  High-harmonic generation (HHG) from a compact, solid-state medium is highly
desirable for applications such as coherent attosecond pulse generation and
extreme ultra-violet (EUV) spectroscopy, yet the typically weak conversion of
pump light to HHG can largely hinder its applications. Here, we use a material
operating in its epsilon-near-zero (ENZ) region, where the real part of its
permittivity vanishes, to greatly boost the efficiency of the HHG process at
the microscopic level. In experiments, we report high-harmonic emission up to
the 9th order directly from a low-loss, solid-state ENZ medium: indium-doped
cadmium oxide, with an excitation intensity at the GW cm-2 level. Furthermore,
the observed HHG signal exhibits a pronounced spectral red-shift as well as
linewidth broadening, resulting from the photo-induced electron heating and the
consequent time-dependent resonant frequency of the ENZ film. Our results
provide a novel nanophotonic platform for strong field physics, reveal new
degrees of freedom for spectral and temporal control of HHG, and open up
possibilities of compact solid-state attosecond light sources.
