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

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 analytical 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.