Analysis of the longitudinal component of the electric field generated by flat and pixelated liquid crystal displays

The longitudinal, z, component of the electric field is investigated for the pixelated and flat liquid crystal displays (LCDs) for monochromatic case. The pixelation process is assumed to occur in free space. The z component is computed in the Fourier domain by using Gauss's Law from the x and y components of the output electric field. The effect of the display parameters are discussed for a y polarized display in a phase only operation. It is found that, in the low frequency regions, the size of the region of the large magnitudes becomes smaller as the width of the active region increases. Moreover, the validity of the scalar theory for a single pixel is evaluated for varying pixel sizes. It is shown that, when the ratio of the width of the active region to wavelength is between 1.5 and 5, the error decays with oscillations between 43% and 5%. When that ratio is larger than 15, the error does not exceed 3%.