Minimum Dielectric-Resonator Mode Volumes

TL;DR

This paper establishes fundamental lower bounds on dielectric resonator mode volumes using Lagrangian duality, revealing that inverse design can significantly outperform traditional sharp-tip structures, especially at nanometer scales, with implications for multiresonant and nonlinear optics.

Contribution

It introduces a method to compute lower bounds on mode volumes for dielectric resonators and demonstrates the potential for inverse design to achieve superior performance.

Findings

Lower bounds on mode volume are computable via Lagrangian duality.

Inverse design can improve mode volume performance by orders of magnitude.

Multiresonant structures face unavoidable efficiency penalties.

Abstract

We show that global lower bounds to the mode volume of a dielectric resonator can be computed via Lagrangian duality. State-of-the-art designs rely on sharp tips, but such structures appear to be highly sub-optimal at nanometer-scale feature sizes, and we demonstrate that computational inverse design offers orders-of-magnitude possible improvements. Our bound can be applied for geometries that are simultaneously resonant at multiple frequencies, for high-efficiency nonlinear-optics applications, and we identify the unavoidable penalties that must accompany such multiresonant structures.