Hologram storage by the photorefractive effect
Creators: name: Moharam, M. Gamal
Publisher: name: University of British Columbia
Year: 2010

description: Exposure of some insulating crystals such as lithium niobate to light of appropriate wavelength induces small changes in the refractive index. This effect has been named the photorefractive effect. It allows phase holograms to be stored in these crystals. The work to be described was undertaken in order to obtain a better understanding of the hologram storage process which is believed to involve the spatial redistribution of photoexcited electrons among traps. This causes a space charge field to develop which modulates the refractive index via the linear electro-optic effect. A new reliable criterion for deciding whether the Raman-Nath or the Bragg regime of diffraction will be observed with a given hologram was proposed. It is shown that the distinction between "thin" and "thick" holograms is invalid as a criterion for which regime operates. The new bulk photovoltaic effect proposed by Glass et al. is an important mechanism in the photorefractive effect in ferroelectric crystals. It is shown that as formulated by Glass et al. it is formally equivalent to a fictional "virtual field" acting on the photo-liberated electrons provided that their migration length is short compared to the grating spacing. Hologram writing by the photorefractive effect was modelled in progressive stages of complexity. All the models were based on the assumption that the transport length of the free electrons is short compared to the grating spacing. This appeared to be a generally accepted assumption. The first treatment allowed for the feedback effect of the space charge field and for the dark conductivity. It was for uniform illumination and constant applied voltage. The effects of the modulation ratio and the applied field were investigated. This treatment was then modified to allow for the effect of the absorption constant in reducing the intensity of the light as it propagates through the crystal. It was shown that the hologram becomes nonuniform through the crystal thickness as a result of this effect. Hologram writing with one-dimensional Gaussian beams was modelled allowing for the feedback effect of the space charge field. A large scale space charge field associated with the envelope of the light pattern was shown to affect the writing process. It was found that an increase in the fractional illumination of the crystal improves the writing process. The dark conductivity is shown to have an important effect on the process. The final model was again for uniform illumination and allowed not only for the feedback effect of the photoinduced field and the effect of the dark conductivity and absorption but also for the interaction between the hologram being written and the light pattern which is writing it. This causes energy transfer between the two writing beams, thus modifying the light pattern. Optical erasure of holograms with the light incident either on and off the Bragg angle was modelled. The treatment allows for the feedback effect of the space charge fields and for the effect of the absorption in reducing the light intensity. The model allowed for the interaction between the diffracted and the reading beams for the case of incidence at the Bragg angle. The resulting interference pattern writes a new hologram which may add to or subtract from the hologram to be erased. An experimental method is described in which a normally incident ancillary light beam of different wavelength than that used to write the hologram allows the diffraction efficiency to be determined without errors due to multiple internal reflections. A limited experimental investigation was made of hologram storage in LiNbO₃. Photocurrent and optical measurement were carried out on the same crystal. Almost 100% relative diffraction efficiency was observed. The value of the virtual field obtained from holographic measurement was found to agree within 10% with the value obtained from photocurrent measurements. During hologram writing, energy transfer of up to 70% between the two writing beams was observed. However, since the "virtual" field in these experiments was much larger than the diffusion equivalent field, the model predicted only about 5% energy transfer. It is, therefore, suggested that the transport length of the photoexcited electrons in the crystal used, was not short compared to the grating spacing. It is also shown that light induced scattering can cause serious error in measuring the diffraction efficiency expecially during optical erasure.