Mode-resolved directional enhancement of spontaneous emission inside/outside finite multilayer hyperbolic metamaterials

The concept of large photonic density of states associated with high-k modes of hyperbolic metamaterials (HMMs) plays a significant role in the interests behind the HMM notion. Despite the theoretical predictions, it is proved that photonic local density of states (LDOS) is not infinite in practical multilayer HMMs. In the present study, a developed theory based on the effective medium approximation is used to probe the finite number of high-k modes in finite multilayer HMMs. The high-k modes are classified in two categories as short-range and long-range propagating modes, strongly dependent on the number of periods. Introducing a mode-resolved transition rate enhancement factor, emission coupling of a quantum emitter, placed inside and in near vicinity of HMM slabs, to the high-k modes is calculated. The results show that the short-range and long-range modes have the commanding influence on transition rate enhancement outside and inside the slabs, respectively. The results point out that HMM slabs having lower number of periods provide higher total LDOS giving rise to larger transition rate enhancement. The results prove the capability of engineering photonic density of states in finite HMMs and pave the way for application-orientated HMMs design.