Dynamics of grating formation in photovoltaic media

Photorefractive crystals have become increasingly important as candidate media for the realization of many optical information processing systems including mass memory,’ neural network implementations,24 and signal processors. ‘-’ Photorefraction in electro-optic crystals is well understood in terms of the band transport model8 which describes it in terms of the following processes: ( 1) the photo-excitation of charged carriers from impurities by a nonuniform intensity pattern, (2) charge transport mechanisms (diffusion, drift, photovoltaic) which move these charges in the conduction band to empty trap sites where they are captured, creating a nonuniform spacecharge field, and (3) nonuniform modulation of the index of refraction via the electro-optic effect. Among the various transport mechanisms, the photovoltaic effect, in which a short-circuit current (or, equivalently, an open-circuit voltage) is generated by illumination of the crystal with light, has been observed only in a few ferroelectric crystals such as LiNb03 and KNb03. Although the photovoltaic effect is accounted for in the Kukhtarev equations,” a transient theory that includes the effects due to the boundary conditions (e.g., openor short-circuited crystal) has not yet been formulated. LiNb03 which can be used for long-term memory storage applications due to its low dark conductivity, exhibits a particularly large photovoltaic effect,’ and such a theory may prove to be useful for further application developments. In this paper, we solve the Kukhtarev equations taking into account various possible boundary conditions to describe the growth and decay of holograms in photovoltaic media. We then give theoretical plots describing the transient behavior of holograms using published values of parameters for LiNbO,. The experimental results, showing different dynamic behaviors during grating formation for different boundary conditions, are then compared with the theoretical calculation. Both experimental result and theoretical simulation show the typical behavior of grating formation which does not occur in nonphotovoltaic media, i.e., when the writing starts from an open-circuited crystal without nonuniform charge distribution, the diffraction efficiency increases to a maximum value then decreases to reach its steady state.