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

Abstract

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.

Diffraction Efficiency and Angular Selectivity of Volume Phase Holograms Recorded in Photorefractive Materials

“…where 00 is a constant and m0 is again defined by equation (8) . This will lead to a change in the recorded refractive index period over that predicted from the interference of the two recording beams .…”

“…This latter effect was taken into account by Moharam and Downloaded by [University of Otago] at 12:09 04 July 2015 Young [7] and by Young et al . [8], who worked out the diffraction efficiency for Bragg incidence, but still neglected fringe bending and assumed a short electron transport length (i .e . they took the electron density to be in phase with the intensity pattern) .…”

Theory of Photorefractive Grating Formation in the Presence of the Bulk Photovoltaic Effect

“…This phase shift is not stationary during recording and erasure, 7,8) and the two-beam coupling output evolves in a complex, oscillatory manner. 9) The experimental difficulties associated with Fe:LiNbO 3 also make comparison of the theory and the experiment difficult. Possibly due to long-lasting, large scale space-charge fields that are created with an exposure to light, there is hardly any reproducibility in the output of two-wave mixing.…”

“…7) Even for a single beam irradiation, scattering grows with time and eventually a significant part of the energy in the signal output is lost. 7,9) The bulk photovoltaic effect plays a role similar to an external field, but they are not equivalent. 10) Inclusion of the bulk photovoltaic effect into the theory of the photorefractive effect has been carried out mainly in two extreme cases.…”

“…Section 1 is the introduction. In §2 the derivation of the expression is stated, and in §3, we conduct a numerical simulation and compare the results with the experimental data obtained by Young et al,9) which is one of the most carefully performed experiments of this kind.…”