# Considerations of Curvature for a Near-Eye Holo-Video Display
## 1 Introduction  
Leaky-mode lithium niobate (LiNbO\({}_{3}\)) devices show promise for near-eye applications. The flat, clear material is a perfect candidate for a low-profile display. The devices are direct-view, monolithic, and highly transparent, in contrast to other proposed technologies [1; 2]. They have low relative fabrication complexity and no backplane (i.e., no backing material required for reflection, absorption, etc.). Furthermore, they potentially support very high bandwidth [3] and do not suffer from quantization error of pixelated devices (i.e., error caused by pixelized spatial sampling) [4; 5; 6]. They can rotate the polarization of light for low noise operation, where the unused light can be eliminated from the final image with a simple polarizer [7]. Finally, they can selectively modulate light based on color in the frequency domain [8; 9].  
Leaky-mode surface-acoustic-wave (SAW) LiNbO\({}_{3}\) devices can be categorized into two groups: edge-exit and face-exit (as illustrated in Figure 1). Edge-exit devices have a wide deflection angle [10] and have various potential applications, notably a holo-video monitor [7; 11]. Face-exit leaky devices, however, suffer from a reduced deflection angle. The main reason to use face-exit devices for a near-eye display is that the output of the display is angled toward the user and requires little to no external redirection (which would not be the case for an edge-exit device) [10; 12]. Another notable reason includes removing the zero-order light from the image without the need for a polarizer, which the edge-exit device requires. Finally, by using the entire face, these devices remove the limit to the numerical aperture created by the edge-exit variety.  
Achieving a large field of view (FOV) has been a challenge for many augmented reality (AR), near-eye technologies, with most managing to achieve somewhere around 20-80\({}^{\circ}\)[13; 14; 15; 16; 17]. Previous 3D display technologies have demonstrated this capability (i.e., alcove holograms), but these were not near-eye transparent displays [18]. Microlens arrays show promise for virtual reality (VR) displays, but these rely on opaque screens to project an image (and thus are not suited to AR) [19] or some external projector to shine light on to the lens array [20]. Some near-eye displays use complex lens systems and/or external cameras to augment the user's FOV, but these are either bulky or add distortions that must then be accounted for [15; 21].  
Our goal is to achieve a full 180\({}^{\circ}\) FOV, while minimizing the sacrifice to angular resolution. To this end, in this paper, we explore models that optimize the FOV parameter. In addition to FOV, we also consider the limitations of co-linear, SAW-driven optical deflection with respect to maximum allowable angle. We also explore various geometries; this allows us to rearrange the boundaries of what we can achieve with this device. Finally, we present one potential instantiation of a binocular display. Our discussion is limited to increasing FOV in one direction (horizontal), since curving the crystal in one dimension is fairly straightforward, whereas bending in two dimensions requires additional complexities that we are unwilling to challenge in this paper.