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Recently, augmented reality (AR) displays have attracted considerable attention due to the highly immersive and realistic viewer experience they can provide. One key challenge of AR displays is the fundamental trade-off between the extent of the field-of-view (FOV) and the size of the eyebox, set by the conservation of etendue sets this trade-off. Exit-pupil expansion (EPE) is one possible solution to this problem. However, it comes at the cost of distributing light over a larger area, decreasing the overall system's brightness. In this work, we show that the geometry of the waveguide and the in-coupler sets a fundamental limit on how efficient the combiner can be for a given FOV. This limit can be used as a tool for waveguide designers to benchmark the in-coupling efficiency of their in-coupler gratings. We design a metasurface-based grating (metagrating) and a commonly used SRG as in-couplers using the derived limit to guide optimization. We then compare the diffractive efficiencies of the two types of in-couplers to the theoretical efficiency limit. For our chosen waveguide geometry, the metagrating's 28% efficiency surpasses the SRG's 20% efficiency and nearly matches the geometry-based limit of 29% due to the superior angular response control of metasurfaces compared to SRGs. This work provides new insight into the efficiency limit of waveguide-based combiners and paves a novel path toward implementing metasurfaces in efficient waveguide AR displays.more » « less
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