alt="equation images"/> whereas maxima occur at 4.2.4 Reflective TN cells
The basic structure of a reflective cell is depicted in Figure 3.12(a). After the light has passed the polarizer placed at an angle α to the x-axis, it is reflected at the rear mirror. Contrary to the untwisted case, we place the mirror at any distance z, and not only at z = d/2. Then the transmission from the input to the mirror is given by the Jones vectors Osσ and Osτ in
Figure 4.10 The reduced intensity of a mixed mode TN display
with the transition matrix
(4.86)
The σ–τ coordinates are shown in Figure 4.1 with the twist angle β from the x-axis. The components 0sσ and 0sτ are reflected at a mirror placed at z = d in Figure 4.1. If the mirror is metallic it cannot sustain an electric field. For this reason, an incident elliptically polarized wave in Figure 4.11 generates the electric field shown with dashed lines in Figure 4.11. This field is reflected and propagates in the z-direction towards the input. The dashed field has a phase shift from the incident field. This phase shift is omitted in the future calculation as it is of no importance for the intensity to be calculated. Therefore, neglecting the phase shift caused by the reflection, we assume the vector with the components Osσ and Osτ at z ≠ 0 as the input for a wave travelling in the opposite direction towards the input. The pertinent transmission matrix Tr is, according to the principle of reciprocity in physics (Yeh and Gu, 1999),
Figure 4.11 Incident (—) and reflected (- - -) elliptically polarized light at the metallic mirror of a reflective cell
(4.87)
where T′ stands for the transpose of T. With T′ we obtain
where Osx and Osy are the reflected Jones vectors at the input in the x–y coordinates. To obtain the component passing through the polarizer, we have to rotate the coordinates by α, resulting in
Osξ and Osη are the components in the ξ−η coordinates in Figure 4.1.
Insertion of Equations (4.85) and (4.88) into Equation (4.89) yields
With T from Equation (4.86), we obtain
and with Equation (4.90)
where the abbreviations in Equation (4.91) have been used. The intensity Iξ passing through the polarizer is
or
The intensity perpendicular to the polarizer is
or
(4.93)
An maximum for Iξ dependent on α is reached by d Iξ/d α = 0. This leads to
and for
