Scaling Law of Purcell Factor in Hyperbolic Metamaterial Cavities with Dipole Excitation

To control the spontaneous emission rate of dipole emitters, a resonant cavity is widely used to provide large electromagnetic mode confinement, thus resulting in the enhanced Purcell effect. Here, hyperbolic metamaterial cavities with different wavevectors are designed to have identical fundamental mode at the same resonant frequency. The anomalous power law for the Purcell factor of the cavity wavevector is investigated with dipole excitation. Different from conventional photonic and plasmonic cavities, a fifth power law PF~(k∕k ₀ ) ⁵ for small wavevectors and a square law PF~(k∕k ₀ ) ² for large wavevectors are demonstrated. The unique optical properties and Purcell factor scaling law of hyperbolic metamaterial cavities will greatly benefit applications in cavity electrodynamics, quantum optics, single photon sources, on-chip quantum computing, and circuits.