Acoustooptic linear heterodyned complex-valued matrix-vector processor

Two-dimensional multi-channel acousto-optic diffraction

In this paper, we have investigated the interaction between acoustic waves generated by an incident light beam propagating through two-dimensional transducers. A set of coupled mode equations for two-dimensional multi-channel acousto-optic inter-modulation are derived, and the solutions are obtained. A new type of two-dimensional multi-channel Bragg acousto-optic modulator is designed by analyzing two-dimensional multi-channel acousto-optic inter-modulation based on the coupled mode theory, and its performance has also been experimentally characterized. The experimental results are in accordance with our theoretical analysis.

Modified engagement method for matrix operation

We describe a modified engagement method for matrix operation based on a two-dimensional crossed-ring interconnection network. Our method incorporates fewer steps than that reported by Bocker et al. [Appl. Opt. 22, 804 (1983)], and its performance is found to be the most efficient (minimum steps) in comparison with other systolic and/or engagement methods for matrix operation. Thus, it may be helpful for other optical and electronic implementations of matrix operations. One compact optoelectronic integrity approach for implementing the modified engagement method is briefly described.

Throughput analysis of digital partitioning with error-correcting codes for optical matrix-vector processors

Digital partitioning and error-correcting codes provide a technique for achieving high-accuracy computations with analog optical matrix-vector processors. We present the results of a detailed throughput analysis of this technique. The results indicate that using one processor per submatrix provides the best compromise between system throughput and hardware requirements over a range of matrix sizes. Errorcorrecting codes are shown to not significantly degrade system throughput for large matrix sizes. Finally, a comparison to digital electronic computers is made.

Modified direct twos-complement parallel array multiplication algorithm for complex matrix operation

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Negative binary arithmetic algorithms for digital parallel optical computation

Based on a negative binary number system, an algorithm with weighted-shifted addition, parallel-array multiplication, and a two-stage-array complex operation is proposed to carry out the multiplication of two complex numbers. The complex multiplication is performed without signs, carries, and recoding. The algorithm is suitable for optical implementation, and an optical parallel architecture is suggested. The experimental result is also given.

Matrix-vector multiplication using digital partitioning for more accurate optical computing

Digital partitioning offers a flexible means of increasing the accuracy of an optical matrix-vector processor. This algorithm can be implemented with the same architecture required for a purely analog processor, which gives optical matrix-vector processors the ability to perform high-accuracy calculations at speeds comparable with or greater than electronic computers as well as the ability to perform analog operations at a much greater speed. Digital partitioning is compared with digital multiplication by analog convolution, residue number systems, and redundant number representation in terms of the size and the speed required for an equivalent throughput as well as in terms of the hardware requirements. Digital partitioning and digital multiplication by analog convolution are found to be the most efficient algorithms if coding time and hardware are considered, and the architecture for digital partitioning permits the use of analog computations to provide the greatest throughput for a single processor. To our knowledge this is the first study to propose the use of digital partitioning for optical matrix processing.