# Static Structures in Leaky Mode Waveguides +
## 1 Introduction  
This study is important to the use of leaky mode modulators as near-eye displays because it seeks to increase the device's field of view without making the fabrication of the device significantly more complex. Currently, near-eye displays are almost exclusively driven by pixelated spatial light modulators [1]. However, leaky mode modulators have a number advantages over pixelated spatial light modulators (SLMs) for the purposes of near-eye holographic display. They require only two mask steps to fabricate. They are transparent. They produce no zero order, no higher orders, and no conjugate images. They do not suffer from quantization error from pixilation, and they require no backplane. Additionally, they have the ability to rotate the polarization of the diffracted signal light for easy noise filtering. Finally, they can also multiplex color in the frequency domain, allowing all colors to be modulated in the same waveguide. However, these advantages notwithstanding, bottom-exit devices (the configuration most useful for near-eye display) suffer from a reduced field of view. In side-exit leaky mode devices, we observe a large multiplication of diffracted light angle because the device is operating in a regime where the grating equation is nonlinear [2; 3]. In a bottom-exit device, leaky mode light passes through a high-spatial-frequency output grating that operates in opposition to the leaky mode diffraction [4]. This second interaction effectively erasadvantage gained from illuminating the acoustic holographic pattern at a glancing angle. The result of the reduction is that the leaky mode device effectively has a smaller achievable field of view (defined in this work as the visible extent at a given depth) or view zone (defined here as the angular extent over which a point is visible). Note that these concepts are duals in this context and will be treated interchangeably in the text. Our previous work identified the narrowing of view angle in bottom-exit devices as a challenge and stated that a solution would be described in a future publication [4]. The main aim of this work is to present that solution to restore or increase the leaky mode device view zone/field of view (see Figure 1) and/or view zone by temporally stitching together multiple diffracted orders of light created by a static internal grating. Other researchers have used higher-order images to increase the display view zone, field of view, and space bandwidth product [5; 6]. This work differs from previous efforts in several ways. First, our holographic pattern is a rapidly moving analog signal and not a pixel pattern with fixed locations. Also, leaky mode devices in near-eye applications can have an extremely high refresh rate--potentially exceeding 100 kHz for a 1 cm free-running surface acoustic wave (SAW) aperture (a leaky mode device can write a one millimeter aperture in approximately one microsecond). This refresh rate is at least two orders of magnitude higher than that of commercial near-eye displays and it allows us the ability to contemplate a line-rate approach to increasing field of view. Additionally, our leaky mode devices are made on a highly transparent lithium niobate substrate which is desirable for near-eye applications. Furthermore, using femtosecond laser pulses, we can create high-contrast, laser-induced gratings in the bulk of the substrate [7; 8] with a number of diffracted orders of visible power. Finally, in addition to spatial light modulation, lithium niobate is an excellent electro-optic substrate which is frequently used to make fast (up to picosecond-rate) phase and amplitude modulators [9]. These unique attributes of a moving pattern, high refresh rate, high-contrast internal gratings, and integrated illumination pulsing are important to our proposed solution for increasing the field of view in bottom-exit leaky mode devices.