Space charge effects 364 INDEX

Figure 3.38. Principle of the photorefractive effect By photoexcitation, charges are generated that have different mobilities, (a) The holographic irradiation intensity proHle. Due to the different diffusion and migration velocity of negative and positive charge carriers, a space-charge modulation is formed, (b) The charge density proHle. The space-charge modulation creates an electric Held that is phase shifted by 7t/2. (c) The electric field profile. The refractive index modulation follows the electric field by electrooptic response, (d) The refractive index profile.

The most useful of the known photorefractives are LiNbC>3 and BaTiC>3. Both are ferroelectric materials. Light absorption, presumably by impurities, creates electron/hole pairs within the material which migrate anisotropically in the internal field of the polar crystal, to be trapped eventually with the creation of new, internal space charge fields which alter the local index of refraction of the material via the Pockels effect. If this mechanism is correct (and it appears established for the materials known to date), then only polar, photoconductive materials will be effective photorefractives. However, if more effective materials are to be discovered, a new mechanism will probably have to be discovered in order to increase the speed, now limited by the mobility of carriers in the materials, and sensitivity of the process. 

We note from Eq. (15) that the space-charge field is shifted in space by n/2 with respect to the intensity pattern [Eq. (11)], which corresponds to a distant shift of Ag/4 in the x direction (Fig. 3d). This space-charge field induces an index volume grating via the Pockels effect (Fig. 3e). The refractive index including the fundamental component of refractive index modulation with magnitude of An can be written as... 

When the space-charge field can be constructed, the index modulation can also be built correspondingly. This mechanism can be a linear EO effect or an index modulation via alignment of the NLO chromophore in a low glass transition... 

The last requirement for a PR effect is the mechanism for index modulation in the response of the space-charge field. Two mechanisms have been found to lead to index change EO response and birefringence. 

Figure 3 Refractive index change associated with the orientational enhancement effect. The arrows represent the direction of the total field Ej which is the sum of the applied and space-charge fields.

The linear electro-optic effect (see Chapter 4) transfers the periodically modulated space-charge field into a refractive index grating ... 

This quantity is independent of the index k because, for the present development, we are ignoring any effects of the space charge. [From eqn. (37), we see that Ek = E0 for all values of k when the space charge is negligible]. Equation (119) above likewise yields Jfe + 1 merely by replacing k by k + 1 in the three places where it occurs. Thus substituting eqn. (119) into the steady-state relation given by eqn. (118) yields... 

The electro-optic effect leads to the modification of the refractive index of a suitable material when an electric field is applied (Figure 8). The electro-optic effect must be present in a photorefractive material, so that the space charge electric field pattern due the relocated charges will lead to a patterned refractive index in the material this is a hologram. 

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