Metagrating meets the geometry-based efficiency limit for AR waveguide in-couplers

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.