# Liquid-Crystal-on-Silicon for Augmented Reality Displays
## 2 LCoS Working Principles
### LC Material Optimization Strategies  
In electro-optic modulation, a general requirement applies to all of the above-mentioned modes: \(d\Delta n/\lambda\) equals a certain value. Regarding electrical properties, the CMOS circuitry limits the operation voltage to \(<\)6 V for small-pitch panels. Such a low voltage can be achieved by increasing the dielectric  
Figure 4: The LC director orientations in the 90\({}^{\circ}\) TN mode: (**a**) Voltage-off state; (**b**) Voltage-on state.  
Figure 5: The LC director orientations in the HG mode: (**a**) Voltage-off state; (**b**) Voltage-on state.  
anisotropy of LC materials, which could be obtained by applying lateral and terminal polar groups (such as F, CN, NCS, CF\({}_{3}\) or OCF\({}_{3}\)) [37; 38; 39], polar CF\({}_{2}\)O bridges [40], and polar heterocycles [41; 42]. However, these components often lead to a compromised nematic temperature range, lower solubility and higher viscosity \(\gamma_{1}\)[38]. Breaking this trade-off, the difluoromethylay bridge (-CF\({}_{2}\)O) [43] and isothi cyanato group (-NCS) [44; 45] could improve \(\Delta\varepsilon\) while retaining a reasonably low \(\gamma_{1}\). Whereas the former breaks the molecular \(\pi\)-\(\pi\) conjugation resulting in a low \(\Delta n\), and the latter gives rise to the annoying charge accumulation effect, which degrades the voltage holding ratio. Here comes the second consideration on electrical properties--the resistivity which determines the voltage holding ratio. Although LCoS devices demand a lower LC resistivity (>10\({}^{12}\)\(\Omega\)-cm) than the active matrix displays (>10\({}^{13}\)\(\Omega\)-cm) [46; 47], it still limits the LC component selection. Compounds with a large \(\Delta\varepsilon\) would require multiple dipoles, which may lead to a compromised \(\gamma_{1}\).  
From the aspect of device configuration, a thinner cell gap helps gain fast response time with the adoption of a slightly higher \(\Delta n\) LC. To be noticed, the toughest color to achieve the 2\(\pi\) phase modulation is red because of the longest wavelength and the lowest birefringence. Various terpenyls and tolanes have been developed for high \(\Delta n\) LCs [48; 49]. Although many precise modifications of the molecular chemical structures have been mentioned [50; 51; 52], such as shifting the location of the mesomorphic core, introducing the lateral substituents into different positions and the various terminals, the high \(\gamma_{1}\) of terpenyls and the poor UV stability of tolanes remains unsolved [53]. Those are the properties not intended to be compromised. Additionally, the voltage shielding effect by alignment layer reduces the effective voltage applied to the LC layer in thin cells [54; 55]. In summary, a delicate balance should be reached between high birefringence, high dielectric anisotropy, low melting point, low viscosity, high resistivity, and good UV stability according to the device configuration. The state-of-the-art LC material development reaches a submillisecond response time for VA [56; 57; 58] and MTN [46; 59] LCoS at 40 \({}^{\circ}\)C, and a \(\sim\)2 ms response time for 2\(\pi\) phase modulation [46; 47]. More than that, these optimization strategies and the developed materials could be applied to other LC phase modulation-based devices such as tunable lenses, scanners, tunable filters, and optically addressed spatial light modulators [60; 61; 62; 63; 64], which may be incorporated in AR systems in other ways.