Jzξ may change from 2.8 × 2π × d to 3.2π × d. Obviously, the larger d the larger is the change of arc Jzξ, however, the necessary addressing voltage increases. For d = 3μ we obtain arc Jzξ= [8.4 × 2π, 9 × 2π], a change of 0.6 × 2π. Figure 3.16 shows in curve 1 with a = 0 a phase-only SLM with a maximum phase shift of 0.75π. Due to Equation (3.88), the other curves with a ≠ 0 cannot possess a constant magnitude, as is also visible in Figure 3.14.
For a = π/2 the linearly polarized light in Figure 3.15 always encounters the refractive index n┴ independent of the tilt, and hence is independent of V (curve 7 in Figure 3.16), which is of no use for a phase shifter.
3.2.5 The DAP cell or the vertically aligned cell
The cell operating with the deformation of aligned phases, called the DAP cell (Glueck, 1995), is the inverse of the Fréedericksz cell. In the field-free state the LC molecules are perpendicularly (or in other words, homeotropically) aligned to the surface of both substrates, as depicted in Figure 3.17. This cell is also called a Vertically Aligned (VA) LCD. In this situation, incoming linearly polarized light with a wave vector
Figure 3.17 The DAP cell or Vertically Aligned (VA) cell in the field-free state
If an electrical field is applied, the LC molecules orient themselves perpendicularly to the field as Δε < 0. This alignment corresponds to the same alignment of the Fréedericksz cell in the field-free state. Hence, all results in Equations (3.40) through (3.87) also apply to the DAP cell, which is exposed to an electric field. The DAP cell is as well suited for phase-only modulators, as the pertinent Equations (3.90) and (3.95) also hold if a voltage V is applied. However, for the voltage-dependent refractive index n(V), we obtain
Figure 3.18 The sputtering of an SiO2 orientation layer under an oblique angle of 70°
A reflective DAP cell with a thickness d/2 can be constructed in the same way as a Fréedericksz cell.
3.2.6 The HAN cell
The Hybrid Aligned Nematic cell (HAN cell) represents a mixture between the Fréedericksz cell and the DAP cell (Glueck, 1995). We investigate the reflective version in Figure 3.19(a), because among untwisted cells they have turned out to be more important. On the plate with the polarizer the LC molecules are in the field-free state in Figure 3.19(a) oriented all in the same direction parallel to the surface of the plate like in a Fréedericksz cell, whereas on the plate with the mirror they are homeotropically oriented. The linearly polarized light enters the cell at an angle α ≠ 0 to the x-axis, as in the transmissive and reflective Fréedericksz cells. The optical anisotropy Δп changes with z described by Δn(z). At z = 0 the light wave encounters the full anisotropy Δn, meaning that Δn(0) = Δn. This is only true for α ≠ 0. At z = d the light encounters no anisotropy as the medium is isotropic with a refraction index n┴, reflecting in Δn(d) = 0. Assuming a linear change of Δn(z) we obtain Δn(z) in Figure 3.19(b), leading to an effective retardation R of
(3.96)
