Orders-of-magnitude reduction in photonic mode volume by nano-sculpting

Three-dimensionally sculpted dielectric nanostructures supporting material(air) confined optical modes with single-emitter mode volumes three(four) orders of magnitude below the diffraction limit, Vr₀ ≈ 0.0004 [λ/(2 n)]³ ( Vr₀ ≈ 0.00003 [λ/2]³), are discovered using topology optimization. Encapsulating the nanostructure by ellipsoidal shells enables seemingly unbounded mode quality factor enhancement (Q > 10⁸ demonstrated numerically) leading to Purcell enhancement above 10¹¹. It is studied how Vr₀ and Q depend on the choice of material, device volume, minimum feature size and number of shells.