  Thermotropic liquid crystals are versatile optical materials that exhibit a
state of matter intermediate between liquids and solids. Their properties can
change significantly with temperature, pressure, or other external factors,
leading to different phases. The transport properties within these materials in
different phases are still largely unexplored and their understanding would
enable exciting prospects for innovative technological advancements. High-order
harmonic spectroscopy proved to be a powerful spectroscopic tool for
investigating the electronic and nuclear dynamics in matter. Here we report the
first experimental observation of high-order harmonic generation in
thermotropic liquid crystals in two different phase states, nematic and
isotropic. We found the harmonic emission in the nematic phase to be strongly
dependent on the relative orientation of the driving field polarization with
respect to the liquid crystal alignment. Specifically, the harmonic yield has a
maximum when the molecules are aligned perpendicularly to the polarization of
the incoming radiation. Our results establish the first step for applying
high-order harmonic spectroscopy as a tool for resolving ultrafast electron
dynamics in liquid crystals with unprecedented temporal and spatial resolution.
