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-related spectral broadening often obscure the spectral signatures of the underlying hybridized light-matter states. Here, we establish a temporal Fourier optics framework based on a space-time Fourier correspondence, which interprets spectral broadening as the Fourier counterpart of temporal attenuation. This perspective introduces a temporal point-spread function (TPSF) that enables direct, synthesis-free reconstruction of the underlying spectral response from experimentally measured spectra by compensating for effective temporal decay before transformation back to the frequency domain. We experimentally validate the framework using deterministic single-molecule Au nanosphere dimers and open Au@Ag nanorod- and nanotriangle-based plasmonic nanocavities coupled to J-aggregate excitons. Across these distinct platforms, TPSF consistently resolves hidden upper and lower polaritonic branches, revealing hybridized light-matter states and strong coupling that remain inaccessible in conventional scattering spectra. The reconstructed spectra agree closely with the recently developed complex-frequency formalism while providing a substantially simpler and experimentally accessible implementation. More broadly, temporal Fourier optics establishes a general framework for recovering dissipation-obscured spectral information, opening new opportunities for spectroscopy, imaging, sensing, and inverse wave measurements across photonics and wave physics.