Modal properties of dielectric bowtie cavities with deep sub-wavelength confinement

We present a design for an optical dielectric bowtie cavity which features deep sub-wavelength confinement of light. The cavity is derived via simplification of a complex geometry identified through inverse design by topology optimization, and it successfully retains the extreme properties of the original structure, including an effective mode volume of $V_\text{eff}= 0.083 \pm 0.001 \; (\lambda_\text{c}/2n_\text{Si})^3$ at its center. Based on this design, we present a modal analysis to show that the Purcell factor can be well described by a single quasinormal mode in a wide bandwidth of interest. Owing to the small mode volume, moreover, the cavity exhibits a remarkable sensitivity to local shape deformations, which we show to be well described by perturbation theory. The intuitive simplification approach to inverse design geometries coupled with the quasinormal mode analysis demonstrated in this work provides a powerful modeling framework for the emerging field of dielectric cavities with deep sub-wavelength confinement.