Spectral nonuniqueness and generalization to unseen topologies

Characterize the nonuniqueness of reconstructing dielectric metasurface structures from transmission spectra and determine whether the Fourier-space inverse-reconstruction framework generalizes to metasurface topologies absent from the seven known structure families.

Background

The inverse model encodes a 2,001-point BIC-band transmission spectrum into complex Fourier coefficients representing a binary 67 × 67 material mask, which is then transformed back into a real-space structure. Its reported evaluation is conditional on a paired dataset comprising seven known metasurface families and does not resolve whether a spectrum uniquely determines a structure or whether the learned inverse mapping transfers to entirely unseen topologies.

The unresolved issues are important because distinct structures can produce similar spectra, and the inverse model currently returns one plausible reconstruction rather than the full set of structures compatible with a given spectrum. Establishing the extent of this spectral nonuniqueness and testing generalization beyond the seven training families would clarify the limits of Fourier-space inverse reconstruction.

References

The seven-family examples in Fig. S11 extend main-text Fig. 5b. Reconstruction is conditional on the paired dataset and known topology classes; spectral nonuniqueness and generalization to unseen topologies remain unresolved.

— Learning qBIC Resonances across Metasurface Families in Dielectric Fourier Space  (2610.11500 - Lei et al., 8 Oct 2026) in Supplementary Note 6, “Inverse reconstruction and its evaluation boundary”