Purcell Effect in Epsilon-Near-Zero Microcavities

Abstract: Epsilon-near-zero (ENZ) photonics presents a powerful platform for integrated photonic systems, enabling a range of novel and extraordinary functionalities. However, the practical implementation of ENZ-based systems is often constrained by high material losses and severe impedance mismatch, limiting the efficient interaction of light with ENZ media. To overcome these challenges, we introduce all-dielectric Bragg reflection microcavities operating at their cutoff frequency as a high-figure-of-merit ENZ resonant platform, providing an ultra-low-loss alternative for studying emission processes in ENZ media. While Bragg cavities are well-established, their potential as ENZ resonant microcavities remains largely unexplored. We investigate the Purcell effect and quality factor in these structures, comparing their performance with those of the perfect-electric-conductor and metallic counterparts. Through analytical derivations based on Fermi's golden rule and field quantization in lossless dispersive media, we establish scaling laws that distinguish these ENZ cavities from conventional resonators. Frequency-domain simulations validate our findings, demonstrating that in all-dielectric ENZ Bragg-reflection microcavities, the Purcell and quality factors scale as $L/\lambda_0$ and $(L/\lambda_0)^3$, respectively, where $L$ is the cavity length and $\lambda_0$ is the resonance wavelength. Our results offer key insights into the design of ENZ-based photonic systems, paving the way for enhanced light-matter interactions in nonlinear optics and quantum photonics.