Liquid Crystal Displays. Ernst Lueder

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obtain the contrast in Equation (3.82) as

(3.84)

The optimum contrast is reached for a = π/4 for which C → ∞ because the denominator in Equation (3.84) is zero for all wavelengths. Further, for a = π/4 the numerator is maximum. The case a = π/4 is shown with dotted lines in Figure 3.11(a). The analyser is perpendicular to the linear polarized light at the output if a field is applied, and hence provides blocking of light independent of λ.

The normally black mode is shown in Figure 3.11(b). The analyser is perpendicular to the angle β = π − α, and allows the intensity Iy′ in Equation (3.73) to pass. This represents the black state. If a large enough field is applied, the light with the electrical field

(3.85)

independent of wavelength can pass the analyser according to Figure 3.11(b). This is the white state. The contrast is with Equations (3.85) and (3.73)

      (3.86)

For the single wavelength λ₀ in Equation (3.79), C is infinite as λ₀ is blocked; this does not apply for other wavelengths in the light. Therefore, contrast in the normally black state is inferior to the contrast in the normally white state in Equation (3.84). An optimum C dependent on α does not exist. For α = π/4 the normally black cell has two parallel polarizers. This configuration will be used for reflective cells.

       3.2.3 The reflective Fréedericksz cell

A reflective cell is depicted in Figure 3.12(a) (Uchida, 1999; Lueder et al., 1998). The polarizer transmits linearly polarized light again at an angle of π/4 to the x-axis in Figure 3.12(b). The illumination is provided either by ambient light or by an external light source above the polarizer. After having travelled through the cell in Figure 3.12(a) with half the thickness d/2 of a transmissive cell, the light is reflected at the mirror usually made of Al and finally exits through the same polarizer. Thus, the reflective cell saves one polarizer. The reflective cell can be designed according to the general principles, which will be outlined now (Lueder et al., 1998). We first recall the operation of a Freedericksz cell with parallel polarizers as depicted in the left column of Figure 3.12(c). We know that linearly polarized incoming light in the direction α = π/4 to the x-axis is blocked at z = d for wavelength λ₀. Due to Equation (3.80), the thickness is d = λ₀/2Δn. We determine at which value z the light is circularly polarized.

      With Equation (3.45) this happens for the first time for δ = π/2, reflecting in

(3.87)

      As sin δ = sin(π/2) > 0 the light is right-handed circularly polarized seen against , as indicated in the middle column of Figure 3.12(c). The highly conductive mirror in the middle column in Figure 3.12(c) reflects this light which is drawn with solid lines in two positions from 1 to 2 for increasing time. Since the mirror cannot sustain an electric field as the high conductance shortens the fields, the field vectors 1 and 2 have to be compensated by vectors 1′ and 2′ of the reflected light shown with dashed lines. The reflected light propagates in the direction of the wave vector , and it represents left-handed circularly polarized light seen against kr. The upwards travelling reflected light in the right column in Figure 3.12(c) images the downward moving light in the left column, and is blocked in the polarizer as linearly polarized light, in the same way as the downward travelling light is at its lower polarizer. The described imaging of the downward wave by the reflected wave can no longer take place if the mirror is not placed at z = d/2. Therefore, many reflective cells are constructed according to the principle discussed. If a voltage V is applied to the reflective cell, the LC molecules orient themselves in parallel to the electric field for Δε > 0. The linearly polarized light travels downward, is reflected, reaches the polarizer unchanged apart from a phase shift and passes the polarizer. Hence, the reflective cell exhibits the same electro-optical performance as the transmissive cell. The performance is given for the normally black Freedericksz cell with parallel polarizers defined by α = π/4 and Equations (3.73) and (3.85).

Figure 3.12 The reflective Fréedericksz cell. (a) Cross-section; (b) top view; (c) explanation of the operation of a reflective cell in the field-free state

The normally white cell with crossed polarizers cannot be transformed into a reflective version as this version has only one polarizer able to realize only parallel polarizers. This fact, however, renders the reflective cell somewhat more economic as the added mirror is cheaper than the saved polarizer.

      The surface of the mirror and the lower edge of the LC material in Figure 3.12(a) are supposed to be located at z = d/2, which is not exactly feasible because of the presence of the ITO and the orientation layers. As both layers are very thin, around 100 nm each, this does not show up in the performance of the cell.

       3.2.4 The Fréedericksz cell as a phase-only modulator

So

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