Page 673 - Introduction to Information Optics

11.4. Information Display Using Electro-Optic Spatial Light Modulators 657

y
Alignment
direction
A\^\ x M/\
Alignment
direction

Alignment layers
Fig. 11.32(a). PAL-SLM when there is no applied field; pure phase change without change of
output polarization if the incident light is linearly polarized along the director's axis.

the phase change can be a pure phase modulation (without changing the
polarization state). For example, consider the case of a linearly polarized light
incident on a PAL-SLM with the light polarization parallel to the director's
axis. The output light will experience a phase change and remains the same
polarization at the exit of the SLM, as shown in Fig. 11.32(a).
For a voltage-controlled phase modulator, we look at the situation in Fig.
11.32(b), where the electric field is applied along the z-direction. The electric
field tends to tilt the molecules as shown in the figure. When the applied
electric field is strong enough, most of the molecules tilt, except those adjacent
to the alignment layer due to the elastic forces at the surfaces. The tilt angle as
a function of the voltage V (strictly speaking, it is the root-mean-square value
of the applied voltage as the voltage is AC across the SLM) has been described
by the following equation [40, 43]:

0,
6 = (11.50)
--2tan 'exp

where V th is a threshold voltage below which no tilting of the molecules occurs
and V Q is a constant, when V - V th = V Q, 9 ~ 50°. For V - V th > K 0, the angle
9 keeps increasing with V, eventually reaching a saturation value of n/2 for