Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths

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Abstract
The time development of optically induced refractive‐index hologram gratings in photrefractive electro‐optic crystals such as lithium niobate and bismuth silicon oxide is analyzed allowing arbitrary electron‐transport lengths and nonsinusoidal grating shapes. In this analysis, diffusion and drift in applied and space‐charge fields as well as the bulk photovoltaic effect (when applicable) are included. Results for the photoinduced space‐charge field are presented for a range of realistic experimental conditions. It is shown that the spatial phase of the space‐charge field and therefore the beam coupling is strongly dependent on the electron‐transport lengths, whereas the magnitude of the field and therefore the diffraction efficiency is not dependent. It is shown that for paraelectric materials (such as BSO) the results of short‐ and long‐transport‐length analyses must converge for long recording times (saturation).