Realization of optical logic and arithmetic operations using both intensity and polarization encoding schemes

In this thesis, the realization of digital computing by optical means will be studied. The processing speed of an electronic computer is inherently limited by its sequential nature. Parallel processing should be used if a higher computational speed is desired. The inherent parallelism, high-bandwidth and non-interfering interconnection properties of optics make it a good candidate for high-speed parallel computing. Optical computing is basically analog because the light parameters can be varied continuously. In order to improve the accuracy, basic values in optical computing should better be quantized to a number of discrete levels, just similar to the binary system used in electronic computing. This forms the basis of digital optical computing. The discrete basic values in digital optical computing can be encoded into the physical parameters of light or they can be represented by specific light patterns. In this thesis, a new encoding scheme that utilizes both light intensity and polarization to represent the operands is proposed. As one more light parameter is used, the number of coding states increases without the need of optical devices with higher discriminant power. The proposed encoding method provides three distinct states which are sufficient for trinay representation. For the representation of binary data, there is one extra state available which gives an extra degree of freedom. Optical logic units based on the proposed encoding method are designed. In space-invariant optical logic unit, the same logical operation is simultaneously executed on all the input operands. This is classified as a single-instruction multiple-data (SIMD) processing in the terminology of parallel processing. By using the extra degree of freedom provided by the proposed encoding method, the encoding states can be made operation-dependent. As a result, different logical results are obtained in different spatial positions of a space-invariant optical system. This leads to the realization of space-variant optical logic which is a kind of multiple-instruction multiple-data (MIMD) processing. In order to realize digital arithmetic by optical means, a binary recursive parallel adder based on the proposed encoding method is designed. However, the need of carry propagation limits the concurrent arithmetic operation by optics. This carry propagation can be shortened by using carry look-ahead addition or by choosing an appropriate number system. A carry look-ahead adder is designed of which the carry bits are pre-generated and they need not to be propagated serially from the least-significant bit to the most-significant bit. In modified signed-digit (MSD) number system, each digit depends on two of its neighbours only and the carry bit will stop propagating after two stages. The proposed encoding scheme contains three distinct states which naturally match the {1, 0, 1} trinary digit set of MSD number representation. Design of MSD adder based on this encoding method will be described.