The Photorefractive Effect

The photorefractive effect is the term used for the changes induced in the refractive index of a material by a redistribution of photogenerated charges. 

There are four different processes involved in the production of this effect. 

Two coherent light beams intersect in the material creating a sinusoidal light intensity pattern 

Application of an external electric field causes the charges generated in the bright regions of the pattern to migrate (in polymers mobile charge carriers are holes) 

The charges are trapped in the dark regions of the pattern forming a space charge grating 

Adapted from Valley and Klein [13] and Moerner and Silence [12] with permission from the American Chemical Society. 

is the electro-optic (or Pockels) coefficient for a given geometry and n is the refractive index. 

Commonly, holes are the mobile charge carriers in photorefractive polymers. Since the migration of holes by diffusion is a rather slow process, a drift is enforced by the application of an external electric field. The latter not only promotes hole migration, but also provides essential assistance during the photo- 

A schematic depiction of the formation of a grating in a polymer film located in an external electric field is shown in Fig. 4.2. 

The grating is written by beams 1 and 2, which enter the film at angles of incidence and 2 with respect to the sample normal. The grating is written at a wave vector Kq at an angle p with respect to the external electric field Eq. The spatial periodicity of the grating is given by Eq. (4-2). 

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Several methods can be used for waveguide fabrication in LiNbOs. Among them, titanium in-diffusion and proton exchange (PE) are the most popular ones since they lead to the formation of well-confined and low-loss layers. PE is mainly applied because it results in a considerable decrease of the photorefractive effect in LiNbOj. However, waveguides obtained by pure PE have reduced EO and NL coefficients and usually a post exchange aimealing (APE) is required for restoration of the EO activity. 

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 photorefractive effect is classified here as a special third order effect for several reasons. First, it is perhaps the least well understood, mechanistically. Second, it represents the area of greatest current... 

Defect Properties and the Photorefractive Effect in Barium Titanate... 

These electrons are thermally ionized from the vacancy and may combine with an available acceptor, thus altering the charge state of the acceptor species. Experiments have shown that such a process can lead to a change in sign of the dominant photocarrier as well as modified gain and response time of the photorefractive effect. 

The molecular PR materials based on the methine dyes are composed of single types of molecules and exhibit the best PR performances. They are chemically pure, structurally well defined, and morphologically stable. They may serve as model materials for detailed photochemical and photophysical studies. Through these model materials, clearer pictures and a deep understanding of the photorefractive effect will emerge. Better mechanistic understanding will surely assist in the search for new PR materials with improved macroscopic properties. 

In the pursuit of improved photorefractive materials, seminal research by a group at IBM led by W. E. Moemer discovered the photorefractive effect in polymers in 1990 [4,40], Photorefractive polymers are generally composite materials... 

The photorefractive effect is usually probed by two beam-coupling experiments, in which one beam gains intensity at the expense of the other. This coupling is a characteristic property of the photorefractive effect. Such an asymmetric coupling requires an asymmetric shifting of the refractive index grating... 

Figure 7 Recording geometry for beam coupling through the photorefractive effect. The LC alignment, enforced by either surface or field effects, is usually homeotropic.

The Photorefractive Effect in Crystals and Amorphous Organic Media... 

Recombination of the mobile charges in dark regions is not necessary for the photorefractive effect to be observed, but it is beneficial. If the mobile charges were to be removed completely, or redistributed uniformly with no dependence on the intensity pattern applied, then an immobile pattern of eounterions would still be... 

Figure 4. The photorefractive effect with and without trapping. Top the intensity pattern on the material. Middle O, anion density +, cation density x, ideal distribution of trapping of mobile holes. Bottom comparison of the net charge distribution in the ideal case (no. of cations - no. of anions + no. of trapped holes, x) with the corresponding space charge field in the absence of any trapping or recombination (no. of trapped holes = 0),------).

Figure 6. The photorefractive effect. Top in an idealized hole transport material, the net charge density is ti radians out of phase with the intensity pattern. Middle the electric field, E, due to this net charge density, p, is given by Gauss law, dEjdx = p/e, and is shifted in phase by njl radians relative to the charge density distribution. Bottom the refractive index will then follow the phase of the electric field. In real materials the charge distribution is not always n radians out of phase relative to the intensity pattern, as competition between drift and diffusion currents leads to a reduced phase shift. The refractive index contrast might therefore be shifted by only n/lO radians relative to the intensity pattern in some polymers.

An important aspect of the photorefractive effect is that the optical response of the material is nonlocal. In Figure 7, the position of the space charge field is displaced to the right of the initial excitation, in the direction of the applied electric field. In the case of a sinusoidal intensity pattern the phase shift between the optical excitation of charges and the electric field their movement produces is a parameter characteristic of a photorefractive material. It depends on the balance between the processes of drift and diffusion of mobile charges and on the number density of sites able to capture the mobile charges. 

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