Page 134 - Introduction to Information Optics

2.7. Processing with Photorefractive Optics

A2 Photorefractive Ai
midium

A2

Fig. 2.36. A two-wave mixing configuration.

lk
r
hologram is illuminated by the reference beam A 2e >' , the diffracted beam is
given by
ik r
0(.x) = r}AiA$A 2e- '' , (2.102)
where ?/ is the diffraction efficiency. Notice that the phase of A 2 cancels out and
ki T
the diffracted beam is the reconstruction of the object beam A{' ' . Similarly,
the reference beam A 2 can be reconstructed by illuminating the hologram with
object beam A r
In addition to holographic analogy, two-wave mixing in most PR crystals
exhibits amplification, which is a unique feature not available in conventional
holography. This occurs most efficiently in crystals where the dynamic PR
index grating is 90° out of phase with respect to the intensity interference
grating, as can be seen in Fig. 2.35. The energy exchange is unidirectional, with
the direction of the energy flow determined by the crystal parameters, such as
the crystal orientation and the sign of the photoionized charge carriers.
Customarily, the beam that loses energy is labeled as the pump beam, and the
beam that becomes amplified is called the probe beam.. Because the light energy
is coupled from one beam to another, two-wave mixing is also known as
two-beam coupling.
In the four-wave mixing configuration, two coherent beams write an index
hologram and a third beam reads the hologram, creating the fourth (i.e.,
output) beam by diffraction, as illustrated in Fig. 2.37. To satisfy the Bragg
condition, the third (read) beam must be counterpropagating relative to one of
the two writing beams. If the read beam has the same wavelength as the writing
beams, the configuration is called degenerate four-wave mixing; if the wave-
lengths of the read beam and write beams are different, it is called nondegener-
ate four-wave mixing. Although degenerate four- wave mixing has been used in
most of the applications demonstrated so far, nondegenerate four-wave mixing
may be used in some cases where the nondestructive reading of the hologram
is required. This can be achieved by choosing a reading wavelength beyond the
spectral response range of the photorefractive medium.