Abstract

An associative memory can be thought of as an array of discriminant functions that maps a selected set of input vectors x to a prescribed set of output binary vectors y. We discuss the use of quadratic discriminant functions of the following form as building blocks for constructing optical associative memories: Quadratic associative memories provide a dramatic increase in storage capacity, defined as the total number of associations that can be stored in the tensor of weights w_ijk, compared to the commonly used linear associative memories because of an increase in the available degrees of freedom. We will discuss two separate methods for storing information in quadratic memories and describe corresponding optical systems for implementing these memories. The first scheme utilizes volume holography to store associations of 1-D vectors. The 3-D volume hologram is used to store and implement the third rank tensor of weights. The second method utilizes planar holograms for information storage in conjunction with square-law nonlinearity to calculate the required quadratic expansion.

© 1986 Optical Society of America