Page 365 - Electrical Properties of Materials

Volume holography and phase conjugation 347

What happens when we illuminate the hologram with the reference wave?
According to the rules of holography, the object wave springs into existence.
Interestingly, we could reach the same conclusion, considering Bragg diffrac-
tion. If a wave is incident upon a material with a periodic structure at an
angle and wavelength that satisfies eqn (13.8), then a diffracted beam of appre-
ciable amplitude will emerge. In fact, under certain circumstances it is possible
to transfer all the power of the incident reference wave into the diffracted
object wave.
What happens when the object wave is not a plane wave but carries some
pictorial information in the form of some complicated amplitude and phase
distribution? Since any wave can be represented by a set of plane waves, and
since the modulation of the dielectric constant is small, one can apply the prin-
ciple of superposition, leading to the result that each constituent plane wave,
and thus the whole picture, will be properly reconstituted.
The photosensitive media most often used are silver halide emulsion (ba-
sically the same as that used for photography but with smaller grain size) and
dichromated gelatin. In the former case, the refractive index modulation is due
to the density variation of silver halide in the gelatin matrix. In the latter case,
the mechanism has still not been reliably identified. It is quite likely that the
refractive index modulation is caused again by density variations mediated by
chromium, but explanations claiming the presence of voids cannot be discoun-
ted. Unfortunately, it is rather difficult to know what goes on inside a material
when chemical processing takes place. We can, however, trust physics. It in-
volves much less witchcraft. So I shall make an attempt to give an explanation
of the origin of dielectric constant modulation in photorefractive materials.
As I mentioned previously, a photorefractive material is both photoconduct- photorefractive crystal
ive and electro-optic. Let us assume again that two plane waves are incident
upon such a material, but now a voltage is applied as well, as shown in
Fig. 13.7. The light intensity distribution [given by eqn (13.7)] is plotted in
Fig. 13.8(a). How will the material react? The energy gap is usually large, so
there will be no band-to-band transitions but, nevertheless, charge carriers (say
V
electrons) will be excited from donor atoms, the number of excited carriers be-
ing proportional to the incident light intensity. Thus, initially, the distribution
+
of electrons (N e ) and ionized donor atoms (N ) is as shown in Fig. 13.8(b) and y
D
(c). Note, however, that the electrons are mobile, so under the forces of diffu-
sion (due to a gradient in carrier density) and electric field (due to the applied
voltage) they will move in the crystal. Some of them will recombine with the Fig. 13.7
donor atoms while some fresh electrons will be elevated into the conduction Two plane waves incident upon a
band by the light still incident. At the end an equilibrium will be established photorefractive crystal across which a
when, at every point in space, the rate of generation will be equal to the rate of voltage is applied.
recombination. A sketch of the resulting electron and donor densities shown in
Fig. 13.8(d). Since the spatial distributions of electrons and ionized donors no
longer coincide, there is now a net space charge, as shown in Fig. 13.8(e). Now
remember Poisson’s equation. A net space charge will necessarily lead to the
appearance of an electric field [Fig. 13.8(f)]. So we have got an electric field
which is constant in time and periodic in space. Next, we invoke the electro-
optic property of the crystal which causes the dielectric constant to vary in
proportion with the electric field. We take r, the electro-optic coefficient, as
positive, so the dielectric constant is in anti-phase with the electric field. We