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An ideal hyperbolic metamaterial (HMM), which has a perfect hyperbolic dispersion curve, theoretically can support modes with indefinite wavenumbers, leading to large photon local density of states (LDOS) and many applications such as enhancing light-matter interactions, spontaneous emission and thermal radiation. Here in this presentation, HMMs based on ultrathin metal-dielectric multilayers have been studied by considering the nonlocal response of electrons in metal. Based on the hydrodynamic model of the nonlocal response, we investigate the effect of nonlocality on the performance (dispersion relation, ray refraction, LDOS and spontaneous emission) of HMMs when gradually approaching the ultrathin limit of the unit cell. We show that nonlocality will induce topological transitions of the iso-frequency surfaces and limit the wavenumber as well as LDOS for both type I and type II HMMs. Under nonlocal treatment, the iso-frequency surface of type II HMM transforms from a hyperbola to a bullet shape, while for type I HMM, the surface splits into two branches: a cylindrical-like branch at high k region and an elliptical branch at the low k region. In the high k region, the nonlocality set a cut-off k for the allowed wavenumbers in both type I and type II HMMs. This cut-off k which is defined by the electron Fermi velocity of the metal intrinsically limits the LDOS and light-matter interactions. These results indicate that in the aim of achieving high performance HMMs, merely thinning the constituent films according to the local theories is no longer valid.
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