# Liquid-Crystal-on-Silicon for Augmented Reality Displays
## 3 Fringing Field Effect and Novel Solution  
To optimize the optical performance of LCoS systematically, several research groups have devoted efforts in device modeling [65; 66; 67]. However, until recently, the fringing field effect (FFE) still remains the major issue to be tackled with [68; 69; 70; 71; 72; 73]. In order to display greyscale images, different pixels could have different voltages. The unequal voltages on adjacent pixels give rises to FFE. As Figure 6 depicts, when a bright pixel is adjacent to two dark pixels, a dark split region may appear in the bright pixel area, and light leakage arises at the edge of the dark pixel, leading to display luminance loss and reduced contrast ratio. The severity of FFE depends on the display mode and the device configuration. Generally speaking, VA has the strongest FFE, resulting in a \(\sim\)30% luminance loss; 90\({}^{\circ}\) MTN is the least sensitive to FFE; while the HG mode is a favored choice for phase modulation. Figure 6 shows the FFE of VA mode with different pixel sizes and cell gap. Because of the small inter-pixel gap, LCs on the pixel edge experience strong horizontal electric field, giving rise to phase distortion. This phenomenon is not obvious in direct-view transmissive LCDs because the inter-pixel region is covered by a large-area black matrix (>5 \(\upmu\)m). The asymmetry of phase retardation/reflection is determined by the alignment direction of the pretilt angle. In Figure 6, the same resolution density is compared, which is determined by pixel pitch \(p\). With a thinner cell gap \(d\), the FFE-affected region is compressed to a narrower edge. Applying this thin cell strategy [69; 70], the cell gap in VA LCoS is optimized to \(d\) < 2 \(\upmu\)m [73].  
FFE is especially pronounced in small-pitch LCoS devices [69], which is highly desirable in augmented reality applications. Because of the reduced pixel pitch and cell gap (\(p\)/\(d\)) ratio, the unwanted horizontal electric field is strengthened [70]. This can be seen from Figure 6: when the resolution density is doubled (\(p\) changes from 16 \(\upmu\)m to 8 \(\upmu\)m), the absolute FFE width \(w\) is relatively stable, while the ratio of the FFE-affected region increases dramatically. Several methods have been proposed to reduce FFE. In 2002, [PERSON] et al. explored how sloped electrodes help reduce FFE with quantitative exploration [68]. An optimal electrode slope of 1 was demonstrated for 80\({}^{\circ}\) MTN cell and 45\({}^{\circ}\) TN cell, while the VA and HG modes call for further improvement. In the same year, a finger-on-plane type common electrode was designed to eliminate the pixel-splitting phenomenon [74]. Whereas the diffraction effect and relatively low optical efficiency hinder its widespread applications [69]. In 2005, [PERSON] et al. minimized FFE by a double-sided electrode design, where the requirements of dual TFTs and pixel registration brings manufacturing challenges [75]. Later, [PERSON] et al. proposed to adopt circularly polarized light in the VA mode for FFE suppression [69]. Though an impressively high optical efficiency and fast dynamic response were demonstrated, hardly can this method be integrated into the preferred normally black reflective VA mode. In other words, the contrast ratio is compromised. In 2015, [PERSON] et al. adopted non-rectangular pixel electrodes for pixel edge FFE compensation [76]. This design works well on large pixels while the degree of structural modification is constrained on small-pitch configurations. To satisfy the urgent need of FFE reduction on small-pitch LCoS devices, here, we propose a novel design of patterned pretilt angle control [77; 78; 79]. The formed inhomogeneous LC director distribution could oppose the FFE induced by neighboring pixels.