Continuous polarization-wavelength mapping with nonlocal metasurfaces

Simultaneous and continuous control over polarization and wavelength-two orthogonal and information-rich degrees of freedom-remains a central challenge in metasurface photonics, long hindered by intrinsic dispersion constraints and structural degeneracy. Here, we customize continuous polarization-wavelength mapping through a nonlocal metasurface platform that decouples birefringent evolution from structural dispersion. We achieve programmable, spectrally resolved polarization shaping across the broadband mid-infrared regime by introducing an equivalent nonlocal Jones matrix formalism and a dimension-interlaced vectorial diffraction neural network. This framework enables fully continuous and arbitrarily prescribed mapping across the joint polarization-wavelength space-beyond the capabilities of segmented or interleaved metasurface designs. We experimentally demonstrate non-degenerate multicolor vectorial holography, broadband achromatic imaging, and arbitrary elliptical polarization multiplexing with high fidelity and minimal crosstalk, maintaining strong channel isolation. Our results establish a scalable route toward continuous-domain photonic encoding, offering a powerful foundation for ultracompact optical communication, vectorial information encryption, and high-dimensional light-field processing.