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Multipole expansions enable rapid numerical modeling of optical scatterer arrays, but choosing expansion centers is ambiguous. We derive optimal centers where multipolar spectra become unique, separately minimizing electric and magnetic quadrupole norms. This significantly reduces computations, benefiting differentiable solvers critical for machine learning photonics design. Analysis of dispersive mutual center positions provides insight into scattering and optical forces. Connections to optomechanics, and quantum/topological photonics are also hinted through links between the number of optimal magnetic centers and the topological metrics of resonant modes.
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Alex Kildishev, Karim Achouri, Daria Smirnova, "Electric and magnetic multipole centers," Proc. SPIE PC12991, Nanophotonics X, PC129910D (11 June 2024); https://doi.org/10.1117/12.3015671