Projective augmented reality displays are an emerging technology combining contextual information from the outside world with artificial information (from a projector) via a beam splitter. An ideal beam splitter reflects with unity efficiency only selected wavelengths encoding the artificial information and over a relatively large range of oblique incident angles (to enable a large eye box), while transmitting with unity efficiency and zero distortion the remainder of the visible spectrum. Here, we engineer nonlocal metasurfaces to support quasi-bound states in the continuum with zero first-order resonant frequency dispersion (a band edge) and at a desired quasi-momentum (operating angle) specified by a zone-folding technique that changes the lattice family (e.g. from hexagonal to rectangular). We then demonstrate arbitrary specification of an elliptical polarization exciting the resonance. Our platform thereby enables arbitrary control over the spectral, momentum, and polarization properties of nonlocal states with maximal Bragg scattering, controlled rationally through a perturbation scheme that produces minimal distortion to the non-resonant light.
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