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Abstract Augmented reality (AR) devices, as smart glasses, enable users to see both the real world and virtual images simultaneously, contributing to an immersive experience in interactions and visualization. Recently, to reduce the size and weight of smart glasses, waveguides incorporating holographic optical elements in the form of advanced grating structures have been utilized to provide light-weight solutions instead of bulky helmet-type headsets. However current waveguide displays often have limited display resolution, efficiency and field-of-view, with complex multi-step fabrication processes of lower yield. In addition, current AR displays often have vergence-accommodation conflict in the augmented and virtual images, resulting in focusing-visual fatigue and eye strain. Here we report metasurface optical elements designed and experimentally implemented as a platform solution to overcome these limitations. Through careful dispersion control in the excited propagation and diffraction modes, we design and implement our high-resolution full-color prototype, via the combination of analytical–numerical simulations, nanofabrication and device measurements. With the metasurface control of the light propagation, our prototype device achieves a 1080-pixel resolution, a field-of-view more than 40°, an overall input–output efficiency more than 1%, and addresses the vergence-accommodation conflict through our focal-free implementation. Furthermore, our AR waveguide is achieved in a single metasurface-waveguide layer, aiding the scalability and process yield control. 

Abstract Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with anS-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (E_of) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).