  Hyperbolic metamaterials show exceptional optical properties, such as
near-perfect broadband absorption, due to their geometrically-engineered
optical anisotropy. Many of their proposed applications, such as
thermophotovoltaics or radiative cooling, require high-temperature stability.
In this work we examine Ag/a-Si multilayers as a model system for the thermal
stability of hyperbolic metamaterials. Using a combination of nanotomography,
finite element simulations and optical spectroscopy, we map the thermal and
optical instability of the metamaterials. Although the thermal instability
initiates at 300C, the hyperbolic dispersion persists up to 500C. Direct finite
element simulations on tomographical data provide a route to decouple and
evaluate interfacial and elastic strain energy contributions to the
instability. Depending on stacking order the instability's driving force is
either dominated by changes in anisotropic elastic strain energy due thermal
expansion mismatch or by minimization of interfacial energy. Our findings open
new avenues to understand multilayer instability and pave the way to design
hyperbolic metamaterials able to withstand high temperatures.
