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

TL;DR

This work shows that 3D topology optimization can push dielectric confinement to unprecedented levels, achieving single-emitter mode volumes well below the diffraction limit and, with ellipsoidal shells, ultra-high quality factors in lossless dielectrics. By leveraging axisymmetric design insights, the authors demonstrate air-confined modes with $V_{r_0} ≈ 3 × 10^{-5} [λ/2]^3$ and solid-confined modes with $V_{r_0} ≈ 8 × 10^{-4} [λ/(2 n_{Si})]^3$, while introducing a shell-based architecture that yields $Q$ exceeding $10^8$ and Purcell factors above $10^{11}$. The work also provides systematic parameter Studies on material index, device volume, and feature size, along with robustness analyses to perturbations, indicating practical viability. Overall, the findings point to a route for extremely strong light–matter interaction in near-lossless dielectric environments and potential microwave-scale realizations with current or near-future fabrication capabilities.

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, $V_{\textbf{r}_0} \approx 4 \cdot 10^{-4} \left[λ/(2 n)\right]^3 \left( V_{\textbf{r}_0} \approx 3 \cdot 10^{-5} \left[λ/2\right]^3\right)$. 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.

Figures (6)

• Figure 1: (a) Planar 2D-patterned dielectric cavity (gray). (b) 3D-sculpted dielectric cavity. (c) Axisymetric 3D-sculpted dielectric cavity. Each panel include a zoom of a quarter of the geometry centered at $\textbf{r}_0$ showing the eletric field magnitude (inferno colormap) of the air-confined mode and lists the associated single-emitter mode volume.
• Figure 2: Single-emitter mode volumes $(V_{\textbf{r}_0})$ for the four optimized structures as a function of allowed device thickness. The minimum feature size allowed for the structure is 10 nm, and the optical intensity is concentrated in the a central air region. The inserts show the optimized geometries for each $(V_{\textbf{r}_0})$-value, with a zoom of the regions surrounding $\textbf{r}_0$.
• Figure 3: (a) (y,z)-plane cut at x=0 of 3D-sculpted $1600$ nm thick structure from Fig. \ref{['FIG:MIN_VR0_3D_STUDY']} with full 3D design freedom. (b) Electric field magnitude in the (x,y)-, (y,z)- and (x,z)-planes through $\textbf{r}_0$ of targeted mode. (c) (y,z)-plane cut at x=0 through device designed using the axisymmetric model. (a) and (c) include overlays showing $\log_{10}\left(\vert \textbf{E} \vert\right)$ for the targeted mode within a radius of $400$ nm of $\textbf{r}_0$.
• Figure 4: Quarter revolution of (a) axisymmetric silicon device with a fixed 2 nm diamater central solid bridge-feature. (b) simplified geometry with ellipsoidal shell and connecting rod. (c) Three-quarter revolution of simplified geometry with six additional ellipsoildal shells. (d) Far-field emission pattern in the (x,z)-plane. (e) Electric near-field components and magnitude. (g) Quality factor of the relevant mode as a function of the number of shells.
• Figure 5: $V_{\textbf{r}_0}$ for sets of sculpted structures as a function of the (a) refractive index, (b) device volume, (c) central bridge width. The inserts show a 90$^o$ revolution of the optimized axisymmetric geometries. The black lines are reference lines for determining orders of proportionality.