wave.


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The work in Regensburg was supported by the European Research Council through grant number 305003 (QUANTUMsubCYCLE) as well as by the Deutsche Forschungsgemeinschaft (through grant number HU 1598/2-1 and GRK 1570) and the work in Marburg by the Deutsche Forschungsgemeinschaft (through SFB 1083 and grant number KI 917/2-2 and KI 917/3-1).

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F.L., M.H. and R.H. carried out the experiment and analysed the data. U.H., S.W.K. and M.K. developed the quantum-mechanical model and carried out the computations. All authors discussed the results and contributed to the writing of the manuscript.

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Correspondence to M. Kira or R. Huber.

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The authors declare no competing financial interests.

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Langer, F., Hohenleutner, M., Huttner, U. et al. Symmetry-controlled temporal structure of high-harmonic carrier fields from a bulk crystal. Nature Photon 11, 227–231 (2017).

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