3.19 The reflective HAN cell. (a) Cross-section; (b) optical anisotropy An(z)
We know from Equations (3.45) and (3.54) that a retardation of λ/4 transforms linearly into circularly polarized light as desired at the mirror of a reflective cell. From (1/2) Δnd = λ/4 we obtain
This is twice the thickness of the reflective Fréedericksz and DAP cells, resulting in a higher fabrication yield. This advantage of the HAN cell was brought about by lowering the effective birefringence. We shall encounter the same effect again with TN cells.
The reflection of the circularly polarized light in the field-free state is depicted in Figure 3.20(a) (Glueck, 1995). After the reflection the wave reaches the polarizer rotated by 90° and is blocked. If a field is applied in Figure 3.20(b), the molecules orient themselves due to Δε > 0 in parallel to the field, birefringence does not take place, and the reflected wave passes the polarizer. The cell is normally black.
For the homeotropic alignment of the molecules, an obliquely evaporated or sputtered SiO2 orientation layer is again a good solution.
Figure 3.20 The operation of a reflective HAN cell. (a) In the field-free state; (b) if a voltage is applied
3.2.7 The π cell
So far we have not dealt with the time needed to switch an LC cell from the black state to the white state, or vice versa. Dynamics of a cell are based on mechanical properties of the LC material, and will be discussed in Section 3.2.8. Some information on switching speed can, however, be derived from the field of directors. That’s how a very fast switching cell, the π cell, has been found (Bos and Koehler, 1984), as will be outlined later in this chapter.
The Fréedericksz cell and the TN cell exhibit a uniform alignment of the molecules with a pretilt α in the opposite direction on the substrates, as shown in Figure 3.21(a) for the on-state of the cell. After the electric field has been switched off, the molecules relax to the off-state, resulting in a low of LC material and a tilting of the molecules. The molecules around the centre of the cell are exposed to a torque, causing aback-flow of the material and trying to rotate them through a large angle to the position in the off-state. This slows down the switching process. Figure 3.21(b) depicts the pretilt of the π cell pointing in the same direction on both substrates. In this case, the molecules in the centre of the cell experience almost no torque while they relax into the off-stage. The angles by which the relaxing molecules have to be tilted are smaller, resulting in a much higher switching speed.
The phenomenon of a ‘back-flow’ causes the ‘optical bounce’ in the electro-optical response to a rectangular voltage in Figure 3.22(a), whereas the response of the π cell in Figure 3.22(b) does not exhibit the prolonged relaxation time. In a TN cell switching off takes, as a rule, 3 to 4 ms, whereas the π cell requires only around 1 ms. However, after 1 ms the relaxation is not yet completely finished, which may not be noticeable at a high enough switching frequency. If the uncompleted relaxation is disturbing, a holding voltage of around 2 V or a polymer stabilization (Vithana and Faris, 1997) arrests the relaxation.
Figure 3.21 The pretilt angles and the relaxation to the off-state. (a) Of a TN cell; (b) of a π cell
As in the HAN cell, the optical anisotropy Δn in the π cell for VLC = 0 changes along the z-axis, which is denoted by Δn(z). As a consequence, the optical retardation R from the input at z = 0 to the output at z = d is
Figure 3.22 The electro-optical response to a square voltage pulse. (a) Of a TN cell with a prolonged relaxation; and (b) of a π cell with a fast relaxation
(3.98)
where Δn(z) depends upon the angle Θe in Figure 3.21(b). We shall derive Δn(Θe) in Chapter 6, leading to Equation (6.29). For a π cell with crossed polarizers, the transmission T is obtained by a straightforward calculation with Jones vectors, yielding
(3.99)
A normally white cell has the first transmission maximum at (π/λ)R = (π/2), or
corresponding to a λ/2-plate. We introduce an effective anisotropy Δneff for the entire optical path in the cell, which is given by
(3.101)
providing, with Equation (3.100),
(3.102)
The term Δneff renders this result similar to Equation (3.97).
The wide viewing angle inherent to the π cell is discussed in Section 6.3.2.
3.2.8 Switching dynamics of untwisted nematic LCDs
We assume that the LC molecules are anchored on the surface at z = 0 at an angle Θ0 to the normal and at z = d under the angle Θd,
