On the trade-off between mode volume and quality factor in dielectric nanocavities optimized for Purcell enhancement

This study explores the effect of geometric limitations on the achievable Purcell factor for single emitters in dielectric structures by employing topology optimization as an inverse design tool to maximize the local density of states. Nanobeams of different lengths with varying fixed central bridge widths are considered to investigate the impact of footprint and geometric length-scale. In single-mode photonic cavities, the Purcell factor is known to be proportional to the ratio of the quality factor Q to the effective mode volume V. Analysis of the optimized nanocavities shows a trade-off between quality factor and mode volume as a function of geometric limitations. Crucially, the design exhibiting the largest Purcell enhancement does not have the highest Q nor the lowest V found in the design pool. On the contrary, it is found that Q consistently drops along with decreasing V as the minimum allowed geometric length-scale decreases while the Purcell factor increases. Finally, the study provides insight into the importance of Q and V for enhancing the Purcell factor under geometric limitations.