Page 659 - Introduction to Information Optics

11.4. Information Display Using Electro-Optic Spatial Light Modulators 643

11.4. INFORMATION DISPLAY USING ELECTRO-OPTIC
SPATIAL LIGHT MODULATORS

In this section, we first discuss the electro-optic effect. We then present an
electron-beam-addressed spatial light modulator and an optically addressed
spatial light modulator as examples, which use the electro-optic effect to
accomplish the important phase and intensity modulation.

11.4.1. THE ELECTRO-OPTIC EFFECT
Many SLMs are based on the electro-optic effect of crystals. This section
presents the electro-optic effect through the use of a mathematical formalism
known as Jones calculus. The refractive index of a birefringent crystal depends
on the direction of the crystal. Specifically, uniaxial birefringent crystals, which
are the most commonly used materials, have two different kinds of refractive
indices. In them, two orthogonal axes have the same refractive index; these are
called ordinary axes. The other orthogonal axis, which is called the extra-
ordinary axis, has a different index. A uniaxial birefringent crystal is shown in
Fig. 11.21. When light propagates along one of the ordinary axes (z — axis) in
the crystal and with the polarization in the x — y plane as shown, the light
experiences two different refractive indices.
The electric field, E, that propagates along the z-axis is then decomposed
into two components along the ordinary and extraordinary axes:
w k z} /(w
E = xA nti ^ °' ~ -° + yA na e '<>' ~ *--'> , (11.30)

where x and y represent the unit vectors along the x- and y-axes, respectively,
k no = (2n//. v)n 0 and k ne — (27t/A,.)n e, respectively, represent the wavenumbers
associated with the different indexes, A v is the wavelength of light in free space,
and and n 0 and n e are the ordinary and extraordinary refractive indexes,
respectively. The Jones vector for £", which is composed of two components of
linear polarization, is defined by:

Note that the Jones vector represents the polarization state of the linearly
polarized plane wave by means of two complex phasors. Referring to the
coordinates of Fig. 1 1.21, we therefore see that the Jones vector for the incident
light (at z — 0) to the birefringent crystal is given by