The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-316

“Real Time Effects in Volume Holographic Materials for Optical Storage, Copying, and Optical Neural Networks”

by Sabino Piazzolla

December 1997

Holographic memories can be a solution to the continuous demand for high capacity, fast access time, and high data transfer rate storage devices required for storage-intensive data processing systems. In fact the inherent properties of holographic memories and optical elements allow high three dimensional storage capacity with fast parallel access. The widespread use of such holographic memories, however, may be limited in part by the lack of availability of a simple to use, economically advantageous, and reliable medium, and, moreover, by their lack of manufacturability. To alleviate these two problems, in this dissertation we present our investigation on the characterization of holographic photopolymers and on hologram copying. The reasons for the interest in using photopolymers for holography lie in the properties of these media: high sensitivity, high resolution, long shelf life, easy dry processing, and low cost.

The holographic grating formation mechanism in photopolymers can be qualitatively described by the following processes: photoinitiation of free radicals, grating formation by free monomer polymerization due to radical initiation, and free monomer diffusion. By linking together the photopolymerization process, free monomer diffusion, and coupled wave theory, we model the temporal dynamics of holographic grating formation, and its associated diffraction efficiency in photopolymers. Particularly, we characterize the (1) grating formation in photopolymers considering a high diffusion rate of the free monomers, (2) the recording of multiplexed holograms, (3) the effects of self diffraction during recording, and (4) the interaction between free monomer diffusion and grating formation at high recording intensity. The theory is validated with a set of experiments that were carried out using DuPont HR-150-38 photopolymer.

In the second part of this dissertation we present and analyze a technique to copy the index or absorption modulation of a multiplexed volume hologram into a secondary volume holographic material. This technique uses a set of self-coherent but mutually incoherent optical sources (I/C recording) and can perform the copy process in a single exposure. By further extending the analysis of our proposed copying technique we determine the conditions for blind copying of multiplexed holograms. Blind copying refers to a copying technique which does not require a priori knowledge of the diffraction efficiency of the individual holograms to create a theoretically exact replica of a master hologram. Furthermore, we define how the recording intensity can influence the different figures of merit of the copy when it is not an exact replica of the master. Fidelity of the copy is one of these parameters, which is functionally dependent on the magnification gain and as well as on the attenuation of the copied diffraction efficiencies of the holograms. Because of the architectural flexibility of the presented system, we extend its application to the case of use of different material for copy and master. Particularly, we studied the compatibility between photorefractive crystals and holographic photopolymers as copy/master materials, because of the attractive possibility of storing in a reliable, permanent and economically convenient material (photopolymers) the information from a trainable and therefore non permanent holographic material (photorefractive crystals).

As an application of our copying technique, we simulated the case of the training of a two layer feedforward optical neural network whose first layer weights are implemented by holograms which are angularly multiplexed in a photorefractive crystal. First we train the network to solve the XOR problem using the back error propagation algorithm; next we copy the holographic weights of the trained network into a secondary holographic medium; then we asses the copy errors in the network when replacing the original master hologram with its copy.

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