Understanding quantum emitters in plasmonic nanocavities with conformal transformation: Purcell enhancement and forces

Nanogaps supporting cavity plasmonic modes with unprecedented small mode volume are attractive platforms for tailoring the properties of light-matter interactions at the nanoscale and revealing new physics. Hitherto, there is a concerning lack of analytical solutions to divide the complex interactions into their different underlying mechanisms to gain a better understanding that can foster enhanced designs. Bowtie apertures are viewed as an effective and appealing nanocavity and are studied here within the analytical frame of conformal transformation. We show how the non-radiative Purcell enhancement of a quantum emitter within the bowtie nanocavity depends strongly not only on the geometry of the nanocavity, but also on the position and orientation of the emitter. For a 20 nm diameter (∅ 20 nm) bowtie nanocavity, we report a change of up to two orders of magnitude in the maximum non-radiative Purcell enhancement and a shift in its peak wavelength from green to infra-red. The changes are tracked down to the overlap between the emitter field and the gap plasmon mode field distribution. This analysis also enables us to understand the self-induced trapping potential of a colloidal quantum dot inside the nanocavity. Since transformations can be cascaded, the technique introduced in this work can also be applied to a wide range of nanocavities found in the literature.