Reflective liquid-crystal displays with asymmetric incident and exit angles

The $2\times 2$ matrix methods are extended to calculate the optical behaviors of reflective liquid-crystal displays with asymmetric incident and exit angles. Both the unfolding method and the backward-eigenwave method are employed to derive the $2\times 2$ matrix representations. The simulation results for symmetric incident and exit angles from these two methods are identical and agree well with those obtained from the $4\times 4$ matrix method when the air–panel surface reflections are neglected. Further, the derived $2\times 2$ matrix methods are applied to the asymmetric cases with different incident and exit angles. The simulated results on the normally black vertical alignment and normally white mixed-mode twisted nematic reflective displays show reasonably good agreement with the reported experimental data. In addition, a rubbing effect related to contrast values is observed and analyzed in asymmetric reflective cases. We also find that this effect has a significant influence on the contrast ratios once the difference between the incident and exit angles becomes large.