Eigenvalue-accelerated LDOS optimization of high- Q optical resonances

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Abstract
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 > 10 6 resonant cavities in 1d and 2d dielectric systems.
Funding Information
  • United States Army Research Office (W911NF-23-2-0121)
  • Simons Foundation
  • Massachusetts Institute of Technology
  • Novo Nordisk Foundation (NNF22SA0081175)
  • Danish National Research Foundation (DNRF147)

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