Interpreting Purcell enhancement of non-Hermitian metasurfaces with spectral parameters

The Purcell effect describes the enhancement of the spontaneous emission rate of an emitter near a resonant structure. However, evaluating the Purcell factor quantitatively and empirically is difficult due to the difficulties in measuring the electromagnetic near field of an optical resonance for calculation of the exact effective modal volume, especially with non-Hermitian resonators. Therefore, we propose an analytical approach to circumvent the need to measure the near field and predict the Purcell enhancement with spectral parameters, which can be directly measured in the far field or fitted from such spectral measurements. Our proposed model predicts the averaged Purcell enhancement by metasurfaces on a photoluminescent medium, and is verified with experimental measurements and numerical simulations of nanoparticle arrays coupled to a fluorescent thin film. The model directly analyzes the photoluminescence enhancement and extraction efficiency of the metasurface, and can be generalized to work with an arbitrarily shaped photoluminescent medium that is coupled to a resonator. This discovery provides a practical and accessible way to understand the underlying mechanisms of photoluminescence enhancement and will facilitate optimization of metasurfaces for efficient extraction of the enhanced luminescence.