Orders of Magnitude Reduction in Photonic Mode Volume by Nanosculpting

Achieving strong light-matter interactions is important for studying and exploiting several physical phenomena. The light-matter interaction strength depends on the optical field intensity in the interaction region, often measured by the Purcell factor, which for a single emitter is proportional to the spectral confinement, quantified by the cavity quality factor Q, and inversely proportional to the spatial localization of light, quantified by the optical model volume V, F∝QV. While plasmonic (metallic) devices can support extreme spatial light confinement, ohmic losses reduce the cavity lifetime, thereby limiting the achievable spectral confinement. It is therefore of both practical and fundamental interest to explore the potential for achieving extreme spatial light confinement in (near) lossless dielectric environments. Employing topology optimization, we explore the limits of spatial light confinement in dielectric environments when allowing for three-dimensional sculpted dielectric nanostructures. Here we discover structures supporting optical modes that are concentrated in material (air) with mode volumes that are three (four) orders of magnitude below the so-called diffraction limit, Vr0 ≈ 4 × 10–4 [λ/(2n)]3 (Vr0 ≈ 3 × 10–5 [λ/2]3). Remarkably, we further discover that encapsulating the nanostructure by ellipsoidal shells enables seemingly unbounded enhancement of the mode quality factor (Q > 108 demonstrated numerically) leading to theoretical Purcell factor enhancement above 1011. It is established how Vr0 and Q depend on the choice of material platform, device volume, minimum feature size, and the number of shells. Finally, a study of sensitivity toward geometric variations is presented, revealing robust behavior under a range of perturbations.