  Multilayer hyperbolic metamaterials consisting of alternating metal and
dielectric layers have important applications in spontaneous emission
enhancement. In contrast to the conventional choice of at least dozens of
layers in multilayer structures to achieve tunable Purcell effect on quantum
emitters, our numerical calculations reveal that multilayers with fewer layers
and thinner layers would outperform in Purcell effect. These discoveries are
attributed to the negative contributions by an increasing layer number to the
imaginary part of the reflection coefficient, and the stronger coupling between
surface plasmon polariton modes on a thinner metal layer. This work could
provide fundamental insights and practical guide for optimizing the local
density of optical states enhancement functionality of ultrathin and even
two-dimensional photon sources.
