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∕k0)5 for small wavevectors and a square law PF~(k∕k0)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.


Mechanical and Aerospace Engineering

Research Center/Lab(s)

Intelligent Systems Center


Funding provided by National Science Foundation (NSF) (DMR-1552871, ECCS-1653032); Office of Naval Research (ONR) (N00014-16-1-2408).

Keywords and Phrases

Natural frequencies; Optical properties; Particle beams; Plasmonics; Quantum computers; Quantum optics, Cavity electrodynamics; Electromagnetic modes; Fundamental modes; Purcell effect; Purcell factor; Quantum Computing; Single-photon source; Spontaneous emission rates, Metamaterials

International Standard Serial Number (ISSN)

0146-9592; 1539-4794

Document Type

Article - Journal

Document Version


File Type





© 2019 Optical Society of America (OSA), All rights reserved.

Publication Date

01 Feb 2019

PubMed ID