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

TL;DR

This paper demonstrates that nano-sculpting dielectric nanostructures can achieve extremely small optical mode volumes and potentially very high quality factors, greatly enhancing light-matter interaction for photonic applications.

Contribution

The study introduces topology optimization to design dielectric nanostructures with unprecedented spatial light confinement and explores how encapsulation with ellipsoidal shells can vastly increase the quality factor.

Findings

Mode volumes are reduced by three to four orders of magnitude below the diffraction limit.

Encapsulation with ellipsoidal shells can lead to quality factors exceeding 10^8.

The Purcell factor can be enhanced above 10^11.

Abstract

Achieving strong light-matter interaction is important for studying and exploiting several physics 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 $V$, $F \propto \frac{Q}{V}$. 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) loss-less 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, $V_{\textbf{r}_0} \approx 4 \cdot 10^{-4} \left[\lambda/(2 n)\right]^3 \left( V_{\textbf{r}_0} \approx 3 \cdot 10^{-5} \left[\lambda/2\right]^3\right)$. Remarkably, we further discover that encapsulating the nanostructure by ellipsoidal shells enables seemingly unbounded enhancement of the mode quality factor ($Q > 10^8$ demonstrated numerically) leading to theoretical Purcell factor enhancement above $10^{11}$. It is established how $V_{\textbf{r}_0}$ and $Q$ depend on the choice of material platform, device volume, minimum feature size and the number of shells. Finally a study of sensitivity towards geometric variations is presented, revealing robust behaviour.