Diffraction efficiency of deep volume holograms

The coupled mode analysis of volume holograms established by Kogelnik 1 predicts a periodic functional behavior for the diffraction efficiency as a function of the index perturbation length product. With absorption constant α, the diffraction efficiency η from a volume index grating is given by where d is the thickness of the hologram, Δ n is the amplitude of the index perturbation, and θ is the angle of incidence of the readout beam with respect to the normal to the surface of the hologram (we assume an unslanted grating). Typically, the amplitude of Δ nd is such that the increasing part of the first period of η is observed. The theory predicts that as Δ nd is increased beyond this region, the diffraction efficiency should drop. Photorefractive crystals, due to their real time holographic feature, are ideal media for observing such a phenomenon. In a photorefractive crystal, Δ n is proportional to the modulation depth intensity interference pattern responsible for writing the hologram. Hence, by merely manipulating the intensities of the writing beams, one can examine the functional behavior of the diffraction efficiency. We show experiments that verify this periodic diffraction efficiency function and hence demonstrate the large Δ nd product achievable with BaTiO 3 .