Eigenvalue-accelerated LDOS optimization of high-Q optical resonances

We demonstrate what is believed to be 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 ≫ 100. Our method is demonstrated by design of Q > 10⁶ resonant cavities in 1d and 2d dielectric systems.