  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.
