The logic of optics and the optics of logic

There have been various attempts to implement the standard logical formalistri, known as "Boolean Logic", stemming from Aristotle, the Stoics, Leibniz, Boole, and Frege. extending to the fuzzy logic developed by Zadch [Into. Ctl. 338 (1965) 353]. That logic, isomorphic, as we now know, with the logic of electric circuitry, was not designed for optical implementation. Nor has there been a notable success in developing such an implementation. We demonstrate a new type of logic designed for implementation by coherent optics. It has the logic of Zadch as a special case just as Zadeh's logic has the logic of Boolean algebra as a special case. Because the new logic operates over a finite set of vectors in the complex domain, we call it Vector Logic. Some Vector Logic operations are very easy to implement, but the universal "Vector NOR" or VNOR gate is quite complex. Optical Vector Logic gates are passive, so they operate at the bandwidth of the signal input and readout. And, of course, the parallel nature of many coherent optical processors can apply here as well to yield SIMD and even MIMD systems. (C) 2003 Elsevier Inc. All rights reserved.