High-order Harmonic Generation (HHG) is an established spectroscopic technique in atoms
and molecules[1]. The advent of HHG in solids[2], paved the way for all-optical
characterisation in condensed media, allowing band structure reconstruction[3], metastable
phase detection[4], and petahertz electronics. Recently, HHG has been observed in liquids
too, demonstrating the flexibility and the capability of this physical phenomenon for studying
matter, showing features that are peculiar to each phase.
Here, a general overview of HHG will be given, showing differences and similarities of HHG
depending on the state of matter, and how it can be used for probing solid-state materials,
with a focus on semiconductors and liquid crystals.
To highlight the differences between the atomic and solid HHG emission, a polarimetry
analysis on the harmonics emitted by bulk germanium will be presented, showing that their
polarisation state does not necessarily follow the one of the driving field, which is unusual for
the atomic and molecular case.
To show the capability of HHG as a spectroscopic tool in solids, a time-resolved scheme will
be introduced, aiming to study ultrafast processes in condensed media. Thanks to the high
nonlinearity of the process, this will possibly allow to study out-of-equilibrium properties of
solids with unprecedented sensitivity with respect to standard femtosecond pump-probe
techniques.
Finally, the experimental observation of HHG emission in thermotropic liquid crystals (TLCs)
will be presented to build a bridge picture passing from solid to liquids. These materials are
of particular interest since they can be found in a mesomorphic state of matter, namely, they
show phase transitions depending on their temperature, allowing to study the HHG process
across phase transitions. Moreover, by applying an external AC voltage, it is possible to align
liquid crystals, giving the possibility to collect the harmonics emission as a function of the
molecular orientation.
[1] Vozzi, C., Negro, M., Calegari, F. et al. Generalized molecular orbital tomography. Nature Phys 7, 822–826
(2011). https://doi.org/10.1038/nphys2029
[2] Ghimire, S., DiChiara, A., Sistrunk, E. et al. Observation of high-order harmonic generation in a bulk crystal.
Nature Phys 7, 138–141 (2011). https://doi.org/10.1038/nphys1847
[3] T. J. Hammond, et. al, All-Optical Reconstruction of Crystal Band Structure, Phys. Rev. Lett. 115,
193603 – Published 5 November 2015
[4] Mina R. Bionta, et. al, Tracking ultrafast solid-state dynamics using high harmonic spectroscopy, Phys. Rev.
Research 3, 023250 – Published 28 June 2021
