Eigenvalue-accelerated LDOS optimization of high-Q optical resonances

TL;DR

This paper introduces an eigenvalue-accelerated method for optimizing high-Q optical resonances, significantly speeding up the inverse design process of resonant cavities by maintaining resonance focus using a shift-invert eigensolver.

Contribution

It presents a novel eigenvalue-based acceleration technique for LDOS optimization, enabling efficient design of ultra-high-Q resonant cavities with improved computational speed.

Findings

Achieved orders-of-magnitude acceleration in LDOS optimization.

Successfully designed resonant cavities with Q > 10^6.

Method applicable to various resonant-response metrics.

Abstract

We demonstrate a new method that yields orders-of-magnitude acceleration in inverse design (e.g. topology optimization) of high-$Q$ resonant cavities to maximize the local density of states (LDOS), and which is also applicable to other resonant-response metrics. The key idea is that, once conventional LDOS optimization has identified a strong resonance, subsequent optimizations can exploit a fast shift-invert eigensolver to ensure that the LDOS remains centered at the resonance peak. We show that this eliminates ill-conditioning at sharp resonances that otherwise dramatically slows LDOS (and similar) optimization for $Q \gg 100$. Our method is demonstrated by design of $Q > 10^6$ resonant cavities in 1d and 2d dielectric systems.