Temporal Fourier Optics Reveals Hidden Hybridized Light-Matter States

Spectral measurements provide fundamental insights into wave systems by revealing resonances, mode hybridization, and light-matter interactions. However, intrinsic dissipation and measurement-induced spectral broadening often conceal the underlying hybridized light-matter states that give rise to measured spectra. Here, we establish a space-time Fourier correspondence that interprets spectral broadening as an effective temporal attenuation, giving rise to a temporal Fourier optics framework for recovering hidden spectral information. Implemented through a temporal point-spread-function (TPSF) reconstruction method, the framework compensates the effective temporal decay before Fourier transformation, directly reconstructing intrinsic spectral responses from experimentally measured spectra without repeated frequency synthesis or model-dependent fitting. We experimentally validate the approach in deterministic single-molecule Au nanosphere dimers and open Au@Ag nanorod- and nanotriangle-based plasmonic nanocavities coupled to J-aggregate excitons. Across these diverse platforms, TPSF consistently reconstructs hidden upper and lower polaritonic branches, thereby revealing the underlying hybridized light-matter states and strong coupling that remain unresolved in conventional scattering spectra. The reconstructed spectra agree closely with the recently developed complex-frequency formalism while offering a considerably simpler and more experimentally accessible implementation. Beyond strong light-matter coupling, temporal Fourier optics establishes a general framework for uncovering physical states hidden by dissipation, opening new opportunities for spectroscopy, imaging, sensing, and inverse wave measurements across photonics and wave physics.