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-217

“Volume Diffraction Phenomena for Photonic Neural Network Implementations and Stratified Volume Holographic Optical Elements”

by Gregory P. Nordin

December 1992

In this thesis we investigate the use of volume holographic optical elements (VHOEs) as an interconnection technology for photonic neural network implementations, and examine the fundamental diffraction properties of stratified volume holographic optical elements (SVHOEs).

In the first half of the thesis the feasibility of employing volume holographic techniques for the implementation of highly multiplexed weighted fan-out/fan-in interconnections (such as required for neural networks) has been analyzed on the basis of interconnection fidelity, optical throughput, and complexity of recording schedule or implementation hardware. These feasibility criteria were evaluated quantitatively using the optical beam propagation method to numerically simulate the diffraction characteristics of volume holographic interconnections recorded in a linear holographic material. We find that conventional interconnection architectures (that are based on a single coherent optical source) exhibit a direct trade-off between interconnection fidelity and optical throughput on the one hand, and recording schedule or hardware complexity on the other. We analyze in detail a recently proposed novel incoherent/coherent double angularly multiplexed interconnection architecture that circumvents this trade-off. This novel architecture is based on the use of a multiple source array of individually coherent but mutually incoherent sources. It either minimizes or avoids several key sources of crosstalk; permits simultaneous recording; and provides enhanced fidelity, interchannel isolation, and throughput performance.

In the second half of the thesis we present a unified treatment of the diffraction properties of stratified volume holographic optical elements (SVHOEs). SVHOEs comprise a recently proposed class of novel diffraction structures in which multiple layers of a thin holographic material are interleaved with optically homogeneous buffer layers. Using the SVHOE concept, holographic materials with otherwise exemplary characteristics that are currently available only in thin film form can be used in structures designed either to access unique SVHOE diffraction properties, or to emulate conventional volume holographic optical elements. Applications discussed herein that are based on novel SVHOE properties include optical array generation, spatial frequency filtering, wavelength notch filtering, and wavelength division multiplexing and demultiplexing.

We also report the implementation of photopolymer-based SVHOEs (using DuPont's Omnidex™ holographic photopolymer material), and the use of an in-situ exposure technique for simultaneous multilayer grating recording. Experimental measurement of the +1 order angular sensitivity of a 7-layer SVHOE structure shows remarkable agreement with both theory and numerical simulation for incidence angles near the Bragg angle. For SVHOEs having modulation layers that individually operate in the Bragg or transition diffraction regimes, the envelope of the SVHOE angular sensitivity is experimentally shown to closely approximate that of a single modulation layer.

In addition, we show that the relative phasing of the diffraction orders as they propagate from layer to layer within an SVHOE having modulation layers that individually operate in the Raman-Nath diffraction regime gives rise to a unique notched diffraction response of the +1 order (for the case of Bragg incidence) as a function of the normalized buffer layer thickness, the grating spatial frequency, and the readout wavelength. For certain combinations of these parameters, Bragg diffraction behavior characteristic of volume holographic optical elements (VHOEs) is observed, while for other combinations pure Raman-Nath behavior periodically recurs. Using these same relative phasing arguments, the principle features of the periodic angular sensitivity of the +1 and -1 orders can be predicted.

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