Hologram writing in lithium niobate: Beam coupling and the transport length in the bulk photovoltaic effect

Holograms were written in a short-circuited antireflection-coated crystal of iron-doped lithium niobate, using essentially uniform illumination of the whole crystal to minimize light-envelope space-charge field effects. The results were compared with the predictions of a computer model which allows for space-charge feedback and for the modification of the writing light pattern by interaction with the hologram being written, but which assumes short transport lengths of electrons (on the scale of the hologram grating spacing) for diffusion, drift, and the bulk photovoltaic effect. The measured ’’virtual’’ field Ev to which the bulk photovoltaic effect is equivalent (for these assumptions) was about 45 kV/cm so that the bulk photovoltaic effect, rather than diffusion, dominated the writing process under the above conditions. The development of the diffraction efficiency was consistent with the computed data but the beam coupling (transfer of energy between the writing beams) was much greater than predicted. The observed beam coupling could occur with the drift-equivalent process of the bulk photovoltaic effect if the transport distance in this effect was on the order of 24 nm, which is larger than has been generally considered probable. In repeated write-erase experiments the beam coupling was variable, more so than the diffraction efficiency. The variability is, we believe, due to parasitic holograms such as are involved in the scattering process observed with these crystals and also to residual space-charge fields from repeated write-erase cycles. If the transport length is indeed long, the term καI used to describe the bulk photovoltaic effect (where κ is a parameter specific to a dopant, α is the absorption coefficient, and I is the intensity) is inapplicable to hologram writing conditions since it implies short transport length. A new representation for this bulk photovoltaic effect allowing for an arbitrary transport length is proposed. This representation is shown to introduce a significant phase shift in the refractive-index pattern relative to the light pattern and can thus account for the beam coupling observed.