Modelling Purcell enhancement of metasurfaces supporting quasi-bound states in the continuum

Abstract: Bound states in the continuum (BIC) exhibit extremely high quality factors due to the lack of radiation loss and thus are widely studied for Purcell enhancement. However, a closer examination reveals that the enhancement is absent at the BIC due to the lack of out-coupling capability, but the strong enhancement is only observed at nearby configuration, namely quasi-BIC. To study this unique behavior of the Purcell enhancement near BIC, we built an analytically model with spectral parameters to analyze the Purcell enhancement on metasurfaces supporting quasi-BIC. Our analytical model predicts the average Purcell enhancement by metasurfaces coupled to a luminescent medium, utilizing parameters that are formulated through the temporal coupled-mode theory and can be derived from measured spectra such as transmissivity and reflectivity. We analyzed several metasurfaces supporting quasi-BIC numerically and experimentally to study the behavior of the spectral parameters as well as the resultant Purcell enhancement. We formulated the interdependence between the quality factor and the out-coupling efficiency, and revealed the existence of optimal detuning from the BIC. We also discovered that our findings are general and applicable towards realistic metasurfaces that are lossy and/or asymmetric. This discovery provides an intuitive model to understand the modal qualities of quasi-BIC and will facilitate optimization of quasi-BIC for luminescence enhancement applications.