Optical computing

The Optical Transpose Interconnection System (OTIS) is a recently proposed model of computing that exploits the special features of both electronic and optical technologies. In this paper we present efficient algorithms for packet routing, sorting, and selection on the OTIS-Mesh.

This paper briefly reviews some of the more popular parallel-computer models-pipelined optical bus, optical transpose interconnect system (OTIS), and partitioned optical passive stars (POPS) network-that employ optical interconnect. The interconnect topology and some simple algorithms for each model are also described.

In this paper, a learning-based feedforward term is developed to solve a general control problem in the presence of unknown nonlinear dynamics with a known period. Since the learning-based feedforward term is generated from a straightforward Lyapunov-like stability analysis, the control designer can utilize other Lyapunov-based design techniques to develop hybrid control schemes that utilize learning-based feedforward terms to compensate for periodic dynamics and other Lyapunov-based approaches (e.g., adaptive-based feedforward terms) to compensate for nonperiodic dynamics. To illustrate this point, a hybrid adaptive/learning control scheme is utilized to achieve global asymptotic link position tracking for a robot manipulator.

A spectral analysis of human blood serum was undertaken by fiber-optic evanescent-wave spectroscopy 1FEWS2 by the use of a Fourier-transform infrared spectrometer. A special cell for the FEWS measurements was designed and built that incorporates an IR-transmitting silver halide fiber and a means for introducing the blood-serum sample. Further improvements in analysis were obtained by the adoption of multivariate calibration techniques that are already used in clinical chemistry. The partial least-squares algorithm was used to calculate the concentrations of cholesterol, total protein, urea, and uric acid in human blood serum. The estimated prediction errors obtained 1in percent from the average value2 were 6% for total protein, 15% for cholesterol, 30% for urea, and 30% for uric acid. These results were compared with another independent prediction method that used a neural-network model. This model yielded estimated prediction errors of 8.8% for total protein, 25% for cholesterol, and 21% for uric acid.

Multiplier circuits play an important role in reversible computation, which is helpful in diverse areas such as low power CMOS design, optical computing, DNA computing and bioinformatics. Here we propose a new reversible multiplier circuit with optimized hardware complexity. The optimized multiplier circuit is compared with the earlier proposals. We have shown that the quantum cost of earlier proposals can be further reduced with the help of existing local optimization algorithms (e.g. template matching, moving rule and deletion rule). A systematic protocol for reduction of quantum cost has been proposed. It has also been shown that the advantage in gate count obtained in some of the earlier proposals by introduction of new reversible gates is an artifact and if it is allowed then every circuit block can be reduced to a single gate. Further, it is shown that the 4x4 reversible gates proposed for designing of a component of multiplier circuit (full adder) is neither unique nor special and many such 4x4 gates may be proposed. As example three such new gates have been presented here and it is shown that the proposed gates are universal. It is also shown that the total cost of our design is minimum.

We have proposed optical tunable CNOT (XOR) and XNOR logic gates using two-dimensional photonic crystal (2DPhC) cavities. Where, air rods with square lattice array have been embedded in Ag-Polymer substrate with refractive index of 1.59. In this work, we have enhanced speed of logic gates by applying two input signals with a phase difference at the same wavelength for 2DPhC cavities. Where, we have adjusted the phases of input and control signals equal with {\pi}/3 and zero, respectively. The response time of the structure and quality factor of the cavities are in the range of femtosecond and 2000, respectively. Then, we have used electro-optic property of the substrate material to change the cavities resonance wavelengths. By this means, we could design the logic gates and demonstrate a tunable range of 23nm for their operation wavelength. The quality factor and the response times of cavities remain constant in the tunable range of wavelength, approximately. The evaluated least ON ...

In this paper we present an analysis of several large Internet traffic traces and focus on large transfers that are suitable to send through all-optical links featuring burst switching technologies. We analyze the payload size for such optical bursts and the possible impact in network performance.

The methodology predicts maximum performance of a given optical computing architecture and evaluates its feasibility. As an application example, we apply this methodology to evaluate the feasibility and performance of the optical content-addressable parallel processor proposed in Appl. Opt. 31, 3241 (1992). The approach consists of two major phases. The first phase involves analytical studies of the effects of design parameters such as cross talk, diffraction-limited beam spot diameter, and pitch on system performance parameters such as signal packing density and skew time. In the second phase, a simulation model and a simulator are introduced by the use of GLAD (General Laser Analysis and Design, an optical software package developed by Applied Optics Research) to evaluate the combined effects of bit-error rate, bit rate, optical power efficiency, available source power, and signal contrast on the performance parameters such as signal packing density, misalignment tolerance, and distance between devices. The methodology presented here investigates the model, not on a component-by-component basis, but as a whole, which produces a more realistic representation of the actual laboratory prototype. The proposed methodology is intended to reduce the optical computing system design time as well as the design risk associated with building a prototype system.

In this paper, we consider the manifold of covariance matrices of order n parametrized by reflection coefficients which are derived from Levinson's recursion of autoregressive model. The explicit expression of the reparametrization and its inverse are obtained. With the Riemannian metric given by the Hessian of a Kähler potential, we show that the manifold is in fact a Cartan-Hadamard manifold with lower sectional curvature bound -4. The explicit expressions of geodesics are also obtained. After that we introduce the notion of Riemannian median of points lying on a Riemannian manifold and give a simple algorithm to compute it. Finally, some simulation examples are given to illustrate the applications of the median method to radar signal processing.

Nous considérons le problème du recalage non-rigide entre images de modalités différentes. Nous proposons un cadre général qui repose sur une formulation variationnelle, que nous appliquons sous la forme de trois algorithmes de recalage multimodal : recalage supervisé par apprentissage de la loi jointe, maximisation de l'information mutuelle, et maximisation du rapport de corrélation. Pour permettre une régularisation de la solution, nous utilisons un opérateur issu de la théorie de l'élasticité. Nous considérons aussi une méthode de régularisation avec préservation des contours. Des résultats expérimentaux préliminaires sur des images synthétiques et des données IRM sont présentés.

Achieving computer vision on microscale devices is a challenge. On these platforms, the power and mass constraints are severe enough for even the most common computations (matrix manipulations, convolution, etc.) to be difficult. This paper proposes and analyzes a class of miniature vision sensors that can help overcome these constraints. These sensors reduce power requirements through template-based optical convolution, and they enable a wide field-of-view within a small form through a refractive optical design. We describe the tradeoffs between the field-of-view, volume, and mass of these sensors and we provide analytic tools to navigate the design space. We demonstrate milliscale prototypes for computer vision tasks such as locating edges, tracking targets, and detecting faces. Finally, we utilize photolithographic fabrication tools to further miniaturize the optical designs and demonstrate fiducial detection onboard a small autonomous air vehicle.

Achieving computer vision on microscale devices is a challenge. On these platforms, the power and mass constraints are severe enough for even the most common computations (matrix manipulations, convolution, etc.) to be difficult. This paper proposes and analyzes a class of miniature vision sensors that can help overcome these constraints. These sensors reduce power requirements through template-based optical convolution, and they enable a wide field-of-view within a small form through a refractive optical design. We describe the tradeoffs between the field-of-view, volume, and mass of these sensors and we provide analytic tools to navigate the design space. We demonstrate milliscale prototypes for computer vision tasks such as locating edges, tracking targets, and detecting faces. Finally, we utilize photolithographic fabrication tools to further miniaturize the optical designs and demonstrate fiducial detection onboard a small autonomous air vehicle.

Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.

We consider the paraxial model for a nonlinear resonator with a saturable absorber beyond the mean-field limit and develop a method to study the modulational instabilities leading to pattern formation in all three spatial dimensions. For achievable parametric domains we observe total radiation confinement and the formation of 3D localised bright structures. At difference from freely propagating light bullets, here the self-organization proceeds from the resonator feedback, combined with diffraction and nonlinearity. Such "cavity" light bullets can be independently excited and erased by appropriate pulses, and once created, they endlessly travel the cavity roundtrip. Also, the pulses can shift in the transverse direction, following external field gradients.

We consider the paraxial model for a nonlinear resonator with a saturable absorber beyond the mean-field limit and develop a method to study the modulational instabilities leading to pattern formation in all three spatial dimensions. For achievable parametric domains we observe total radiation confinement and the formation of 3D localised bright structures. At difference from freely propagating light bullets, here the self-organization proceeds from the resonator feedback, combined with diffraction and nonlinearity. Such "cavity" light bullets can be independently excited and erased by appropriate pulses, and once created, they endlessly travel the cavity roundtrip. Also, the pulses can shift in the transverse direction, following external field gradients.

Cavity solitons ͑CSs͒ are localized structures appearing as intensity peaks in the homogeneous background of the field emitted by a nonlinear microresonator. We experimentally and theoretically study the switch-on process of cavity solitons in semiconductor amplifiers. The switching time has two contributions: a lethargic lapse following the application of the switching pulse and a characteristic buildup time. While the latter is not significantly affected by the control parameters, the former crucially depends on them. Optimization of the parameters leads to a switch-on time of less than one nanosecond, assessing the CS competitiveness for all-optical applications.

We consider a semiconductor microcavity driven by a coherent and stationary holding beam, in two distinct configurations. In the first, no carriers are injected in the multiple-quantum-well structure and the optical nonlinearity is governed by an excitonic resonance. The second corresponds to that of a vertical-cavity surfaceemitting laser kept slightly below threshold. We describe both configurations using a unified model that includes both field diffraction and carrier diffusion. We calculate numerically both the time evolution and the stationary profile of the solitonic solutions, using a generalization of the radial integration technique introduced by Firth and Scroggie ͓Phys. Rev. Lett. 76, 1623 ͑1996͔͒. We analyze the instability that forms spatial patterns and especially cavity spatial solitons. We predict the existence of these solitons in various parametric domains for both configurations. We demonstrate that these results are independent of the periodic boundary conditions used in the simulations. We show that, introducing a simple phase modulation in the holding beam, one can eliminate the motions of solitons that arise from noise and from amplitude gradients. The solitons are robust with respect to parametric variations, to carrier diffusion, and even to some amount of self-defocusing. This picture points to the possibility of realizing arrays of solitonic pixels using semiconductor microresonators.

A series of computer experiments was performed to determine the relative performance of simulated annealing, quenched annealing, and a least-squares iterative technique for image reconstruction for Single Photon Emission Computed Tomography (SPECT). The simulated SPECT geometry was of the pinhole aperture type with 32 pinholes and 128 or 512 detectors. To test the robustness of the reconstruction techniques upon arbitrary geometries, a 360 detector geometry with a random detector pixel factor matrix was tested. Eight computer-simulated 10 cm diameter planar phantoms were used with 1,961 two mm2 reconstruction bins and a range of 3 000 to 50 000 000 detected photon counts. Reconstruction quality was measured by a normalized squared error picture distance measure. Over a wide range of noise, the simulated annealing method was found to be slightly favorable to the iterative method in reconstruction quality, although it required greater reconstruction time. Quenched annealing was faster than simulated annealing with comparable reconstruction quality. Methods of efficiently controlling the simulated annealing algorithm are presented. I. BACKGROUND A. Simulated Annealing Methods IMULATED annealing, a generalized optimization S method, was introduced as a general purpose global optimization method [l], [2] and is an extension of the Metropolis algorithm [3]. Simulated annealing has been most successful on problems with many constraints and multiple interactions that disallow linear programming methods and prevent analytic solutions [4]. The Metropolis method enables the calculation of equilibrium properties of interacting molecule configurations [3]. The distribution of molecules in a physical system is given by the Boltzmann distribution C e-E / k T where E is the energy of a configuration, T is the temperature of the system, k is the Boltzmann constant, and C is a normalizing constant. The equilibrium properties of simulated physical systems can be determined using a simulated system that can generate random configurations of that system. By weighting those configurations by their equi-Manuscript

Microphysical and optical properties of the main aerosol species on a peri-urban site have been investigated during the ESCOMPTE experiment. Ammonium sulfate (AS), nitrate (N), black carbon (BC), particulate organic matter (POM), sea salt (SS) and mineral aerosol (D) size distributions have been used, associated with their refractive index, to compute, from the Mie theory, the key radiative aerosol properties as the extinction coefficient K ext , the mass extinction efficiencies r ext , the single scattering albedo x 0 and the asymmetry parameter g at the wavelength of 550 nm. Optical computations show that 90% of the light extinction is due to anthropogenic aerosol and only 10% is due to natural aerosol (SS and D). 44 F 6% of the extinction is due to (AS) and 40 F 6% to carbonaceous particles (20 F 4% to BC and 21 F 4% to POM). Nitrate aerosol has a weak contribution of 5 F 2%. Computations of the mass extinction efficiencies r ext , single scattering albedo x 0 and asymmetry parameter g indicate that the optical properties of the anthropogenic aerosol are often quite different from those yet published and generally used in global models. For example, the (AS) mean specific mass extinction presents a large difference with the value classically adopted at low relative humidity (h < 60%) (2.6 F 0.5 instead of 6 m 2 g À 1 at 550 nm). The optical properties of the total aerosol layer, including all the aerosol species, indicate a mean observed single-scattering albedo x 0 = 0.85 F 0.05, leading to an important absorption of the solar radiation and an asymmetry parameter g = 0.59 F 0.05 which are in a reasonably good agreements with the AERONET retrieval of x 0 ( = 0.86 F 0.05) and g ( = 0.64 F 0.05) at this wavelength.

Early work in automatic problem-solving focused on what Newell has called “weak methods ” While these problemsolving strategies are quite general and are formally tractable, they are insufficient in practice for solving problems of any significant complexity. During the last decade, a number of techniques have been developed for improving the efficiency of these strategies. Since these techniques operate within the context of the general strategies, they are termed here problem-solving tactics. The bulk of this paper consists of a description of the problem-solving strategies and a catalogue of tactics for improving their efficiency.This is followed by an attempt to

The construction and operation of a 50-MHz 64 x 16 bit fiber-optic bit-serial delay-line memory is described. It consists of LiNbO 3 directional coupler switches, fused-fiber couplers, and a 4.17-km fiber loop. It is a subsystem of a bit-serial optical computer under construction by our group. We discuss delay and clock source stability requirements for the long delay line in the face of a limited phase error tolerance. The reliability testing of the memory subsystem is described. The degradation of data in the memory loop as the phase error tolerance is exceeded by a small amount is studied through the temperature dependence of the memory loop. Data are presented for the memory-loop stability with respect to temperature variations. The memory subsystem design and construction is presented. The results of these experiments support the feasibility of a 100-MHz 128 x 16 bit memory.

This paper exploits physical models of time-varying brightness in image sequences to estimate optical flow and physical parameters of the scene. Previous approaches handled violations of brightness constancy with the use of robust statistics or with generalized brightness constancy constraints that allow generic types of contrast and illumination changes. Here, we consider models of brightness variation that have time-dependent physical causes, namely, changing surface orientation with respect to a directional illuminant, motion of the illuminant, and physical models of heat transport in infrared images. We simultaneously estimate the optical flow and the relevant physical parameters. The estimation problem is formulated using total least squares (TLS), with confidence bounds on the parameters.

Reversible logic is emerging as an important research area having its application in diverse fields such as low power CMOS design, digital signal processing, cryptography, quantum computing and optical information processing. This paper presents a new 4*4 universal reversible logic gate, IG. It is a parity preserving reversible logic gate, that is, the parity of the inputs matches the parity of the outputs. The proposed parity preserving reversible gate can be used to synthesize any arbitrary Boolean function. It allows any fault that affects no more than a single signal readily detectable at the circuit's primary outputs. Finally, it is shown how a fault tolerant reversible full adder circuit can be realized using only two IGs. It has also been demonstrated that the proposed design offers less hardware complexity and is efficient in terms of gate count, garbage outputs and constant inputs than the existing counterparts.

This paper presents a new model for prediction of wave propagation in indoor and outdoor environments. The method is based on twodimensional ray-tracing techniques using image theory to determine all valid paths. The computation of fields is based on geometrical optics and uniform theory of diffraction. A new approach for transmitted rays through the walls is proposed and validated by comparison with results obtained via the finite-difference time-domain method. Results for a practical indoor environment are presented by mapping the received power.

A new optical binary pixel pattern recognizer for optical symbolic substitution (OSS) digital computation is proposed. Using optical spatial shift and optical phase-conjugate AND operations, input symbolic pattern recognition can be performed. Some initial experimental results obtained with picosecond laser pulses are presented.

The design, construction, and operational testing of a five-stage, fully interconnected 32 x 16 switching fabric by the use of smart-pixel (2, 1, 1) switching nodes are described. The arrays of switching nodes use monolithically integrated GaAs field-effect transistors, multiple-quantum-well p-i-n detectors, and self-electro-optic-device modulators. Each switching node incorporates 25 field-effect transistors and 17 p-i-n diodes to realize two differential optical receivers, the 2 x 1 node switching logic, a single-bit node control memory, and one differential optical transmitter. The five stages of node arrays are interconnected to form a two-dimensional banyan network by the use of Fourier-plane computer-generated holograms. System input and output are made by two-dimensional fiber-bundle matrices, and the system optical hardware design incorporates frequency-stabilized lasers, pupil-division beam combination, and a hybrid micro-macro lens for fiber-bundle imaging. Optomechanical packaging of the system utilizes modular kinematic component positioning and active thermal control to enable simple rapid assembly. Two preliminary operational experiments are completed. In the first experiment, five stages are operated at 50 Mbits/s with 15 active inputs and outputs. The second experiment attempts to operate two stages of second-generation node arrays at 155 Mbits/s, with eight of the 15 active nodes functioning correctly along the straight switch-routing paths.

We consider a traffic-groomed optical network consisting of N nodes arranged in tandem. This optical network is modeled by a tandem queueing network of multi-rate loss queues with simultaneous resource possession. Two approximation methods are proposed for the analysis of this queueing network assuming that the total number of servers in each multi-rate loss queue is very large. The accuracy of these two approximation methods as well as the accuracy of the familiar link independence algorithm is verified by simulation. As an additional contribution, the simulation estimates have been obtained using adaptive rareevent simulation techniques based on importance sampling. This is because call blocking probabilities tend to be very small and it is not feasible to estimate them using standard simulation techniques

This paper is concerned with the design of optical and optoelectronic circuits. In particular new designs for an exclusive-OR circuit, set-reset trigger flip-flop, and a programmable logic array (PLA) are proposed. The PLA utilizes optical properties and performs computation on binary images using optical parallel logic devices, lenses, etc. This work is then extended to the design of erasable programmable logic devices.

We discuss various aspects of building an integrated optoelectronic system that is based on the concept of planar optics. A particular optical interconnection system has been fabricated and demonstrated. It provides parallel interconnections with 1024 optical channels that could be useful as an optical backplane in an optoelectronic multichip module. We consider the design and the fabrication of the optical system, schemes for the hybrid integration with optoelectronic device arrays, and the thermal management of an integrated system. The proposed hybrid integration scheme is based on mature technologies such as thermal anodic bonding and flip-chip bonding. Possibilities for efficient heat sinking are described.

Alcohol abuse is a major problem in the United States. The most common measurement tool used in law enforcement for the determination of alcohol concentration in subjects is the breath analyzer (BrAC), and subjects know when they are being measured. However , when surrept i t ious measurements of BrAC in freely moving humans are sought, then hyperspectral remote-sensing measurement techniques must be used. In this work, two remote sensing methods for the estimation of BrAC were studied. A clinical trial involving human subjects was performed to assess the supposition that molecular factor computing (MFC) near-infrared (NIR) hyperspectral imaging and speech analysis using laser interferometry could be used to noninvasively estimate BrAC in subjects at a distance. A conventional breath analyzer was used to prov ide reference measurements. MFC NIRS imaging measurements gave a standard error of prediction (SEP) for a global model (all subjects) for blood alcohol of 8.1 mg/dL (0.0081%) a...

In this paper we assess the benefits of using statistical techniques to ascertain the shareability of protection channels when computing shared mesh restored lightpaths. Current deterministic approaches require a detailed level of information proportional to the number of active lightpaths, and do not scale well as traffic demands and network grow. With the proposed approach we show that less information, independent of the amount of traffic demand, is sufficient to determine the shareability of protection channels with remarkable accuracy. Experiments also demonstrate that our approach yields faster computation times with no significant penalty in terms of capacity usage.

Distributed, IP-based control architecture has been proposed for switched optical mesh networks, as a means to automate operations, enhance interoperability and facilitate the deployment of new applications. While distributed control in general enhances scalability and flexibility, it also offers challenges to path computation, especially for shared mesh restored paths, because of the summarization of link state information disseminated by the routing protocol. This paper discusses the tradeoffs between the path computation efficiency and the abstraction level of link state information. Several heuristic algorithms for computing shared mesh restored paths are described, which require different levels of abstraction and summarization of link resource sharing information. The performance of these algorithms is compared in term of the efficiency of network capacity utilization, the computation complexity, and the amount of required network information. We show that with appropriately aggregated link state information the proposed path computation algorithms are able to utilize the network resource very efficiently.

A feed-forward backpropagating neural network is trained to achieve and maintain control of the unstable periodic orbits embedded in a chaotic attractor. The controlling algorithms used for training the network are based on the now standard scheme developed by Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)], including variants that utilize previous perturbations and/or delayed time-series data.

Architectures for optical processors designed to solve bounded instances of NP-Complete problems are suggested. One approach mimics the traveling salesman by traveling beams that simultaneously examine the different possible paths. The other approach uses a preprocessing stage in which O(n 2) masks are constructed, each representing a different edge in the graph. The choice and combination of the appropriate (small) subset of these masks yields the solution. The solution is rejected in cases where the combination of these masks totally blocks the light and accepted otherwise. We present detailed designs for basic primitives of the optical processor. We propose designs for solving Hamiltonian path,

Architectures for optical processors designed to solve bounded instances of NP-Complete problems are suggested. One approach mimics the traveling salesman by traveling beams that simultaneously examine the different possible paths. The other approach uses a preprocessing stage in which O(n 2) masks are constructed, each representing a different edge in the graph. The choice and combination of the appropriate (small) subset of these masks yields the solution. The solution is rejected in cases where the combination of these masks totally blocks the light and accepted otherwise. We present detailed designs for basic primitives of the optical processor. We propose designs for solving Hamiltonian path,

Two architectures for optical processors designed to solve instances of NP-Complete problems, trading space for time, are suggested. The first approach mimics the traveling salesman by an exponential number of traveling beams, that simultaneously examine the different possible paths. The other approach uses a pre-processing stage in which O(n 2) masks consisting of an exponential number of locations, are constructed; each representing a different edge in the graph. The choice and combination of the appropriate (small) subset of these masks yields the solution. The solution is rejected in cases where the combination of these masks completely blocks the light and accepted otherwise. We present detailed designs for basic primitives of the optical processor. We propose designs for solving instances of Hamiltonian path,

In this paper, we study a class of VLSI organizations with optical interconnects for fast solutions to several image processing tasks. The organization and operation of these architectures are based on a generic model called OMC, which is proposed to understand the computational limits in using free space optics in VLSI parallel processing systems. The relationships between OMC and shared memory models are discussed in this paper. Also, three physical implementations of OMC are presented. Using OMC, we present several parallel algorithms for fine grain image computing. We categorize our results in the following order. First, we present a set of processor efficient optimal O(log N) algorithms and a set of constant time algorithms for finding geometric properties of digitized images. Finally, we focus on special purpose designs tailored to meet both the computation and communication needs of problems such as those involving irregular sparse matrices.

An optical setup fur the computation of the sector transfurm is presented in this paper. The device is based on pinhole imaging and processing with the computer generated mask. Computation of the transform does not require image rotation, and therefore processing is done fully in parallel. Extensions of the transform are also discussed.

The registration of cardiac images is relevant for the diagnosis of cardiac pathologies. In the case of SPECT (Single Photon Emission Computer Tomography) datasets, this is difficult because of the low resolution of the images. In this paper we present a new registration method for 3D images with poor resolution. Our method is based on the maximization of the mutual information (MI) using a new interpolation method which significantly improves the result of an MI-based strategy on low resolution images. We also use a different optimization strategy than other MI-based algorithms, typically achieving errors of the order of one pixel. We also discuss experimental results of our method.

We present a new optical method for solving bounded (input-length-restricted) NP-complete combinatorial problems. We have chosen to demonstrate the method with an NP-complete problem called the traveling salesman problem (TSP). The power of optics in this method is realized by using a fast matrix-vector multiplication between a binary matrix, representing all feasible TSP tours, and a grayscale vector, representing the weights among the TSP cities. The multiplication is performed optically by using an optical correlator. To synthesize the initial binary matrix representing all feasible tours, an efficient algorithm is provided. Simulations and experimental results prove the validity of the new method.

We study families of Boolean circuits with the property that the number of gates at distancet fanning into or out of any given gate in a circuit is bounded above by a polynomial in t of some degreek. We prove that such circuits require size ( n1+1=k= logn) to compute several natural families of functions, including sorting, finite field arithmetic,

Optical computing elements offer benefits over traditional CMOS-based electronic logic gates such as increased performance and reduced power. Using polarization to encode the information to be processed allows for the possibility of nonbinary switching theory to be applied that further offers the benefit of reducing the number of required elements in an optical computing circuit. A methodology for synthesizing non-binary optical computing circuits is described and experimental results are provided that justify the approach.