Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities

We propose a photonic crystal nanocavity design with self-similar electromagnetic boundary conditions, achieving ultrasmall mode volume (V_{eff}). The electric energy density of a cavity mode can be maximized in the air or dielectric region, depending on the choice of boundary conditions. We illustrate the design concept with a silicon-air one-dimensional photon crystal cavity that reaches an ultrasmall mode volume of V_{eff}∼7.01×10^{-5}λ^{3} at λ∼1550  nm. We show that the extreme light concentration in our design can enable ultrastrong Kerr nonlinearities, even at the single-photon level. These features open new directions in cavity quantum electrodynamics, spectroscopy, and quantum nonlinear optics.