Page 661 - Introduction to Information Optics

1 1.4. Information Display Using Electro-Optic Spatial Light Modulators 645

to J out may be realized by applying the matrix M pr as follows:

out = M pr(A)/ in = A / in, (1 1.36)

where M pr is the Jones matrix of the phase retarder.
The refractive indices of certain types of crystals can be changed according
to the external applied electric field. This induces birefringence in the crystals
and is called the electro-optic effect. Two commonly used crystals for SLMs,
based on the electro-optic effect, are electro-optic crystals and liquid crystals.
In electro-optic crystals, the applied electric field redistributes the bonded
charges in the crystals. This causes a slight deformation of the crystal lattice.
As a result of this, the refractive indices of the crystals are changed according
to the applied electric field [31]. In the case of liquid crystals, an external
electric field exerts torque on the electric dipole in each liquid crystal molecule.
This causes the rotation of the dipole in the liquid crystal, which induces
different phase retardation for the propagating light through the liquid crystal.
For a detailed discussion of the electro-optic effect in liquid crystals, refer to
[32].
Electro-optic phase retardation can be described mathematically through
the use of the Jones matrix. For the linear (or Pockets) electro-optic effect in
uniaxial crystals, the refractive indices are changed linearly proportional to the
applied electric field and the Jones matrix for the effect, as given by:

with A = (2n/A)yE zd, where y, E z, and d represent the electro-optic coefficient,
the magnitude of the applied electric field along the z-direction, and the length
of the crystal, respectively. Note that in the Pockels effect, a change in the
electric field along the z-axis induces phase retardation along the x- and >'-axes
[19,31]. Figure 11.22 shows an intensity modulation system that is composed
of an electro-optic crystal and two polarizers.
A polarizer is an optical device that allows light with a certain polarization
state to pass through. The polarizers, shown in Fig. 11.22, allow polarization
transmit through their polarization axes along the x and y directions, respect-
ively. The Jones matrices of the two polarizers for the x and y directions are
given by

(H.38)