Probing Solid-State Matter with High-Order Harmonic Generation Spectroscopy

When an intense mid-infrared (MIR) laser pulse interacts with matter, photons with energies that are integer multiples of the incident photon's energy are emitted. This process, known as High-order Harmonic Generation (HHG), was first discovered in noble gases^1,2, and then applied to molecules³, solids⁴, and liquids⁵.Focusing on solid-state HHG, this process was described as a sequence of three steps. In the first step, the interaction of the material with the driving field promotes an electron in the conduction band, leaving a hole in the valence band. In the second step, electrons and holes are accelerated in the respective bands by the external driving field. Due to the non-linearity of the band dispersion, intra-band harmonics are emitted. In the third and last step, electrons and holes can recombine, thus generating inter-band harmonics.<br/>This highly non-linear phenomenon conveys information about the originating medium, making high-order harmonic generation spectroscopy (HHGS) a powerful technique for probing matter in solid state. Significant examples are provided by all-optical band structure reconstruction and Berry phase measurement^6,7. HHG can also be used as a probe of electronic and lattice dynamics initiated by a secondary pump pulse preceding the HHG driving field. This time-resolved HHGS (tr-HHGS) approach has the capability to probe phase transition and phonon dynamics with unprecedented spatial and temporal resolution⁸.<br/>In our work, we applied HHGS and tr-HHGS for the characterization of two semiconductor materials, germanium, and tellurium.<br/>We performed HHGS measurements in bulk germanium (001) driven by a linearly polarized MIR field centered at 3.2 μm. By focusing an intense linearly polarized MIR field, and collecting the harmonics generated in reflection, we observed harmonics up to the 15^th order and we fully characterized the harmonic yield as a function of the crystal axis direction. All the harmonics reflect the cubic symmetry of the material but show very different behavior as a function of the driving field intensity and polarization direction. This is a signature of the non-linear dynamics taking place during the process. Moreover, we fully characterized the polarization state of the emitted harmonics up to the 7^th order as a function of the crystal axis direction, showing that it can significantly diverge from the driving field polarization and demonstrating the emission of light at specific wavelengths having strong ellipticity. This could be attributed to the interference of different harmonic emission pathways, which can allow us to extract information about the complex sub-cycle ultrafast electron dynamics in germanium when it undergoes strong field interactions.<br/>Furthermore, we used tr-HHGS for probing phase transitions in tellurium, an elemental semiconductor with <i>chiral</i> crystal structure. Preliminary results show how the extreme sensitivity of HHGS can be used for tracking the lattice and electron dynamics induced by the pump.<br/><br/>References:<br/><br/>¹P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993)<br/>²M. Lewenstein et al., Phys. Rev. A 49, 2117 (1994)<br/>³Velotta R., et al., High-Order Harmonic Generation in Aligned Molecules, Phys. Rev. Lett. 87, 183901<br/>⁴Ghimire, S., DiChiara, A., Sistrunk, E. et al. Observation of high-order harmonic generation in a bulk crystal. Nature Phys 7, 138–141 (2011).<br/>⁵Luu, T.T., Yin, Z., Jain, A. et al. Extreme–ultraviolet high–harmonic generation in liquids. Nat Commun 9, 3723 (2018).<br/>⁶Vampa G., et al., All-Optical Reconstruction of Crystal Band Structure, Phys. Rev. Lett. 115, 193603<br/>⁷T. T. Luu and H. J. Wörner, Nat. Commun. 9, 916 (2018).<br/>⁸M. R. Bionta, Tracking ultrafast solid-state dynamics using high harmonic spectroscopy, Phys. Rev. Research <b>3</b>, 023250