Abstract

The arithmetic unit presents a substantial challenge to those interested in the long term goal of ultrafast all-optical general purpose computers (1 Ch. 10). Previously we demonstrated an optical adder using electron trapping materials for which the speed seems to be limited to hundreds of nanseconds (2). The multiplication of images in 160 fs was recently demonstrated by means of four-wave mixing in a new polymer material (3). We present a conceptual method of using such a material in a loop to perform pipeline digital arithmetic operations such as addition and multiplication. Only the word operands are entered at each cycle while the loop performs 2-D operations so that the rate of computation in the polymer is several orders of magnitude higher than that for data entry and removal. The method uses a modification of the transition function proposed previously for computation with cellular automata or symbolic substitution (4), (1 Ch. 15). Cellular automata on an infinite plane were shown by Dr. Von Neuman to provide universal-constructor machines capable of endlessly self reproducing new Turing machines, each of which can compute anything that can be computed by logical or mathematical reasoning (5,6). Others have subsequently provided rules for such mappings (7). Flexibility is achieved because the operation performed may be changed by replacing an optical control image. This idea of treating control information optically in the same manner as data has been highly developed in pattern logic which has been experimentally demonstrated for an optical ripple-carry adder (8, 1 Ch 9 and 10). The correlation operation required for the cellular automata is performed by four wave mixing and is independent of the control information, the data, and their locations on the array. The mapping of a full adder and a 3-bit multiplier onto such a computer are shown. The problems of achieving short pipelines for small latency are discussed and alternative possible improvements mentioned. A proposed optical set up is shown which includes a loop around a four wave mixing experiment such as that in paper (3). Some difficulties anticipated in performing such an experiment are considered.

© 1995 Optical Society of America