KeywordsCoherent Ising Machine
Doing math with laser
Probabilistic graphical model
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PublisherThe University of Arizona.
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AbstractAnalog optical computing uses nonlinear optics and photonics to bring new approaches to attacking several important computational problems that current electronic computational platforms struggle to perform efficiently in terms of energy consumption and time. In this dissertation, Chapter 2, I will demonstrate optical implementation of Probabilistic Graphical Models (PGMs) which are tools that are used to compute probability distributions over large and complex interacting variables. They have applications in social networks, speech recognition, artificial intelligence, machine learning, and many more areas. Our analysis indicates that the optical implementation provides substantial reduction of power and area compared to the electronic-based solutions as problems become large. For a network with 1 million nodes and 100 alphabet size, our proposed wavelength multiplexed all-optical implementation requires approximately 200 kilowatts (kW) of power as compared with 1.47 gigawatts (GW) and 1.7 megawatts (MW) using CPU-based and subthreshold VLSI-based systems, respectively. The optical-based solution is tolerant to shot noise and imperfections of optical modules used in the architecture as well. We also present an all-optical implementation of a PGM through the sum-product message passing algorithm (SPMPA) governed by a wavelength multiplexing architecture. As a proof-of-concept, we demonstrate the use of optics to solve a two node graphical model governed by SPMPA and successfully map the message passing algorithm onto photonics operations. The essential mathematical functions required for this algorithm, including multiplication and division, are implemented using nonlinear optics in thin film materials as well as bulk materials. The multiplication and division are demonstrated through a logarithm-summation-exponentiation operation and a pump-probe saturation process respective. The fundamental bottlenecks for the scalability of the presented scheme are discussed as well. In Chapter 3, I will present a coherent Ising machine (CIM) and discuss its importance for solving combinatorial problems. Combinatorial optimization problems over large and complex systems have many applications in social networks, image processing, artificial intelligence and a variety of other areas. Finding the optimized solution for such problems in general are usually in the non-deterministic polynomial time (NP)-hard complexity class. Some NP hard problems can be easily mapped to minimizing an Ising energy functional. I will demonstrate an analog all-optical implementation of a CIM based on a network of injection-locked multicore fiber (MCF) lasers. The Zeeman terms and the mutual couplings appearing in the Ising Hamiltonians are implemented using spatial light modulators (SLMs). As a proof-of-principle, we demonstrated the use of optics to solve several Ising Hamiltonians with size of N=3 (triangle topology), N=4 (square lattice), N=7 (1D chain) and N=13 example. We have obtained the exact ground state of the Ising Hamiltonians over several trials, while some of the trials converged on local minima. Overall, the average accuracy of the CIM for finding the ground state energy was ~ 90 % for 120 trials. Our results represent a curious effect in an analog non-linear optical system whose minimum energy state may encode interesting Ising-like computational problems. However, our results do not imply an analog solver for NP Hard problems. We identify several fundamental and experimental bottlenecks in the scalability, programmability, and most importantly the solution quality (approximation to the optimal solution) of the CIM we built, most of which also apply to various other proposals for analog Ising solvers discussed in the recent scientific literature. In the last chapter of the dissertation, Chapter 4, I will discuss linear and nonlinear optical behavior of a novel sulfur based polymer. These polymers are attractive for near-IR (NIR) and mid-IR applications. The two photon absorption (TPA) coefficient (β) and second order refractive index (n2) of Chalcogenide Hybrid Inorganic/Organic Polymers (CHIPs) from poly(sulfur-random-(1,3-diisopropenylbenzen) (poly(S-r-DIB)) are measured via the Z-scan technique. In this study, we have investigated the linear and nonlinear optical behavior of two types of CHIPs where the weight percent of sulfur is varied (poly(S50%-r-DIB50%) and poly(S70%-r-DIB30%)). The TPA coefficients for poly(S50%-r-DIB50%) and poly(S70%-r-DIB30%) are obtained to be 0.11 cm/GW and 0.063 cm/GW respectively. The n2 for poly(S50%-r-DIB50%) and poly(S70%-r-DIB30%) are measured to be 2.45×10-15 cm2/W and 3.06×10-15 cm2/W respectively and are in good agreement with Miller’s rule prediction. These materials exhibit low cost, low temperature processing, high transparency in the near to mid-IR range (except for few vibrational absorption peaks) and relatively high refractive index, providing a unique set of properties for optics and photonics device applications.
Degree ProgramGraduate College